EEUROPEAN ORGANISATION FOR NUCLEAR RESEARCH (CERN)
Submitted to: EPJC CERN-EP-2020-10816th July 2020
Alignment of the ATLAS Inner Detector in Run-2
The ATLAS Collaboration
The performance of the ATLAS Inner Detector alignment has been studied using pp collisiondata at √ s =
13 TeV collected by the ATLAS experiment during Run 2 (2015 to 2018) ofthe Large Hadron Collider (LHC). The goal of the detector alignment is to determine thedetector geometry as accurately as possible and correct for time-dependent movements. TheInner Detector alignment is based on the minimization of track-hit residuals in a sequence ofhierarchical levels, from global mechanical assembly structures to local sensors. Subsequentlevels have increasing numbers of degrees of freedom; in total there are almost 750 000.The alignment determines detector geometry on both short and long timescales, where shorttimescales describe movements within an LHC fill. The performance and possible trackparameter biases originating from systematic detector deformations are evaluated. Momentumbiases are studied using resonances decaying to muons or to electrons. The residual sagitta biasand momentum scale bias after alignment are reduced to less than ∼ −1 and 0.9 × − ,respectively. Impact parameter biases are also evaluated using tracks within jets. © 2020 CERN for the benefit of the ATLAS Collaboration.Reproduction of this article or parts of it is allowed as specified in the CC-BY-4.0 license. a r X i v : . [ h e p - e x ] J u l ontents χ method for alignment 83.3 Solving the linear system of alignment equations 11 Appendix A Track fitting with multiple Coulomb scattering effects The precise reconstruction of the trajectories of charged particles created in proton–proton ( pp ) andheavy-ion collisions at CERN’s Large Hadron Collider (LHC) is a key ingredient in many of the physicsprocesses studied by the ATLAS Collaboration. Almost every measurement performed using the ATLASdetector [1], from Standard Model processes to searches for new physics phenomena, relies on the accuratereconstruction of charged particles.In order to reconstruct the trajectories of charged particles, ATLAS uses the Inner Detector (ID) trackingsystem to provide efficient, robust and precise position measurements of charged particles as they traverse2he detector. The energy deposits from charged particles (hits) recorded in individual detector elements ofthe ID are used to reconstruct their trajectories (tracks) and estimate the associated track parameters. Theprecision achieved for the track parameters is determined by several factors: the intrinsic resolution ofsensitive devices; the knowledge of the magnetic field; the distribution of material in and before the ID andthe knowledge of it; and the knowledge of the geometry, i.e. the location and orientation, of the detectorelements. The purpose of the detector alignment is to determine, as precisely as possible, the actualgeometry of the active detector elements of the tracking system, and to follow changes in the geometrywith time.Poor knowledge of the actual geometry of the active detector elements results in a deterioration of theresolution of reconstructed track parameters. The criteria for the minimum precision required were definedin order to limit the degradation of the resolution of the track parameters for high-momentum tracks to lessthan 20% in comparison to a perfectly aligned detector [2]. In addition, correlated geometrical distortionscan lead to systematic biases in the reconstructed track parameters. Correlated systematic biases can beintroduced either by real detector deformations to which the alignment procedure has little sensitivity or bythe procedure used to determine the alignment parameters. These correlated biases are referred to as ‘weakmodes’ of the alignment.In this document, the ATLAS ID alignment procedure and its performance during Run 2 of the LHC ispresented. A new layer of pixel sensors was included in the detector for Run 2, which posed additionalchallenges for the alignment of the detector compared to those faced during Run 1 [3, 4]. The greatest newchallenge was the short-timescale movement of parts of the detector during data taking.This paper is organised as follows: a brief description of the ATLAS detector is given in Section 2.Section 3 presents the formalism of the ATLAS track-based ID alignment. Section 4 introduces thedifferent alignment levels and Section 5 discusses the detector stability and describes the time-dependentalignment. The performance of the ATLAS Run 2 alignment is presented in terms of track parameterbiases in Sections 6 and 7. Concluding remarks are made in Section 8. The ATLAS detector [1] at the LHC is a multipurpose particle detector with a forward–backward symmetriccylindrical geometry that covers nearly the entire solid angle around the collision point. The global ATLASreference frame is a right-handed Cartesian coordinate system, where the origin is at the nominal pp interaction point, corresponding to the centre of the detector. The positive x -axis points to the centre ofthe LHC ring, the positive y -axis points upwards and the z -axis points along the beam direction. Polarcoordinates ( r , φ ) are used in the transverse plane, φ being the azimuthal angle around the beam pipe. Thepseudorapidity is defined in terms of the polar angle θ as η = − ln tan ( θ / ) . Angular distance is measuredin units of ∆ R ≡ (cid:112) ( ∆ η ) + ( ∆ φ ) .ATLAS consists of the ID (described in Section 2.1), electromagnetic and hadronic calorimeters, a muonspectrometer and a magnet system. Lead/liquid-argon sampling calorimeters provide electromagneticenergy measurements with high granularity and a steel/scintillator-tile hadronic calorimeter covers thecentral pseudorapidity range of | η | < .
7. The endcap and forward regions are instrumented withliquid-argon calorimeters for measurements of both electromagnetic and hadronic showers up to | η | = . | η | = .
7, fast detectors for triggering over | η | < .
4, and three large superconducting toroid3agnets with eight coils each. The ATLAS detector has a two-level trigger system to select events foroffline analysis [5].
The ATLAS ID [2, 6] consists of three subdetectors utilising three technologies: silicon pixel detectors,silicon strip detectors and straw drift tubes, all surrounded by a thin superconducting solenoid providing a2 T axial magnetic field [7]. The ID is designed to reconstruct charged particles within a pseudorapidityrange of | η | < . pp collisions at a centre-of-mass energy √ s =
13 TeV, the ID collected data with anefficiency greater than 99% [10].
Figure 1: A 3D visualisation of the structure of the barrel of the ID. The beam pipe, the IBL, the Pixel layers, the fourcylindrical layers of the SCT and the three layers of TRT barrel modules consisting of 72 straw layers are shown.
The innermost part of the inner detector consists of a high-granularity silicon pixel detector and includesthe insertable B-layer (IBL) [11, 12], a new tracking layer added for Run 2 which is closest to the beamline and designed to improve the precision and robustness of track reconstruction. The IBL consists of280 silicon pixel modules arranged on 14 azimuthal carbon fibre staves surrounding the beam pipe at aradius of 33.25 mm. Each stave is instrumented with 12 two-chip planar modules, covering the region of | η | < .
7, and 8 single-chip modules with 3D sensors [13, 14], four at each end of the stave (2 . < | η | < Table 1: Summary of the main characteristics of the ID subdetectors. The intrinsic resolution of the IBL and the Pixelsensors are reported along r – φ and z , while for SCT and TRT only the resolution along r – φ is given [1, 11]. For SCTand TRT the element size refers to the spacing of the read-out strips and the diameter of the straw tube, respectively. Subdetector Element size Intrinsic resolution [µm] Barrel layer radii [mm] Disk layer |z| [mm]IBL 50 µm ×
250 µm 10 ×
60 33.25Pixel 50 µm ×
400 µm 10 ×
115 50.5, 88.5, 122.5 495, 580, 650SCT 80 µm 17 299, 371, 443, 514 from 839 to 2735TRT 4 mm 130 from 554 to 1082 from 848 to 2710
The local coordinate system of an individual sensor of the detector is a right-handed system frame withthe origin placed in the geometrical centre of the sensor. The local coordinate system for each subsystemcomponent is illustrated in Figure 2. The convention used is the following: the local- x axis points alongthe most sensitive direction of the sensor. This corresponds to the shorter pitch side for Pixel and IBLmodules, and perpendicular to the strip-orientation for the SCT. In the silicon detectors, the local- y axis isoriented along the long side of the sensor (i.e. longer pitch direction for the Pixels and IBL and the stripdirection in the SCT), while the local- z direction is orthogonal to the local x – y plane. In the case of theTRT, the local- y axis points along the wire: either in the same direction as the global z -axis (barrel) orradially outwards (endcaps). In the barrel, the local- z axis points radially outwards (from the origin of theglobal frame to the straw centre). In the endcaps, the local- z axis points outwards (parallel to the beamline). The local- x axis is perpendicular to both the TRT wire and the radial direction.Hits are reconstructed in the local reference frame. As the SCT consists of double-sided modules, aseparate local frame is associated with each side of the module. The TRT measures the radial distance ofthe primary ionisation from the wire as √ x + z , taking both x and z in the local frame. This section reviews the formalism for in situ alignment of the ATLAS ID using reconstructed tracks. Theconcept of Global χ alignment is introduced, followed by a discussion of ‘weak modes’ (Sections 3.2.4and 6) and how they can be avoided by adding constraints on track parameters. The section closes with adetailed description of the alignment procedure and its implementation within the ATLAS software.5 RT EndCap(z > 0)Silicon Barrel Silicon EndCap(z > 0)Silicon EndCap(z < 0)TRT EndCap(z < 0)
TRT Barrel
Figure 2: Schematic representation of the ATLAS global reference frame ( x , y , z ) and the local reference frameof each component of the ID. The Pixel, IBL, and SCT modules are grouped in the ‘Silicon’ category. For eachcomponent, the local- x axis points along the most sensitive direction; the local- z axis points away of the ATLAScentre; and the local- y direction is chosen according to the right-handed frame. For TRT tubes, the local referenceframe is determined by the orientation of the module they are mounted on. For visualisation purposes only, the localreference frame is referred to as ( x (cid:48) , y (cid:48) , z (cid:48) ) in the drawing. The approach used is based on the Newton–Raphson method and determines both the trajectory parametersand a set of alignment parameters, α . In this context, α are chosen as the six degrees of freedom (DoF) ofeach alignable structure that uniquely define its position and orientation in space. These correspond tothree translations ( T x , T y , T z ) and three rotations ( R x , R y , R z ) . Translations are relative to the origin of thereference frame of each alignable structure and rotations are around the Cartesian axes. The Newton–Raphson method uses an iterative approach to find the best fit to a set of measurementsof a track left in the detector by a charged particle traversing active detector elements. The quality ofthe fit is characterised by a track χ , determined from the distances between the hits in the detector,which constitutes the track measurements, and the fitted track (residuals). The trajectory of a track in amagnetic field is parameterised by a set of five parameters. The chosen parameterisation in ATLAS is: τ = ( d , z , φ , θ , q / p ) , where d and z are the transverse and longitudinal impact parameters and φ and θ the azimuthal and polar angles of the track, all defined at the point of closest approach to the z -axisof the reference frame [22]. The ratio q / p is the inverse of the particle momentum ( p ) multiplied by itscharge ( q ) (see Ref. [4] for more details).The track χ is calculated from all measured track-hit residuals, r i = e i ( τ ) − m i . where m i is the positionof the i th measurement, and e i is the position of the intersection of the fitted track with the surface on whichthe i th measurement is made. The determination of the intersection position ( e i ) includes the measurementin question, which causes r i to be a biased residual. The track χ is defined, using vector notation, as χ = r (cid:62) Ω − r , (1)6here r is the vector of track residuals and Ω is the covariance matrix of the corresponding measurements. The parameters of a track’s trajectory, τ , are those that minimise this χ . The minimisation is done usingthe first and second derivatives of the χ with respect to τ . Defining the derivative G = d r / d τ , thecondition for the minimisation of the χ is (cid:18) d χ d τ (cid:19) (cid:62) = G (cid:62) Ω − r = . (2) τ m i − e i − ( τ ) r i = e i ( τ ) − m i Figure 3: Schematic representation of a charged particle crossing detector planes. The measurement, m i , on each the i th layer is indicated by a red star. Also shown are the fitted track trajectory for a given set of track parameters, τ (black line), the position of the intersection of the fitted track with the surface on which the i th measurement is made, e i ( τ ) (green ellipse), and the residuals, r i (blue line). In practical terms, the values of τ satisfying Eq. (2) are found using an iterative procedure by evaluatingthe first and second derivatives of χ with respect to the track parameters of the current iteration, τ . If thederivative G were constant, then the problem would be linear and the solution would be exact. In general,the derivative G depends on the track parameters themselves. Therefore, the procedure is repeated until aconvergence criterion is met.The track fit can be further improved by adding parameters, θ , which attempt to account for the effects ofmultiple Coulomb scattering (MCS) of the particle with the detector components, as detailed in Appendix A.Consequently, the residuals now also depend on θ and the variance of the scattering angles, Θ : χ = r (cid:62) Ω − r + θ (cid:62) Θ − θ . (3)Thus, χ has to be minimised for τ and θ simultaneously. The derivatives of residuals with respect totrack and scattering parameters are defined as G ≡ ∂ r / ∂ τ and S ≡ ∂ r / ∂ θ , respectively. In the following, The local position and uncertainty of each measurement are provided by the corresponding subsystem after applying its ownclustering and hit reconstruction techniques. The Pixel detector uses an artificial neural network, trained on simulation, todetermine the position of a cluster and its uncertainty [23]. The SCT parameterises the position of the cluster and its uncertainty,using simulation, as a function of the number of strips in the cluster and the incident angle of the particle. For the TRT the driftradius and its uncertainty is calibrated using an iterative procedure in data and simulation [21]. χ method for alignment including MCS is described and the following simplified notation isadopted: ρ ≡ (cid:18) r θ (cid:19) , V ≡ (cid:18) Ω Θ (cid:19) , π ≡ (cid:18) τθ (cid:19) , and H ≡ (cid:18) G S ∂ θ ∂ τ = ∂ θ ∂ θ = I (cid:19) . (4) χ method for alignment χ method for alignment The Global χ is a track-based alignment method which uses a χ built from a large sample of reconstructedtracks and their associated hits in the detector elements being aligned. The alignment parameters aredetermined by minimising the Global χ with respect to the alignment parameters: χ = (cid:213) i χ i , (5)where χ i is the χ of the i th track as given by Eq. (3). The residuals used in Eq. (5) depend on thealignment parameters ( α ) as both, the measurements and the track extrapolations depend on α , the formerdirectly and the latter through the fitted track parameters. Therefore, the minimisation of χ withrespect to α uses the total derivative operator with respect to α , which can be expressed as:dd α i = ∂∂α i + (cid:213) j d π j d α i ∂∂π j . (6)The d π / d α term is determined from the condition that, once χ is at a minimum, χ is also at aminimum with respect to the track parameters:dd α ∂ χ ∂ π = . (7)Using Eq. (7) in Eq. (6), this results in:d π d α = − (cid:32) ∂ χ ∂ π (cid:33) − ∂ χ ∂ α ∂ π , which allows the nested dependence of the π on α to be resolved, thereby removing the need to determineboth (the track parameters and alignment parameters) simultaneously.Ignoring second-order derivatives, using the covariance matrix of the track parameters, C , expressed as C = (cid:32) ∂ χ ∂ π (cid:33) − = (cid:16) H (cid:62) V − H (cid:17) − , (8)and defining A as the derivative of the residuals with respect to the alignment parameters: A ≡ ∂ ρ ∂ α , (9)8sing Eqs. (8) and (9) the total derivative operator with respect to α can be rewritten as: (cid:18) dd α (cid:19) (cid:62) = (cid:18) ∂∂ α (cid:19) (cid:62) − A (cid:62) V − HC (cid:18) ∂∂ π (cid:19) (cid:62) . The first- and second-order derivatives of χ with respect to α are thus: Y ≡ (cid:32) d χ d α (cid:33) (cid:62) = (cid:213) tracks A (cid:62) V − ( V − HCH (cid:62) ) V − ρ , (10) M ≡ d χ d α = (cid:213) tracks A (cid:62) V − ( V − HCH (cid:62) ) V − A . (11)Here, the term HCH (cid:62) represents the covariance of the track parameters in the measurement space, whereasthe covariance of the residuals of the track fit is given by R = V − HCH (cid:62) . χ alignment In analogy to the general method for track fitting (Section 3.1) an iterative approach is used to solve for thealignment parameters. The first- and second-order derivatives are obtained using Eqs. (10) and (11) andevaluated for an initial set of alignment parameters, α . Such an initial geometry description is availablefrom design drawings, survey measurements, or previous alignment results. The alignment corrections, tothe initial geometry, are given by X ≡ ∆ α = − (cid:32) d χ d α (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) α (cid:33) − (cid:32) d χ d α (cid:33) (cid:62) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) α ≡ −M − Y . (12)The above step is repeated for successive iterations until a convergence criterion is met and ∆ α is negligible.This requires re-fitting the tracks using the updated geometry (initial alignment constants α plus theircorrections ∆ α ), to obtain new residuals and new derivatives, and solving again to compute the next set ofcorrections to the alignment constants. If the initial track parameters, π , minimise χ for a given α , Eq. (10) simplifies to (cid:32) d χ d α (cid:33) (cid:62) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) π o , α = (cid:213) tracks A (cid:62) V − ρ , (13)as the term H (cid:62) V − ρ is zero. Consequently, if the measurements are independent and V is diagonal, thederivative with respect to a particular parameter α i only receives contributions from residuals for which A elements are non-zero. In other words, if α i is an alignment parameter of a given detector module,only the measurements in this module contribute to the first-order derivative of χ with respect to α i .Therefore, contributions to the χ from measurements in other subdetectors and MCS effects can beignored. This useful property is labelled as the so-called locality ansatz [24] and provides an importantsimplification for the software implementation. 9 .2.4 Adding constraints on track parameters It is of particular importance to assure that the determination of the track parameters is free from systematicbiases that can occur due to poorly determined ‘weak modes’ of the alignment. These modes are geometrydistortions that leave the χ of the fitted tracks nearly unchanged and typically lead to an incorrectsolution of the alignment. They can be controlled by imposing constraints on track parameters [25].Examples of such constraints, discussed in detail in Sections 6 and 7, are the beam-spot constraint, trackparameter constraints from external detector systems (e.g. calorimeters), and constraints determined usingreconstructed physics events (e.g. mass constraints from narrow resonances). These constraints are includedin the Global χ method by adding extra terms to the expression for the χ in Eq. (5). For one track themodified contribution to χ is χ = ρ (cid:62) V − ρ + ( π − q ) (cid:62) T − ( π − q ) , (14)where q is a vector defining the constraint on π and T is its covariance matrix.In the ATLAS implementation, this constraint is implemented by adding a pseudo-measurement on atrack [22]. The solution for the alignment parameters is given by Eq. (12), where for each constrained trackthe covariance matrix is now defined as C = (cid:18) d χ d π (cid:19) − = (cid:16) H (cid:62) V − H + T − (cid:17) − . In this context, the first-order derivative of the Global χ is given by (cid:18) d χ d α (cid:19) (cid:62) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) α = (cid:213) tracks A (cid:62) V − ( V − HCH (cid:62) ) V − ρ ( α ) − A (cid:62) V − HCT − ( π ( α ) − q ) . (15)If the tracks have been re-fitted with the imposed constraint, the locality ansatz drastically simplifiesEq. (15), reducing it to Eq. (13). This property is used in the ATLAS implementation. Often one has some prior knowledge of the geometry from either survey measurements or mechanicalconstraints. These constraints can be included by adding terms to the χ in Eq. (5). In the general case,one can write χ = (cid:213) tracks ρ (cid:62) V − ρ + ( α − a ) (cid:62) W − ( α − a ) , (16)where a is a vector defining the constraint on α and W is its covariance matrix. The added term leads toextended expressions for the first and second derivatives of χ with respect to α (Eqs. (10) and (11)): Y −→ Y + W − ( α − a ) , (17) M −→ M + W − , while the solution is computed using Y and M in Eq. (12).The special case when a ≡ α and W is diagonal, i.e. when the alignment parameters are constrained totheir initial values, is further discussed in Section 3.3.3.10 .2.6 The Local χ method The main advantage of the Global χ method arises from its rigorous treatment of correlations betweenalignable objects through the tracks connecting them. However, this approach becomes technicallychallenging when the number of alignment parameters is very large, such as in the case of the alignment ofindividual TRT straws ( ≈
700 000 parameters). In order to overcome this challenge, a simplified version ofthe χ approach (the Local χ method) is used. It is based on the minimisation of the same χ , Eq. (5),but the implicit dependence on the fitted track parameters is dropped, reducing Eq. (6) to a simpler form:dd α = ∂∂ α . Consequently, Eqs. (10) and (11) are reduced to: (cid:32) d χ d α (cid:33) (cid:62) = (cid:213) tracks A (cid:62) Ω − r d χ d α = (cid:213) tracks A (cid:62) Ω − A . In addition, the problem is reduced to separate systems of equations describing individual alignablemodules. The Local χ method eliminates the numerical challenges of the Global χ since only systemsof equations with up to six parameters (albeit many of them) need to be solved. However, due to the loss ofthe correlations between alignable objects, the Local χ method needs a much larger number of iterationsto converge. In general, the properties of the matrix representing a system of linear equations determine the most suitablesolution technique. The matrix M in Eq. (11) as defined in the Global χ ansatz is found to be symmetricand singular and to have a poor matrix condition number if no constraints are applied. The addition ofappropriate constraints generally renders the matrix positive definite. The singular nature of the matrixis the result of detector movements that leave a track’s χ unchanged. The simplest examples are globaltransformations of the detector (either translations or rotations), which are generally singular modes. Atrivial way to remove these global degrees of freedom is to fix a detector element, making it the referencepoint for all other detector elements. This method has the unwanted drawback of arbitrarily selecting onedetector module as the reference frame. In the following section, two methods used to obtain a solutionto the alignment system of linear equations are discussed along with how ‘weak modes’ are removed ormitigated.
The symmetric matrix M is decomposed into its diagonal basis: P D P (cid:62) where D is a diagonal matrixcontaining the eigenvalues of M , and P is a matrix containing the eigenvectors of M . Of course, in the Rotations within a magnetic field or translations in an inhomogeneous magnetic field may not be singular modes but for practicalpurposes may essentially be so. They are typically extremely poorly constrained because track trajectories are not significantlymodified by small changes in the magnetic field. λ i ) with: X i D = − λ i Y i D and σ ( X i D ) = √ λ i , (18)where X i D and Y i D are the i th component of vectors XXX D and YYY D in the diagonal basis, with YYY D = P (cid:62) YYY .Singular and weak modes must be excluded as their eigenvalues are zero or have an arbitrarily largeassociated uncertainty, respectively. Although this can be achieved in many ways, the primary methodemployed is to set D − i , i = D (cid:48)− which provides the solution: XXX = − P D (cid:48)− P (cid:62) YYY . The DSPEV function in the LAPACK [26] software package is used as a baseline in the ATLASimplementation to diagonalise large matrices. Alternative implementations using ROOT [27], EIGEN [28]and CLHEP [29] linear algebra classes are also available. In general, the computation time for matrixdiagonalisation scales as O( DoF ) and solutions for very large systems become untenable on a singlemachine. If the initial matrix is poorly conditioned, the accuracy of the numerical solution can be limitedby the precision of 64-bit floating-point computations for problems exceeding O (10 000) DoFs. Even for very large problems, direct solvers offer an accurate and CPU-efficient method for solving sparselinear equations. In addition, less memory is required as no matrix is inverted or diagonalised in theprocess. The LDLT Cholesky factorisation method provided within EIGEN [28] is used within the ATLASID alignment and takes less than 10 minutes to solve an alignment problem with 35 000 parameters (theapproximate number of parameters needed to align all modules in the ID simultaneously) on a modernCPU. Direct solving is used when aligning thousands of degrees of freedom (usually when aligning atindividual module level). Obtaining a direct solution does not offer the possibility of eliminating specificeigenmodes. Thus, other preconditioning techniques are used in order to extract a meaningful solution(e.g. Section 3.3.3). It is noteworthy that, although not extensively utilised within ATLAS, it is possible toiteratively find the eigenvalues and associated eigenvectors of large systems by solving M x = λ x for x and λ [30], which can be useful in understanding the weak modes of very large systems and identifying theunderconstrained degrees of freedom. As introduced in Section 3.2.5, setting a ≡ α and having a diagonal W constrains the alignment parametersto their initial values. Here, W denotes a diagonal matrix with diagonal elements: σ ( α i ) , providing thetolerances to the corrections of the alignment parameters.For this special case, the top row of Eq. (17) simplifies to Eq. (10) and the diagonal of the matrix M inEq. (11) is incremented by the reciprocal of assumed variances of alignment corrections: (cid:16) M + W − (cid:17) XXX = − YYY . (cid:213) j (cid:0) σ ( α i ) σ ( α j ) M ij + I ij (cid:1) X j σ ( α j ) = − σ ( α i ) Y i (19)yielding an equation in which the corrections to the alignment parameters are normalised to their assumeduncertainties ∆ α i −→ ∆ α i / σ ( α i ) . Apart from the extra identity matrix I , Eq. (19) is exactly equivalent toEq. (12).To illustrate the effect of such a constraint, consider the case that all σ ( α i ) are equal ( σ ( α i ) = σ c ). The extraidentity matrix does not affect the eigenmodes of M , but adds an offset to its spectrum of eigenvalues: M (cid:48) = M + I / σ c , D (cid:48) = D + I / σ c , λ (cid:48) i = λ i + / σ c . The solution in the diagonal basis, Eq. (18), takes the form: X i D = λ i + / σ c Y i D and σ ( X i D ) = (cid:112) λ i + / σ c . (20)Hence, one obtains a solution explicitly free from ill-defined (weak) modes. This operation does not requirean explicit diagonalisation and can be used as preconditioning prior to fast solving, providing powerfulcontrol over solutions for an arbitrarily large number of DoFs. Due to the typically exponential nature ofthe eigenspectrum, Eq. (20) represents a solution with a clear cut-off in the diagonal basis for λ i (cid:28) / σ c .This technique is extensively used in the ATLAS implementation. The ID is composed of a large number of active detector components (see Section 2.1 for details). Eachcomponent or grouped collection of modules (e.g. a subdetector) can be treated as an alignable structure.The alignment is performed at different hierarchical levels following the assembly structure of the ID.Starting with the largest physical structures at level
1, the detector subsystems are aligned separated intoendcaps and barrel regions in order to correct for collective movements.
Level
Level
Time-dependent alignment is performed for each LHC fill prior to data reconstruction to determine if thedetector, or individual subsystems, have moved significantly compared to a reference alignment. Suchdetector movements occur on different timescales, which are classified as short, medium, or long.13hort timescales describe movements during a single LHC fill that are a result of variations of the thermalload of the ID. These movements are caused by fluctuations in the power consumption of the front-endelectronics, due to variations in the trigger rate, that additionally affect the temperature of the coolingsystem. On medium timescales, in the range of days to a month, changes to the environmental conditionsof the detector, such as ramping the magnetic field or cycling the power or cooling systems, often lead tosignificant movements of the detector. Slow gradual movements of the subsystems over several months(long timescales) were also observed and attributed to mechanical relaxations after sudden changes.An automated time-dependent level 1 alignment is performed within the ATLAS prompt calibrationloop [10] to address all known time-dependent movements, as detailed in Section 5. These results aremonitored and new alignment corrections are automatically obtained during the calibration period. Theyserve as input for the bulk reconstruction of the corresponding dataset.
The baseline alignment constants are a set of reference constants that serve as initial estimates for thetime-dependent refinements of the alignment. In order to achieve an accurate detector alignment and aminimisation of track parameter biases over a data-taking period, a large quantity of data are used (typically ∼ − ). The levels of alignment performed are summarised in Table 2. The alignment using the global χ method typically converges within two to four iterations for levels 1 and 2, while at least four iterationsare required at level 3 (silicon). The TRT level 3 (straw level) uses the local χ method and requires up to30 iterations to converge, owing to the large number of DoFs.Depending on the alignment level, some DoFs may be fixed during the alignment procedure if poorsensitivity is expected. Alignment levels targeting the silicon subdetectors use all tracks, whereas alignmentlevels including the TRT require tracks based on silicon and TRT hits. In order to remove weak modesfrom the alignment solution, appropriate constraints are added to the global χ method (see Section 3.2.4).Different constraints are considered depending on the expected misalignment and DoF for each alignablestructure, listed in Table 2. Additionally, each subsystem can be aligned at any required level independentlyfrom the others. Further subdivision of alignment levels into smaller physical detector components, e.g.the division of individual barrel layers into staves, is also supported and used. At level 1, the SCT barrel iskept fixed due to its good stability and to serve as reference for the rest of the structures. As described in Section 3.2, the solution of the Global χ is the one that minimises the track-hit residuals.Figures 4 to 6 show track-hit residual distributions for data and simulation in different ID subdetectors.Data and simulation correspond to a set of muons selected in Z → µ + µ − candidate events triggered by thelowest-threshold unprescaled single and dimuon triggers. The simulation sample was generated with thePowheg-Box v1 Monte Carlo event generator [31–33] at next-to-leading order (NLO) in α S interfacedto Pythia 8.186 [34] for the modelling of the parton shower, hadronisation, and underlying event, withparameter values set according to the AZNLO tune [35]. The CT10 (NLO) set of parton distributionfunctions (PDF) [36] was used for the hard-scattering processes, whereas the CTEQ6L1 PDF set [37] wasused for the parton shower. Events are required to contain two muons (satisfying ‘medium’ quality criteriaas defined in Ref. [38]) with opposite charge and p T >
20 GeV. In addition, requirements on the openingangle between the two muons, γ ( µ + , µ − ) > ◦ , and their invariant mass, 70 GeV < m µ + µ − <
110 GeV,14 able 2: Typical alignment configurations used throughout Run 2 data taking to derive baseline alignment constants.Translational degrees of freedom (DoF) are denoted by a T , rotational ones by an R . As shown in Figure 2, TRTbarrel straws run parallel to the beam line. That corresponds to T z at level T y at level T z TRT split into barrel and 2 endcaps 3 All except T z Si 2 Pixel and IBL barrel split into layers 4 All Beam spot,Pixel endcaps split into disks 6 All momentum bias, andSCT barrel split into layers 4 All impact parameter biasSCT endcaps split into disks 18 AllSi 3 Pixel and IBL barrel modules 1736 All Beam spot,Pixel endcaps modules 288 T x , T y , R z momentum bias,SCT barrel modules 2112 All impact parameter bias, andSCT endcaps modules 1976 T x , T y , R z module placement accuracyTRT 2 TRT barrel split into barrel modules 96 All except T y Momentum bias andTRT endcaps split into wheels 80 T x , T y , R z impact parameter biasPixel and SCT detectors fixedTRT 3 TRT straws 351k T x , R z Pixel and SCT detectors fixed are imposed. In Figures 4 to 6, both data and simulation correspond to 2 fb −1 of data collected during 2018.Statistical uncertainties in data and simulation are included in all the figures, although barely visible asthey are negligible.Adequate agreement is seen between data and simulation in the residual distributions, where differencesare quantified in terms of the ‘full width at half maximum’ (FWHM) figure of merit. A similar level ofagreement is observed for the data collected during the other years of Run 2. In the case of the IBL, Pixeland SCT barrel, larger residual widths are observed in data. As shown in Section 5.3, the Run 2 alignmentaccuracy and stability in the central pseudorapidity range for both the Pixel and SCT barrel modules iscontrolled to a precision better than 0.5 µm and 2 µm in local- x and local- y , respectively. Consequently,several other possible causes of the observed discrepancy between data and simulation are considered, suchas imperfect modelling of the interactions of muons with detector material in the simulation, the materialdescription, delta ray production modelling, mis-modelling of the detector response (and resolution) insimulation, and residual biases not uniform across individual modules in data. The latter particularlyimpacts the local- y track-hit residuals in Figure 4. The poorest agreement is seen for the IBL residuals,which have not yet been corrected for sensor distortions, in contrast to the Pixel layers. The sensor distortioncan result in track-hit residual biases of up to 10 µm within a given module, thus causing a broadening of theoverall distribution [39]. The shape of the IBL modules was recently parameterised with Bernstein–Bézierfunctions and will be corrected in the track fitting procedure for Run 3 data taking. The cause of thesmall bias of 4 µm in the IBL local- y track-hit residuals in simulation in Figure 4 is currently unidentified.Simulated samples use a perfectly aligned detector with no track-based alignment correction, hence thisbias originates from the track or cluster reconstruction. On data, this small reconstruction bias is removedby the alignment without a significant effect on alignment precision.15 · m m H i t s on t r a cks / - - m residual [ x Local-
Data 2018Simulation = 13 TeVs
ATLAS - m + mfi Z IBL
Data 2018 m m (mean: 0 FWHM/2.35: 12) Simulation m m (mean: 0 FWHM/2.35: 10) · m m H i t s on t r a cks / - - - m residual [ y Local-
Data 2018Simulation = 13 TeVs
ATLAS - m + mfi Z IBL
Data 2018 m m (mean: 0 FWHM/2.35: 86) Simulation m m (mean: -4 FWHM/2.35: 66) Figure 4: The IBL local- x (left) and local- y (right) residual distributions for the Z → µ + µ − data sample comparedwith simulated data. The distributions are integrated over all hits on tracks in barrel modules. · m m H i t s on t r a cks / - - m residual [ x Local-
Data 2018Simulation = 13 TeVs
ATLAS - m + mfi Z Pixel barrel
Data 2018 m m (mean: 0 FWHM/2.35: 8) Simulation m m (mean: 0 FWHM/2.35: 7) · m m H i t s on t r a cks / - - - m residual [ y Local-
Data 2018Simulation = 13 TeVs
ATLAS - m + mfi Z Pixel barrel
Data 2018 m m (mean: 0 FWHM/2.35: 78) Simulation m m (mean: 1 FWHM/2.35: 63) Figure 5: The Pixel local- x (left) and local- y (right) residual distributions for the Z → µ + µ − data sample comparedwith simulated data. The distributions are integrated over all hits on tracks in barrel modules. This section discusses the main sources of time variation in ID geometry and the methods implementedto mitigate these effects within the ATLAS prompt calibration loop [10]. In addition, the stability of theID in Run 2 is summarised, final time-dependent corrections for all subsystems are presented, and theprecision of the alignment is determined. All results use pp collision data at √ s =
13 TeV. The alignmentprecision for heavy-ion data in Run 2 is at least as good as the final precision of pp collision data, as theinstantaneous luminosity, and therefore the thermal load variations in the ID, is typically lower.16 · m m H i t s on t r a cks / - - m residual [ x Local-
Data 2018Simulation = 13 TeVs
ATLAS - m + mfi Z SCT barrel
Data 2018 m m (mean: 0 FWHM/2.35: 23) Simulation m m (mean: 0 FWHM/2.35: 21) · m m H i t s on t r a cks / - - - m Residual [
Data 2018Simulation = 13 TeVs
ATLAS - m + mfi Z TRT barrel
Data 2018 m m (mean: 0 FWHM/2.35: 135) Simulation m m (mean: 0 FWHM/2.35: 135) Figure 6: The local- x residual distributions in the SCT (left) and TRT (right) for the Z → µ + µ − data sample comparedwith simulated data. The distributions are integrated over all hits on tracks in barrel modules. Detector movements on short timescales are particularly challenging, since the ID track-based alignmentcalculates an average position correction for the time interval under study. The procedure used to correct for rapid movements must balance two competing effects: the alignmentcorrections must be determined in time intervals that are short enough to capture the motion of the particulardeformation, but long enough to include sufficient data to obtain precise corrections.
During the Run 2 commissioning of the IBL, it was already noticed that the IBL staves can be distortedby hundreds of micrometers relative to the design geometry. It was soon observed that these distortionsdepend on the operating temperature and correspond to module displacement in the azimuthal directionof the staves, equivalent to their local- x direction. The distortion was understood to be caused by tight,asymmetric mechanical coupling of materials with different coefficients of thermal expansion (CTE). Thecorrelation between temperature and the size of the IBL distortion was studied using cosmic-ray data inMarch 2015 with a controlled variation of the IBL temperature, T set , in the range − ◦ C to 15 ◦ C [40]. Thesize of the distortion was measured in situ using the track-based alignment and a fit to a model determinedfrom a three-dimensional finite-element analysis. This model parameterises the IBL distortion in local- x , δ x ( z ) , using a parabolic function, δ x ( z ) = B − Mz (cid:16) z − z (cid:17) , (21)where z is the global- z coordinate of the module, z ≡ . B is the baseline describing the overall translation of the stave in local- x , and M is the magnitude This time interval varies from a few minutes to several hours depending on the configuration of the alignment task.
17f the distortion at the stave centre. The temperature gradient of M with respect to T set is found to bed M / d T set = (− . ± . ) µm / K. The local- y position shows no temperature-dependent effect within20 µm uncertainty, whereas the local- z (bending out of the plane of the stave) was not included in this study.The IBL distortion is shown in Figure 7 for different T set values using 2015 and 2016 pp collision data.From the initial data taking in Run 2 through September 2015, the IBL power consumption per modulewas found to be stable, and fluctuations in T set were within ∼ . ( δ x ( z ) < ) [40]. This situation changed with the rapid increase in integrated luminosity per LHC fillafter September, which induced an increase in the low-voltage (LV) currents in the IBL module front-endelectronics. This increase was traced back to radiation-induced leakage current in transistors [41]. Thechange in LV currents depends on the total ionisation dose. Studies show that the increase reaches a peakvalue for radiation doses between 10 and 30 kGy and decreases for higher doses to a value close to thepre-irradiation case. Global z position [mm]300 − − − C a li b r a t ed a v e r age l o c a l x [ mm ] − − − C (Sep 2015) ° = -10 set T C (May 2016) ° = +15 set T C (June 2016) ° = +5 set T Data 2015+2016IBL
ATLAS
Figure 7: IBL local- x position in the transverse plane averaged over all 14 IBL staves for 2015 data using T set = − ◦ C(red open squares), and for 2016 data using different T set ( + ◦ C, solid blue circles; + ◦ C, solid green triangles).No error bars associated with data are shown. The IBL distortion was constant during all three LHC fills. Here,only the correction due to the IBL distortion is shown. The baseline, which describes the overall translation of thewhole stave, is subtracted using Eq. (21). The fit represents only a first-order correction. Additional corrections arecomputed as part of the detailed alignment corrections at a later stage.
These variations in the LV currents caused an increase in IBL module temperatures that resulted in changesin IBL distortions on short timescales. In this context, values of δ x ( z ) of up to 30 µm were observedbetween LHC fills and up to 10 µm within a single fill, corresponding to a variation of 0.5 µm h −1 . Another systematic deformation on short timescales is a change in the vertical position (global- y direction)of the Pixel detector by up to 8 µm at the start of an LHC fill. Figure 8 shows the Pixel detector verticalmovement from the start of an LHC fill. The position is computed every 20 minutes, which is the shortest18ime interval used in the ATLAS prompt calibration loop. As is evident from Figure 8, the average positionacross an LHC fill does not accurately describe the position of the Pixel detector. R e l a t i v e v e r t i c a l po s i t i on o f t he P i x e l [ mm ] ATLAS = 13 TeVsData 2016,
Pixel vertical position every 20 minutesInstantaneous luminosity (LHC fill 5030)LHC fill average Pixel vertical position ] - s - c m Lu m i no s i t y [ Figure 8: The Pixel detector vertical ( T y ) movement as a function of the time since the start of an LHC fill. Theaverage Pixel T y for the entire run (dashed blue line) is compared with its time evolution and with the instantaneousLHC luminosity. The error bars represent the statistical uncertainty. The cause of this movement is understood to be the following. When the Pixel detector is switched onat the start of a fill, modules reach their new temperature almost immediately as a result of the strongthermal coupling between the modules and the evaporative cooling system [1, 42]. The LV current in theread-out electronics also increases immediately, while the temperature in the Pixel detector volume risesgradually during the first 60 minutes. The smaller mass load due to the change in density of the bi-phasecooling liquid causes the Pixel detector to rise. After this initial rise, as the instantaneous luminosity andthus the occupancy decreases over the course of the fill, LV digital currents, module temperature and Pixelvolume temperature gradually decrease as well. This in turn causes an additional slow drift in the directionopposite to the initial movement. The speed of this slow drift depends on the peak luminosity per LHC fill.This speed increased during 2016 to reach values of 0.2 µm h −1 , as shown in Figure 9. The vertical speed isdetermined as the average speed of the Pixel detector excluding the first hour after the start of data taking.This vertical drift was monitored and corrected for throughout Run 2. In an effort to mitigate the effects of systematic short-timescale distortions and ensure adequate data qualityfor all analyses relying on tracking, conceptual improvements within the alignment framework and strategywere made. A key improvement was the introduction of a new alignment DoF, B x , to parameterise the IBLdistortion deformation magnitude M . The B x DoF correlates the local- x coordinate of each module alongthe IBL stave using the parabolic function defined in Eq. (21). Minimising the global χ with respect to B x provides corrections for varying degrees of IBL stave distortion using a single DoF, which can be donewith small amounts of data. In contrast, a full level 3 alignment, which relies on a large amount of data,had been required previously, which did not allow short-timescale movements to be determined.19 -1 s -2 cm Online peak luminosity [100 0.2 0.4 0.6 0.8 1 m / hou r ] μ P i x e l v e r t i c a l s peed [ ATLAS = 13 TeVsData 20162016
Figure 9: Vertical speed of the Pixel detector as a function of the peak luminosity of an LHC fill, extracted fromalignment corrections. Only fills longer than 8 hours are considered.Table 3: Typical alignment configurations used throughout Run 2 data taking to derive dynamic alignment corrections.Level Description Structures DoF1 CL IBL 1 All DoF incl. B x , except R z Pixel detector 1 AllSCT endcaps (SCT barrel fixed) 2 All except T z TRT split into barrel and 2 endcaps 3 All except T z IBL bowing IBL staves 14 B x Pixel, SCT, and TRT detectors fixed
The automated alignment scheme that is performed within the ATLAS prompt calibration loop in Run 2data taking determines level 1 and IBL B x (per stave) dynamic alignment constants every 20 minutes at thestart of a fill and every 100 minutes for the rest of the fill. This level of granularity in time is adequate tomitigate the effects of short-timescale vertical movements on track parameter resolution. The alignment isperformed in two iterations of the level 1 calibration loop (level 1 CL) followed by two dedicated iterationsto correct for IBL distortions. The B x correction in the level 1 CL corresponds to a collective, uniformcorrection for all IBL staves. The dedicated IBL bowing iterations determine B x individually for eachstave, as summarised in Table 3. The SCT barrel is used as the reference in the dynamic alignment. The performance of the dynamic alignment scheme using 2016 pp collision data is shown in Figures 10and 11. The average bowing magnitude of the 14 IBL staves relative to the baseline alignment is compared20ith the results of the dynamic alignment in Figure 10. Figure 11 shows the average IBL distortioncomputed after different alignment corrections versus time in the form of luminosity blocks (LB), whichcorrespond to stable data-taking conditions in periods of approximately one minute. It also compares theunbiased local- x residuals computed using the a fill-averaged correction (for illustration only) with thoseobtained after computing the full dynamic alignment correction, which is derived in short time-intervals.A clear improvement in the residual distributions is seen after applying dynamic alignment corrections.Figures 10 and 11 illustrate that, averaged over an LHC fill, even very large values of M (up to 30 µm) areaccurately corrected for using B x as an alignment DoF. These features were present for all Run 2 data,although there was some saturation of the effect in the later years of Run 2, as observed in the radiationdamage studies of the IBL [41].The long-term trend of the Pixel and IBL detector movements relative to the baseline alignment correctionis shown in Figure 12 for the average B x correction, the global T x correction, and the global T y correction.For the sake of clarity, the plots in Figure 12 show only a fraction of the Run 2 data; the remaining datafollow the same trend. - - m ] m A v e r age I B L d i s t o r t i on m agn i t ude [ = 13 TeVsData 2016 ATLAS
Baseline alignmentDynamic alignment C o = +15 set T C o = +5 set T Figure 10: Bowing magnitude averaged over the 14 IBL staves relative to the baseline alignment (blue full circles)and the geometry after dynamic alignment (red open circles) with its statistical uncertainty. The IBL operationtemperature (T set ) for each period is shown.
The final alignment precision of each ID subsystem is determined from the track-hit residuals of individualsilicon modules for each LHC fill in 2015 and 2016 data taking after the dynamic alignment correctionsare applied. These dynamic alignment corrections are computed either for large structures (e.g. the Pixeldetector) as a collective movement of all modules or using a simplified parameterisation (like B x ). In this The unbiased residual does not include the measurement in question when determining the intersection position ( e i ) of thefitted track with the surface.
200 400 600 800 1000 1200 1400 1600Luminosity block20 - - m ] m A v e r age I B L d i s t o r t i on m agn i t ude [ ATLAS
Data 2015 (LHC fill 4560)dynamic alignmentfill-averaged alignmentbaseline alignment - - · m m H i t s on t r a cks / Data 2015 (LHC fill 4560)dynamic alignmentfill-averaged alignmentbaseline alignment m m m, FWHM/2.35=13 m =0 m m m m, FWHM/2.35=21 m =0 m m m m, FWHM/2.35=27 m =-14 m ATLAS
Figure 11: IBL distortion magnitude in the transverse plane per luminosity block (LB) range (left) and the IBL local- x unbiased residual distributions (right) for an LHC fill averaged over all 14 IBL staves. The open blue squares (baselinealignment) show the average IBL distortion in the transverse plane after the baseline ID alignment. The open redcircles show the fill-averaged correction and the solid black circles show the full dynamic alignment correction. context, less significant module-to-module movements remain uncorrected by the dynamic alignment. Thiseffect is seen as a residual time-dependent misalignment or ‘instability’ of the modules. This instabilityis estimated for each silicon layer and module z -position by integrating modules over φ into one group.Results are presented for the ‘in-plane’ translation DoFs only (local- x and local- y ).For each module, the average track-hit residual, (cid:104) r x , y (cid:105) , is computed for each LHC fill, for both local- x andlocal- y , on a set of calibration data, whose size is approximately independent from the fill conditions. Itsstatistical uncertainty, σ r x , y /√ N , where N is given by the number of tracks per module and σ r x , y is thestandard deviation of the residuals, is computed assuming that the residual distribution is approximatelyGaussian. The dispersion σ (cid:104) r x , y (cid:105) of the distribution in (cid:104) r x , y (cid:105) obtained from all LHC fills is an estimate ofthe total instability of the module position after all alignment corrections are applied. This total uncertaintycan be divided into a statistical component ( σ r x , y /√ N ) and a component describing residual instability dueto uncorrected time-dependent movements and stochastic fluctuations, σ time x , y : σ (cid:104) r x , y (cid:105) ∼ σ time x , y ⊕ σ r x , y √ N . As the size of the statistical contribution per module per LHC fill is generally small, σ time x , y is estimated by σ time x , y ≡ (cid:115) σ (cid:104) r x , y (cid:105) − (cid:18) σ r x , y √ N (cid:19) . Figures 13 to 15 show the estimated instability in local- x and local- y of the Pixel and SCT barrel layers asa function of module z -position. Figure 16 shows the local- x and local- y instabilities of the modules in thePixel endcap layers. The alignment in the central pseudorapidity range for both the Pixel and SCT barrelmodules is controlled to a precision better than 0.5 µm and 2 µm in local- x and local- y , respectively. Thislevel of control is considered to be very good given the time-dependent corrections of O(
10 µm ) due to theIBL distortion and the vertical movement of the Pixel detector. The same level of precision is not achievedfor the outermost IBL modules (3D sensors) corresponding to the range | η | > .
5. There the alignment22 ate 2016Jun 09 Jun 16 Jun 23 Jun 30 Jul 07 Jul 14 Jul 21 Jul 28 m ] μ D i s t o r t i on m agn i t ude c hange [ − − − − − ATLAS = 13 TeVsData
Date 2016Jun 09 Jun 16 Jun 23 Jun 30 Jul 07 Jul 14 Jul 21 Jul 28 m ] μ H o r i z on t a l c o rr e c t i on [ − − − IBL Pixel
ATLAS = 13 TeVsData
Date 2016Jun 09 Jun 16 Jun 23 Jun 30 Jul 07 Jul 14 Jul 21 Jul 28 m ] μ V e r t i c a l c o rr e c t i on [ − IBL Pixel
ATLAS = 13 TeVsData
Figure 12: Average correction of the IBL bowing magnitude, B x , (top), IBL and Pixel detector’s horizontal position, T x , (middle), IBL and Pixel detector’s vertical position, T y , (bottom) relative to the baseline alignment in 2016 pp collision runs between LHC technical shutdown period 1 and LHC machine development period 1. The correctionis calculated every 20 minutes for the first 60 minutes of the data taking, and every 100 minutes for the rest of thedata-taking period. Each connected series of points represents a continuous data-taking period. precision in local- x (local- y ) is measured with an uncertainty better than 3 µm (15 µm). This region isparticularly challenging due to the low number of tracks. Moreover, the tracks in this region have onlysmall overlap with other ID tracking layers. Furthermore, the large IBL local- y uncertainty may be relatedto a deformation of IBL staves in local- z over time, which is not corrected for in the prompt calibrationloop.The instability for Pixel endcap modules is larger than for barrel modules; the local- x and local- y instabilitiesare 2–4 µm and 4–7 µm, respectively. This instability corresponds to the size of the movements of thePixel endcap modules relative to the baseline alignment over time. The precision achieved is nearly one23rder of magnitude better than the required precision [2]. This required precision was defined in orderto limit the degradation of the resolution of the track parameters for high-momentum tracks to less than20% in comparison with a perfectly aligned detector. While succeeding in its primary goal, these results,specifically the residual Pixel endcap movements, also imply that the current dynamic alignment scheme,which allows time-dependent alignment of the entire Pixel detector as one unit, is not optimal. A higherlevel of precision might be achieved if the Pixel endcap disks were aligned individually. This improvementis under study for LHC Run 3, including detailed cross-checks for new weak modes that may be introduceddue to the additional DoFs within the calibration loop. - - - - -
10 110 m ] m Lo c a l x e s t i m a t ed i n s t ab ili t y [ IBL PIX1PIX2 PIX3
Data 2015+2016 = 13 TeVs
ATLAS
Figure 13: Estimated σ time x as a function of the module global- z position for the IBL and Pixel barrel layers. Thevertical bar on each marker represents the standard deviation of the estimated value over modules at the same z -position along different staves. The global- z position is slightly modified from its true value for visualisationpurposes. - - - - m ] m Lo c a l y e s t i m a t ed i n s t ab ili t y [ IBL PIX1PIX2 PIX3
Data 2015+2016 = 13 TeVs
ATLAS
Figure 14: Estimated σ time y as a function of the module global- z position for Pixel barrel layers. The vertical baron each marker represents the standard deviation of the estimated value over modules at the same z -position alongdifferent staves. The global- z position is slightly modified for the different Pixel layers for visualisation purposes. - - - - m ] m Lo c a l x e s t i m a t ed i n s t ab ili t y [ SCT1 SCT2SCT3 SCT4
Data 2015+2016 = 13 TeVs
ATLAS
Figure 15: Estimated σ time x as a function of module global- z position for SCT barrel layers. The vertical bar on eachmarker represents the standard deviation of the estimated value over modules at the same z -position along differentstaves. The global- z position is slightly modified for the different SCT layers for visualisation purposes. ayer-2 Layer-1 Layer-0 Layer-0 Layer-1 Layer-2 Pixel endcap layer01234567 m ] m E s t i m a t ed l o c a l x i n s t ab ili t y [ Negative z-side Positive z-sideData 2015+2016 = 13 TeVs
ATLAS
Layer-2 Layer-1 Layer-0 Layer-0 Layer-1 Layer-2
Pixel endcap layer02468101214 m ] m E s t i m a t ed l o c a l y i n s t ab ili t y [ Negative Z-side Positive Z-sideData 2015+2016 = 13 TeVs
ATLAS
Figure 16: Estimated σ time x , y as a function of module η index for Pixel endcap layers. The vertical bar on each markerrepresents the standard deviation of the estimated value over modules of the same layer. Momentum biases
The alignment corrections described in Sections 4 and 5 target misalignments that change the χ of thetrack fit in Eq. (1). In contrast, correlated geometrical distortions referred to as weak modes leave the χ of the fitted tracks virtually unchanged and can systematically bias the reconstructed track parameters.Momentum biases induced by correlated detector misalignments can generally be classified into twocategories:• Sagitta deformations consist of detector geometry distortions in the bending plane that affect thereconstructed track curvature differently for positively and negatively charged particles (Figure 17left).•
Length scale biases are characterised by detector geometry distortions along the track trajectoryand affect the reconstructed curvature identically for positively and negatively charged particles(Figure 17 right).These biases can be mitigated through the use of constraints either on track parameters (Section 3.2.4) oron alignment parameters (Section 3.2.5), or on both simultaneously. Residual momentum biases, aftercorrections to the detector alignment have been made, are sufficiently small that they can be accounted forby directly correcting track parameters. detector layers (cid:70) real hit position (cid:70) reconstructed hit position real trajectory fitted trackFigure 17: A simplified representation of two common weak modes that bias the track momentum. A sagitta bias(left) is caused by a deformation in the bending plane of the tracks, e.g. a rotation of the detector layers dependinglinearly on the radius. A length scale bias (right) caused by a deformation along the track trajectory, e.g. a radialexpansion of the detector layers depending linearly on the radius. The real (dashed black line) and fitted (solidblack line) particle trajectories are shown. Red stars indicate real measurement positions and grey stars show thereconstructed hit positions (biased measurements).
Displacements of the reconstructed hits in the bending plane orthogonal to the track path result in acharge-antisymmetric alteration of the track curvature, which is parameterised as p (cid:48) = p ( + q p T δ sagitta ) − , (22)27here the un-primed quantities correspond to the true values, the primed quantities correspond to thereconstructed values, q refers to the sign of the electric charge of the particle and δ sagitta is a bias parametercommon to all measured momenta and uniquely defines the detector geometry deformation.Two iterative methods are used to determine the sagitta biases. The first method uses Z → µ + µ − decays.The second uses the electromagnetic calorimeter as a reference, and utilises the ratio of the measured energydeposited in the calorimeter ( E ) to the momentum ( p ) measured by the ID for electrons and positrons.Both methods allow the detector to be segmented arbitrarily in η and φ , allowing the study of localisedsagitta biases. Sagitta biases have, to a great extent, been corrected for during the determination of thealignment constants by adding constraints to the parameters of the tracks used to perform the detectoralignment, as given by Eqs. (14) and (16) and explained in Sections 3.2.4 and 3.2.5, and also in Refs. [3,43]. The methods used to calculate the constraints are described below, and the residual sagitta biases afteralignment corrections are shown. Z → µ + µ − decays The invariant mass, m , of two highly relativistic opposite-charge particles is given approximately by m = p + p − ( − cos γ ) , where p + and p − are the magnitudes of the momenta of the positively and negatively charged particles, and γ is defined as their opening angle. In the following, + and − superscripts refer to the properties of thepositively and negatively charged muons respectively. Sagitta biases can be measured using any particle(of reasonably narrow width) that decays into pairs of stable particles. In LHC conditions, resonances thatdecay into pairs of muons (such as J / ψ , Υ and Z ) present the advantage that the dimuon signature canbe clearly distinguished from the large hadronic background. For δ sagitta studies, Z → µ + µ − decays arepreferred due to the high momentum of the Z decay products. Data quality selection criteria, summarisedin Table 4, are applied to both the selected muon candidates and the dimuon system. In total, more than70 million Z → µ + µ − candidate events were selected.In general, geometrical distortions that bias sagitta measurements can be localised in specific regionsof the detector. As a result, the sagitta bias parameter explicitly depends on the path of the track,which can be approximated by the direction of the track at the pp interaction point, given by η and φ : δ sagitta → δ sagitta ( η, φ ) . The difference at leading order in δ sagitta ( η, φ ) between the reconstructed dimuoninvariant mass using the uncorrected geometry ( m µµ ) and the expected mass ( m Z ) for each event is givenby: m µµ − m Z ≈ m Z (cid:0) p (cid:48) + T δ sagitta ( η + , φ + ) − p (cid:48)− T δ sagitta ( η − , φ − ) (cid:1) . (23)An iterative procedure is used to determine δ sagitta ( η, φ ) . For the i -th iteration, δ sagitta , i ( η, φ ) is computedfor every muon in the Z → µ + µ − sample with: δ sagitta , i ( η, φ ) = − q m µµ − m Z m Z (cid:0) + q p (cid:48) T (cid:104) δ sagitta , i − ( η, φ )(cid:105) (cid:1) p (cid:48) T + (cid:104) δ sagitta , i − ( η, φ )(cid:105) , (24)where (cid:104) δ sagitta , i − ( η, φ )(cid:105) is the mean of the previous iteration for all muons in that ( η, φ ) region. The valueof m µµ is computed as in Eq. (23) also using the mean of δ sagitta from the previous iteration. The iterationsare repeated until convergence is reached. 28 able 4: Event selection criteria for Z → µ + µ − (Section 6.1.1) and Z → e + e − (Section 6.1.2) candidate events for theanalyses of the sagitta biases in data. Events triggered by the lowest-threshold unprescaled single and double electronand muon triggers are used to select Z → µ + µ − and Z → e + e − event candidates. γ ( µ + , µ − ) is the opening anglebetween the muons. ∆ d ( µ + , µ − ) and ∆ z ( µ + , µ − ) are defined as the difference in d and z between the two muons. Selection criteria Z → µ + µ − Z → e + e − Lepton selection Two muons associated Two electrons associatedwith the primary vertex with the primary vertex p T >
12 GeV E T >
25 GeV | η | < . | η | < . d significance < 4Dilepton selection 70 GeV < m µ + µ − <
110 GeV | m e + e − − m Z | <
30 GeV | ∆ d ( µ + , µ − )| < . | ∆ z ( µ + , µ − )| < . γ ( µ + , µ − ) > ◦ Both muon candidates are required to satisfy the ‘medium’ quality criteria as defined in Ref. [38]. The reconstructed vertex with the largest (cid:205) p of its tracks. Excluding the transition region between the barrel and forward calorimeters. The significance is defined as | d |/ σ ( d ) , where σ ( d ) is the uncertainty on the d from the track fit. Both electron candidates are required to satisfy the ‘loose’ quality criteria as defined in Ref. [45].
The method, as described by Eq. (23), is only sensitive to relative sagitta biases in different sectors of thedetector. An alternative method, comparing the p T spectrum of the µ + and µ − [44] was also tested. Thismethod is sensitive to global sagitta biases, although it is also subject to detector acceptance effects andrequires more data to achieve the same statistical precision as the mass-based method.Figure 18 shows the measured sagitta distortions depending on the track direction using this technique.The central barrel region of the detector is largely free of sagitta bias, while the endcap regions exhibitsome areas of small residual sagitta bias. The distribution of δ sagitta for the full Run 2 data is shown inFigure 18. Figure 19 shows the average δ sagitta versus η and φ , as well as its RMS. The distributions, splitby data-taking year, have compatible shapes indicating a consistent and stable detector geometry duringRun 2. E / p ratio of electrons and positrons Assuming that the calorimeter response is independent of the charge of the incoming particle and that aperfectly aligned detector reconstructs the momentum of charged particles correctly, charge-dependentmomentum biases are expected to manifest themselves as differences in the E / p ratio of these particles.This ratio is defined as the ratio of the calorimeter energy measurement ( E ) to the track momentummeasurement ( p ). This technique is mainly suitable for electrons and positrons. In the presence of a sagittabias, the (cid:104) E / p (cid:105) ratio would be modified as (cid:104) E / p (cid:48) (cid:105) = (cid:104) E / p (cid:105) + q (cid:104) E T (cid:105) δ sagitta , where E T ≡ E / cosh η isreferred to as the transverse energy. Assuming that the average transverse momentum of positrons and29 .5 − − − − − η − − − φ − − − − ] [ T e V s ag i tt a δ ATLAS Data 2018, 59.9 fb − µ + µ → = 13 TeV, Z s − − − − [TeV Sagitta δ a r b i t r a r y un i t s ATLAS Data 2016 18, 137.2 fb − µ + µ → = 13 TeV, Z s Mean = 0.018TeV RMS = 0.085TeV
Figure 18: Sagitta biases versus η and φ (left) for 2018 data and the overall sagitta biases in the Run 2 data (right) forthe Z → µ + µ − method. The error bars represent the statistical uncertainty. − − − − − η − − ] [ T e V s ag i tt a δ M ean Data 2016Data 2017Data 2018
ATLAS Data 2016 18, 137.2 fb − µ + µ → = 13 TeV, Z s − − − − − η ] [ T e V s ag i tt a δ R M S Data 2016Data 2017Data 2018
ATLAS Data 2016 18, 137.2 fb − µ + µ → = 13 TeV, Z s − − − φ − − ] [ T e V s ag i tt a δ M ean Data 2016Data 2017Data 2018
ATLAS Data 2016 18, 137.2 fb − µ + µ → = 13 TeV, Z s − − − φ ] [ T e V s ag i tt a δ R M S Data 2016Data 2017Data 2018
ATLAS Data 2016 18, 137.2 fb − µ + µ → = 13 TeV, Z s Figure 19: Measured sagitta biases versus η (top) and φ (bottom) using the Z → µ + µ − method. The average (left)and the RMS (right) of the sagitta bias is shown. The markers of the data points of the different years are slightlyshifted in η and φ for better visibility. The error bars represent the statistical uncertainty. .5 − − − − − η − − − φ − − − ] [ T e V s ag i tt a δ ATLAS Data 2018, 59.9 fb − e + e → = 13 TeV, Z s − − − − [TeV Sagitta δ a r b i t r a r y un i t s ATLAS Data 2016 18, 137.2 fb − e + e → = 13 TeV, Z s Mean = 0.064TeV RMS = 0.116TeV
Figure 20: Sagitta biases versus η and φ (left) for 2018 data and the overall sagitta biases of the Run 2 data (right) forthe E / p method. The error bars represent the statistical uncertainty. electrons is equal, the sagitta bias can be estimated [3] as δ sagitta = (cid:104) E / p (cid:48) (cid:105) + − (cid:104) E / p (cid:48) (cid:105) − (cid:104) E T (cid:105) . The value of δ sagitta is determined iteratively, correcting the momentum using Eq. (22), taking into accountany biases introduced by the aforementioned assumptions. It should be noted that biases in the calorimeterenergy scale cancel out to first order and any residual dependence would be reduced by this iterativeprocedure. In addition, this method is, by construction, sensitive to global sagitta biases. Data qualityselection criteria are applied to both the selected electron candidates and the electron–positron system andare summarised in Table 4.Figure 20 shows the δ sagitta as obtained from the E / p method. These results support the observations fromSection 6.1.1: the central barrel region of the detector is largely free of sagitta bias, while the endcapregions exhibit regions of small residual sagitta bias. Compared to Figure 18 (right) a global offset of ∼ −1 can be seen in Figure 20 (right) indicating the presence of a small global sagitta bias. Figure 21shows the average δ sagitta versus η and φ , as well as its RMS. The δ sagitta distributions from the E / p methodsplit by data-taking year have comparable shape to those obtained from the Z → µ + µ − mass method,further supporting the observation of a consistent and stable detector geometry during Run 2. The changein position due to the residual sagitta bias ( ∼ −1 ) when extrapolating a track from the detector originto the outermost SCT endcap disk (radius of 500 mm and a z -axis distance of 2720 mm from the detectororigin) is less than 10 µm. Displacements of the reconstructed hits parallel to the track direction result in a charge-symmetric alterationof the measured track curvature. In a tracker with a solenoidal magnetic field these can be induced bychanges in the radial or longitudinal length scale of the detector with little impact on the track fit quality.31 .5 − − − − − η − − ] [ T e V s ag i tt a δ M ean Data 2016Data 2017Data 2018
ATLAS Data 2016 18, 137.2 fb − e + e → = 13 TeV, Z s − − − − − η ] [ T e V s ag i tt a δ R M S Data 2016Data 2017Data 2018
ATLAS Data 2016 18, 137.2 fb − e + e → = 13 TeV, Z s − − − φ − − ] [ T e V s ag i tt a δ M ean Data 2016Data 2017Data 2018
ATLAS Data 2016 18, 137.2 fb − e + e → = 13 TeV, Z s − − − φ ] [ T e V s ag i tt a δ R M S Data 2016Data 2017Data 2018
ATLAS Data 2016 18, 137.2 fb − e + e → = 13 TeV, Z s Figure 21: Sagitta biases versus η (top) and φ (bottom) for the E / p method. The average (left) and the RMS (right)of the sagitta bias is shown. The markers of the data points of the different years are slightly shifted in η and φ forbetter visibility. The error bars represent the statistical uncertainty. If the actual radius of a detector module, R , is assumed to be R ( + ε r ) , then for small distortions ( | ε r | (cid:28) p (cid:48) T = p T ( + ε r ) p (cid:48) z = p z . (25)Equation (25) assumes that the length scale in the bending plane also expands by a factor ( + ε r ) , whichimplies that dimensions of sensitive detector modules would also expand by the same factor. If it is assumedthat detector modules do not expand in the bending plane then the reconstructed transverse momentum willbe biased by a factor of ( + ε r ) .Similarly, if the actual longitudinal dimension of a detector module, z , is assumed to be z ( + ε z ) , thereconstructed momentum will be : p (cid:48) T = p T p (cid:48) z = p z ( + ε z ) . (26)32inear combinations of both the radial and longitudinal biases are also considered. It is worth noting thatthere is a degeneracy between the effects of a bias in the magnetic field and a global scaling of the detector(radial and longitudinal: ε s ), as both lead to a momentum bias of the form ppp ( + ε s ) . Consequently, if B isassumed to be B ( + ε s ) the particle momentum scales as ppp ( + ε s ) .The relationship between the reconstructed invariant mass of a particle decaying into two muons ( m (cid:48) µµ ),and the true mass ( m µµ ), assuming that the radial and longitudinal biases in Eqs. (25) and (26) are bothsmall, is given by: m (cid:48) µµ ≈ m µµ + E + E − (cid:104) (cid:0) β + T (cid:1) − βββ + T · βββ − T (cid:105) ε r ( η + , φ + ) + E + E − (cid:104) (cid:0) β − T (cid:1) − βββ + T · βββ − T (cid:105) ε r ( η − , φ − ) + E + E − (cid:104) (cid:0) β + z (cid:1) − βββ + z · βββ − z (cid:105) ε z ( η + , φ + ) + E + E − (cid:2) ( β − z ) − βββ + z · βββ − z (cid:3) ε z ( η − , φ − ) , where the βββ = ppp / E is the velocity of the particle. This approximation is valid to first order in ε .In a simpler case, where only a global radial and longitudinal bias are present, the reconstructed mass is: m (cid:48) µµ ≈ m µµ + E + E − (cid:2) βββ + T − βββ − T (cid:3) ε r + E + E − (cid:2) βββ + z − βββ − z (cid:3) ε z , which, in the limit where the muon mass is ignored leads to m (cid:48) µµ ≈ m µµ + m µµ ε r sin α + m µµ ε z cos α ≈ m µµ + m µµ (cid:0) ε s + ε r (cid:48) sin α (cid:1) , where sin α = E + E − (cid:2) βββ + T − βββ − T (cid:3) / m µµ , (27) ε s = ε z , and ε r (cid:48) = ε r − ε z is the difference between the radial and longitudinal components of themomentum scale. Thus, by measuring the mass as function of sin α it is possible to differentiate between radial and scalebiases. Figure 22 shows the measured scale using J / ψ and Z decays into µ + µ − in the barrel of the ID. Theresults show a clear momentum scale bias but no significant radial scale ( ε r (cid:48) ) as the reconstructed mass isconstant as a function of sin α .An analysis using an iterative procedure similar to the δ sagitta method, Eq. (24), is also performed. Here,the momentum scale factor ( ε s ) is computed and consequently used to update the momentum of the tracksat the next iteration. This method allows biases to be measured as a function of any kinematic or geometricparameter. The results as a function of the track p T are presented in Figure 23. The magnitude of themomentum scale bias is observed to be constant as a function of track p T as expected from a length scaleor magnetic field strength bias.The magnitude of the measured scale bias is consistent for the two studies, demonstrating that there is aglobal momentum scale bias of ε s ≈ − . × − . This result is in agreement with the momentum scale atthe ID for muons [38]. As previously highlighted, the origin of such a global momentum scale bias cannotbe unambiguously resolved by these studies. For the massless case, defining cos α = E + E − (cid:2) βββ + z − βββ − z (cid:3) / m µµ one obtains sin α + cos α = a sin0.99850.9990.999511.00051.001 r e f m / mm m = 13 TeVsData 2017-18 ATLAS - m + m fiy J/ -3 · – = (-0.85 s e -3 · – = ( 0.03 r' e PDG m a sin0.99850.9990.999511.00051.001 r e f m / mm m = 13 TeVsData 2017-18 ATLAS - m + m fi Z -3 · – = (-0.87 s e -3 · – = ( 0.08 r' e PDG m Figure 22: Ratio of the measured mass to the reference as a function of sin α . Due to event kinematics, J / ψ → µ + µ − events (left) cover the entire sin α range while Z → µ + µ − events (right) cover a smaller range. Error bars representthe statistical uncertainty. The red lines show the fit to Eq. (27) from which the values of ε s and ε r (cid:48) are extracted.
10 20 30 40 50 60 70 80 90 100 [GeV] T p0.0015 - - - s e Data 2018 -m+m fi y J/ = 13 TeVs
ATLAS
10 20 30 40 50 60 70 80 90 100 [GeV] T p0.0015 - - - s e Data 2018 -m+m fi Z = 13 TeVs
ATLAS
Figure 23: The measured momentum scale bias ε s as a function of track p T . Error bars represent the statisticaluncertainty. Left: J / ψ → µ + µ − decays; right: Z → µ + µ − decays. The weak modes of the alignment can also lead to a bias in the transverse ( d ) and longitudinal ( z ) impactparameters. For example, a rotation of the IBL or radial distortions of the Pixel layers can lead to transverseimpact parameter biases. The quality of the detector alignment can be assessed by analysing impactparameter biases as a function of track p T and η . For this study, events are selected using a combination ofsingle-jet triggers with several jet p T thresholds starting at 100 GeV. The standard ATLAS event cleaningselection is applied, ensuring that all detectors were fully operational. In order to disentangle the biases dueto residual misalignment from those originating from the track reconstruction algorithms, recorded dataare compared with a dijet Monte Carlo simulation sample generated with Pythia [46]. The primary vertexof each selected event must have at least three tracks associated with it. Tracks are selected by requiringthem to be assigned to jets using ghost association [47], a procedure that treats them as four-vectors ofinfinitesimal momentum magnitude during the jet reconstruction and assigns them to the jet with whichthey are clustered. Jets are reconstructed using the anti- k t algorithm [48] with radius parameter R = .
4. Inaddition, tracks are required to have at least 9 silicon (Pixels + SCT) hits for | η | ≤ .
65, at least 11 silicon34its for | η | > .
65, a maximum of 2 SCT holes , no Pixel hole, p T > | η | < .
5, and an openingangle ∆ R ( track , jet ) < . p T of 3 GeV corresponds to thelowest momentum threshold typically used within the alignment to reduce MCS effects (see Section 3.1).The impact parameters are obtained relative to the primary vertex by extrapolating the particle trajectory toits position. This is particularly relevant for the longitudinal impact parameter, as the width of the luminousregion in the z direction is very broad. The impact parameter biases are extracted by iteratively fitting thedistribution of impact parameters relative to the primary vertex with a Gaussian function within a ± σ range until the fitted µ and σ are stable within 1%. The resulting value of the Gaussian mean ( µ ) representsthe estimate of the impact parameter bias.Figure 24 shows the transverse and longitudinal impact parameter biases as a function of the deliveredluminosity in Run 2. Data collected in 2016 have a period-dependent d bias of − + Data collected in 2017 and 2018 showoverall d biases of less than 1 µm. The longitudinal impact parameter bias is negligible and constant acrossthe years (below 0 . η , respectively. The small bias in thelongitudinal impact parameter as a function of track η is present in simulation and data and is consequentlynot introduced by the track-based alignment because it is not applied to simulation (where perfect alignmentis assumed). The resulting bias has no significant effect on the ATLAS tracking performance as thelongitudinal impact parameter resolution is on the order of 100 µm for tracks with p T >
10 GeV. A hole is defined as a missing hit in a module where a hit is expected, based on the extrapolation of the particle trajectory to themodule surface. This procedure is adopted as the impact parameter distributions have long tails. The impact parameters of tracks used in ATLAS physics analyses are corrected by a time-dependent constant to remove theobserved biases. In addition, this bias will be corrected in future data processing campaigns. Integrated luminosity [fb20 40 60 80 100 120 140 160 m ] µ [ 〉 d 〈 − − − Data 2016Data 2017Data 2018
ATLAS = 13 TeVs ] Integrated luminosity [fb20 40 60 80 100 120 140 160 m ] µ [ 〉 z 〈 − − − Data 2016Data 2017Data 2018
ATLAS = 13 TeVs
Figure 24: The transverse (left) and longitudinal (right) impact parameter biases as function of the Run 2 deliveredluminosity. The red dotted line indicate the change in the underlying ATLAS ID alignment geometry description.This splits the 2016 data in two periods. The grey dotted lines indicate the change of the data-taking years. The ∼ − corresponding to 2015 data are not shown in this plot. Only statistical uncertainties are shown. [GeV] T p10 m ] µ [ 〉 d 〈 − − − SimulationData 2016Data 2017Data 2018
ATLAS = 13 TeVs [GeV] T p10 m ] µ [ 〉 z 〈 − − − SimulationData 2016Data 2017Data 2018
ATLAS = 13 TeVs
Figure 25: The transverse (left) and longitudinal (right) impact parameter biases as function of the track p T . The2016 data entries in this figure are taken from the second part of the 2016 data visible in Figure 24; the first part ofthe 2016 data also show no impact parameter dependence on track p T . − − − − − m ] µ [ 〉 d 〈 − − SimulationData 2016Data 2017Data 2018
ATLAS = 13 TeVs η − − − − − m ] µ [ 〉 z 〈 − − SimulationData 2016Data 2017Data 2018
ATLAS = 13 TeVs
Figure 26: The transverse (left) and longitudinal (right) impact parameter biases as function of the track η . The 2016data entries in this figure are taken from the second part of the 2016 data visible in Figure 24; the first part of 2016data also shows no impact parameter dependence on track η . Conclusion
This paper describes the precision alignment of the ATLAS Inner Detector (ID) for Run 2 and quantifiesthe impact of alignment uncertainties on track parameter biases. The alignment procedure consists ofa track-based algorithm that minimises track-hit residuals. It calculates the track parameters at eachmeasurement surface and encodes the relationship between track-hit residuals and the alignment parametersof each alignable structure. To resolve ambiguities, it imposes externally determined constraints on trackparameters, e.g. using tracks from resonance decays. The alignment procedure is performed at differenthierarchical levels, starting from the largest physical structures and proceeding to individual detectormodules or sensor elements. The number of degrees of freedom increases for each subsequent alignmentlevel. In total, more than 36 000 degrees of freedom are considered when aligning all silicon modules(IBL, Pixel and SCT) and more than 700 000 degrees of freedom are added for the TRT.It has been observed that operational conditions affect the positions of ID elements. The Pixel detectormoves rapidly upwards every time the data acquisition is activated. The staves of the IBL bow depending onthe temperature; the degree of variation depends on the thermal load and is a function of the accumulatedradiation dose and of the luminosity. The remaining detector structures are quite stable during an LHC fill;the movements of individual modules in the barrel have an RMS at the micrometer level while those in theendcap regions range from 2 µm to O(
10 µm).An automated alignment procedure that corrects for relatively rapid movements of the Pixel detector andIBL and the relative positions of all of other subdetectors is executed for every LHC fill for which theID collects data. The detailed alignment of all the other structures (subdetectors, barrel, endcaps, layers,disks, modules or wires) is determined in dedicated alignment campaigns. The impact of alignment weakmodes, namely distortions that leave the track fit quality largely unchanged and can bias the measured trackparameters, is minimised during these campaigns by employing external constraints on track parameters.Independent measurements are performed to quantify potential biases, enabling them to be largely removed.The residual sagitta bias and momentum scale bias after the full Run 2 alignment are reduced to less than ∼ −1 and 0.9 × − , respectively. Remaining track parameter biases do not significantly impactATLAS physics analyses. 39 ppendix A Track fitting with multiple Coulomb scattering effects
The track fit can be improved by allowing the charged particle to scatter as it passes through material in thedetector. To include the effects of multiple scattering, terms are added directly to the track χ as it is donein Eq. (3), which can be written as: χ = (cid:213) i (cid:18) r i ( τ , θ ) σ i (cid:19) + (cid:213) j ( ˆ θ − θ j ) Θ j j . It should be noted that the residuals now also depend on the scattering angles, θ . The scattering expectationvalue, ˆ θ , is zero and its variance, Θ j j , depends on the particle momentum and amount of material traversed.The uncertainty of the i -th measurement is denoted by σ i .The χ has to be minimised for τ and θ simultaneously. Defining the derivative of residuals with respectto track and scattering parameters to be: G ≡ ∂ r ∂ τ S ≡ ∂ r ∂ θ the derivatives of χ with respect to the track and scattering parameters are:12 d χ d τ = G (cid:62) Ω − r ,
12 d χ d θ = S (cid:62) Ω − r + Θ − θ . Neglecting second-order derivatives of residuals, the second derivatives of χ with respect to perigee andscattering parameters are: 12 d χ d τ = G (cid:62) Ω − G ,
12 d χ d θ = S (cid:62) Ω − S + Θ − ,
12 d χ d θ d τ = G (cid:62) Ω − S . The above can be written down in a compact form using Eq. (4):12 d χ d π = H (cid:62) V − ρ ,
12 d χ d π = H (cid:62) V − H . cknowledgements We thank CERN for the very successful operation of the LHC, as well as the support staff from ourinstitutions without whom ATLAS could not be operated efficiently.We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFWand FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC andCFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia;MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS andCEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF and MPG, Germany; GSRT, Greece; RGC andHong Kong SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST,Morocco; NWO, Netherlands; RCN, Norway; MNiSW and NCN, Poland; FCT, Portugal; MNE/IFA,Romania; MES of Russia and NRC KI, Russia Federation; JINR; MESTD, Serbia; MSSR, Slovakia; ARRSand MIZŠ, Slovenia; DST/NRF, South Africa; MINECO, Spain; SRC and Wallenberg Foundation, Sweden;SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, UnitedKingdom; DOE and NSF, United States of America. In addition, individual groups and members havereceived support from BCKDF, CANARIE, Compute Canada and CRC, Canada; ERC, ERDF, Horizon2020, Marie Skłodowska-Curie Actions and COST, European Union; Investissements d’Avenir Labex,Investissements d’Avenir Idex and ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thalesand Aristeia programmes co-financed by EU-ESF and the Greek NSRF, Greece; BSF-NSF and GIF, Israel;CERCA Programme Generalitat de Catalunya and PROMETEO Programme Generalitat Valenciana, Spain;Göran Gustafssons Stiftelse, Sweden; The Royal Society and Leverhulme Trust, United Kingdom.The crucial computing support from all WLCG partners is acknowledged gratefully, in particular fromCERN, the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3(France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC(Taiwan), RAL (UK) and BNL (USA), the Tier-2 facilities worldwide and large non-WLCG resourceproviders. Major contributors of computing resources are listed in Ref. [49].
References [1] ATLAS Collaboration,
The ATLAS Experiment at the CERN Large Hadron Collider , JINST (2008)S08003.[2] ATLAS Collaboration, ATLAS Inner Detector: Technical Design Report, 1 , ATLAS-TDR-4, CERN,1997, url: https://cds.cern.ch/record/331063 .[3] ATLAS Collaboration,
Study of alignment-related systematic effects on the ATLAS Inner Detectortrack reconstruction , ATLAS-CONF-2012-141, 2012, url: https://cds.cern.ch/record/1483518 .[4] ATLAS Collaboration,
Alignment of the ATLAS Inner Detector and its Performance in 2012 ,ATLAS-CONF-2014-047 (2014), url: https://cds.cern.ch/record/1741021 .[5] ATLAS Collaboration, , ATL-DAQ-PUB-2016-001 (2016), url: https : / / cds . cern . ch /record/2136007 . 416] ATLAS Collaboration,
ATLAS Inner Detector: Technical Design Report, 2 , ATLAS-TDR-5, CERN,1997, url: https://cds.cern.ch/record/331064 .[7] M. Aleksa et al.,
Measurement of the ATLAS solenoid magnetic field , JINST (2008) P04003.[8] ATLAS Collaboration, A measurement of material in the ATLAS tracker using secondary hadronicinteractions in TeV pp collisions , JINST (2016) P11020, arXiv: .[9] ATLAS Collaboration, Study of the material of the ATLAS inner detector for Run 2 of the LHC ,JINST (2017) P12009, arXiv: .[10] ATLAS Collaboration, ATLAS data quality operations and performance for 2015-2018 data-taking ,JINST (2020) P04003, arXiv: .[11] ATLAS Collaboration, ATLAS Insertable B-Layer Technical Design Report , ATLAS-TDR-19, 2010,url: https://cds.cern.ch/record/1291633 , Addendum: ATLAS-TDR-19-ADD-1, 2012,url: https://cds.cern.ch/record/1451888 .[12] B. Abbott et al.,
Production and integration of the ATLAS Insertable B-Layer , JINST (2018)T05008, arXiv: .[13] C. Da Via et al.,
3D silicon sensors: Design, large area production and quality assurance for theATLAS IBL pixel detector upgrade , Nucl. Instrum. Meth. A (2012) 321.[14] G. Darbo,
Experience on 3D Silicon Sensors for ATLAS IBL , JINST (2015) C05001, arXiv: .[15] G. Aad et al., ATLAS pixel detector electronics and sensors , JINST (2008) P07007.[16] A. Abdesselam et al., The barrel modules of the ATLAS semiconductor tracker , Nucl. Instrum. Meth.A (2006) 642.[17] A. Abdesselam et al.,
The ATLAS semiconductor tracker end-cap module , Nucl. Instrum. Meth. A (2007) 353.[18] ATLAS Collaboration,
Operation and performance of the ATLAS semiconductor tracker , JINST (2014) P08009, arXiv: .[19] E. Abat et al., The ATLAS TRT barrel detector , JINST (2008) P02014.[20] E. Abat et al., The ATLAS TRT end-cap detectors , JINST (2008) P10003.[21] ATLAS Collaboration, Performance of the ATLAS Transition Radiation Tracker in Run 1 of theLHC: tracker properties , JINST (2017) P05002, arXiv: .[22] P. F. Akesson et al., ATLAS Tracking Event Data Model , (2006), ATL-SOFT-PUB-2006-004, url: http://cds.cern.ch/record/973401 .[23] ATLAS Collaboration,
A neural network clustering algorithm for the ATLAS silicon pixel detector ,JINST (2014) P09009, arXiv: .[24] A. Bocci and W. Hulsbergen, TRT alignment for SR1 cosmics and beyond , (2007), url: http://cds.cern.ch/record/1039585 .[25] P. Bruckman,
Alignment of the ATLAS Inner Detector Tracking System - Solving the Problem , Nucl.Phys. B (Proc. Suppl.) (2009) 158.[26] E. Anderson et al.,
LAPACK Users’ Guide , Third edition, Society for Industrial and AppliedMathematics, 1999, isbn: 0-89871-447-8. 4227] R. Brun and F. Rademakers,
ROOT - An Object Oriented Data Analysis Framework , Nucl. Instrum.Meth. A (1997) 81, See also http://root.cern.ch/ .[28] G. Guennebaud, B. Jacob et al.,
Eigen v3 , http://eigen.tuxfamily.org, 2010.[29] http://proj-clhep.web.cern.ch/proj-clhep/ .[30] E. Polizzi,
Density-matrix-based algorithm for solving eigenvalue problems , Phys. Rev. B (112009) 115112, arXiv: .[31] P. Nason, A new method for combining NLO QCD with shower Monte Carlo algorithms , JHEP (2004) 040, arXiv: hep-ph/0409146 .[32] S. Frixione, P. Nason and C. Oleari, Matching NLO QCD computations with parton showersimulations: the POWHEG method , JHEP (2007) 070, arXiv: .[33] S. Alioli, P. Nason, C. Oleari and E. Re, A general framework for implementing NLO calculationsin shower Monte Carlo programs: the POWHEG BOX , JHEP (2010) 043, arXiv: .[34] T. Sjöstrand et al., An introduction to PYTHIA 8.2 , Comput. Phys. Commun. (2015) 159, arXiv: .[35] ATLAS Collaboration,
Measurement of the Z / γ ∗ boson transverse momentum distribution in pp collisions at √ s = TeV with the ATLAS detector , JHEP (2014) 145, arXiv: .[36] H. L. Lai et al., Global QCD analysis of parton structure of the nucleon: CTEQ5 parton distributions ,Eur. Phys. J. C (2000) 375, arXiv: hep-ph/9903282 .[37] J. Pumplin et al., New Generation of Parton Distributions with Uncertainties from Global QCDAnalysis , JHEP (2002) 012, arXiv: hep-ph/0201195 .[38] ATLAS Collaboration, Muon reconstruction performance of the ATLAS detector in proton–protoncollision data at √ s = TeV , Eur. Phys. J. C (2016) 292, arXiv: .[39] J. Wollrath, Sensor shapes and weak modes of the ATLAS Inner Detector track-based alignment ,(2019), arXiv: .[40] ATLAS Collaboration,
Study of the mechanical stability of the ATLAS Insertable B-Layer , ATL-INDET-PUB-2015-001, 2015, url: https://cds.cern.ch/record/2022587 .[41] ATLAS Collaboration,
Radiation induced effects in the ATLAS Insertable B-Layer readout chip ,ATL-INDET-PUB-2017-001 (2017), url: http://cds.cern.ch/record/2291800 .[42] J. Jiménez Peña,
ATLAS Inner Detector alignment and analysis of the
Wtb vertex structure withsingle top quarks , PhD thesis: Universitat de Valencia (Spain) (2018), url: https://cds.cern.ch/record/2644636/ .[43] ATLAS Collaboration,
Common Framework Implementation for the Track-Based Alignment of theATLAS Detector , ATL-SOFT-PUB-2014-003 (2014), url: https://cds.cern.ch/record/1670354 .[44] CMS Collaboration,
Alignment of the CMS tracker with LHC and cosmic ray data , JINST (2014)P06009, arXiv: .[45] ATLAS Collaboration, Electron reconstruction and identification in the ATLAS experiment usingthe 2015 and 2016 LHC proton–proton collision data at √ s = TeV , Eur. Phys. J. C (2019) 639,arXiv: . 4346] T. Sjöstrand, S. Mrenna and P. Z. Skands, A Brief Introduction to PYTHIA 8.1 , Comput. Phys.Commun. (2008) 852, arXiv: .[47] M. Cacciari and G. P. Salam,
Pileup subtraction using jet areas , Phys. Lett. B (2008) 119, arXiv: .[48] M. Cacciari, G. P. Salam and G. Soyez,
The anti- k t jet clustering algorithm , JHEP (2008) 63,arXiv: .[49] ATLAS Collaboration, ATLAS Computing Acknowledgements , ATL-SOFT-PUB-2020-001, url: https://cds.cern.ch/record/2717821 .44 he ATLAS Collaboration
G. Aad , B. Abbott , D.C. Abbott , A. Abed Abud , K. Abeling , D.K. Abhayasinghe ,S.H. Abidi , O.S. AbouZeid , N.L. Abraham , H. Abramowicz , H. Abreu , Y. Abulaiti ,B.S. Acharya , B. Achkar , L. Adam , C. Adam Bourdarios , L. Adamczyk , L. Adamek ,J. Adelman , M. Adersberger , A. Adiguzel , S. Adorni , T. Adye , A.A. Affolder , Y. Afik ,C. Agapopoulou , M.N. Agaras , A. Aggarwal , C. Agheorghiesei , J.A. Aguilar-Saavedra ,A. Ahmad , F. Ahmadov , W.S. Ahmed , X. Ai , G. Aielli , S. Akatsuka , M. Akbiyik ,T.P.A. Åkesson , E. Akilli , A.V. Akimov , K. Al Khoury , G.L. Alberghi , J. Albert ,M.J. Alconada Verzini , S. Alderweireldt , M. Aleksa , I.N. Aleksandrov , C. Alexa ,T. Alexopoulos , A. Alfonsi , F. Alfonsi , M. Alhroob , B. Ali , S. Ali , M. Aliev ,G. Alimonti , C. Allaire , B.M.M. Allbrooke , B.W. Allen , P.P. Allport , A. Aloisio ,F. Alonso , C. Alpigiani , E. Alunno Camelia , M. Alvarez Estevez , M.G. Alviggi ,Y. Amaral Coutinho , A. Ambler , L. Ambroz , C. Amelung , D. Amidei ,S.P. Amor Dos Santos , S. Amoroso , C.S. Amrouche , F. An , C. Anastopoulos , N. Andari ,T. Andeen , J.K. Anders , S.Y. Andrean , A. Andreazza , V. Andrei , C.R. Anelli ,S. Angelidakis , A. Angerami , A.V. Anisenkov , A. Annovi , C. Antel , M.T. Anthony ,E. Antipov , M. Antonelli , D.J.A. Antrim , F. Anulli , M. Aoki , J.A. Aparisi Pozo ,M.A. Aparo , L. Aperio Bella , N. Aranzabal Barrio , V. Araujo Ferraz , R. Araujo Pereira ,C. Arcangeletti , A.T.H. Arce , F.A. Arduh , J-F. Arguin , S. Argyropoulos , J.-H. Arling ,A.J. Armbruster , A. Armstrong , O. Arnaez , H. Arnold , Z.P. Arrubarrena Tame , G. Artoni ,H. Asada , K. Asai , S. Asai , T. Asawatavonvanich , N. Asbah , E.M. Asimakopoulou ,L. Asquith , J. Assahsah , K. Assamagan , R. Astalos , R.J. Atkin , M. Atkinson , N.B. Atlay ,H. Atmani , K. Augsten , V.A. Austrup , G. Avolio , M.K. Ayoub , G. Azuelos ,H. Bachacou , K. Bachas , M. Backes , F. Backman , P. Bagnaia , M. Bahmani ,H. Bahrasemani , A.J. Bailey , V.R. Bailey , J.T. Baines , C. Bakalis , O.K. Baker ,P.J. Bakker , E. Bakos , D. Bakshi Gupta , S. Balaji , R. Balasubramanian , E.M. Baldin ,P. Balek , F. Balli , W.K. Balunas , J. Balz , E. Banas , M. Bandieramonte ,A. Bandyopadhyay , Sw. Banerjee , L. Barak , W.M. Barbe , E.L. Barberio , D. Barberis ,M. Barbero , G. Barbour , T. Barillari , M-S. Barisits , J. Barkeloo , T. Barklow , R. Barnea ,B.M. Barnett , R.M. Barnett , Z. Barnovska-Blenessy , A. Baroncelli , G. Barone , A.J. Barr ,L. Barranco Navarro , F. Barreiro , J. Barreiro Guimarães da Costa , U. Barron , S. Barsov ,F. Bartels , R. Bartoldus , G. Bartolini , A.E. Barton , P. Bartos , A. Basalaev , A. Basan ,A. Bassalat , M.J. Basso , R.L. Bates , S. Batlamous , J.R. Batley , B. Batool , M. Battaglia ,M. Bauce , F. Bauer , P. Bauer , H.S. Bawa , A. Bayirli , J.B. Beacham , T. Beau ,P.H. Beauchemin , F. Becherer , P. Bechtle , H.C. Beck , H.P. Beck , K. Becker , C. Becot ,A. Beddall , A.J. Beddall , V.A. Bednyakov , M. Bedognetti , C.P. Bee , T.A. Beermann ,M. Begalli , M. Begel , A. Behera , J.K. Behr , F. Beisiegel , M. Belfkir , A.S. Bell , G. Bella ,L. Bellagamba , A. Bellerive , P. Bellos , K. Beloborodov , K. Belotskiy , N.L. Belyaev ,D. Benchekroun , N. Benekos , Y. Benhammou , D.P. Benjamin , M. Benoit , J.R. Bensinger ,S. Bentvelsen , L. Beresford , M. Beretta , D. Berge , E. Bergeaas Kuutmann , N. Berger ,B. Bergmann , L.J. Bergsten , J. Beringer , S. Berlendis , G. Bernardi , C. Bernius ,F.U. Bernlochner , T. Berry , P. Berta , A. Berthold , I.A. Bertram , O. Bessidskaia Bylund ,N. Besson , A. Bethani , S. Bethke , A. Betti , A.J. Bevan , J. Beyer , D.S. Bhattacharya ,P. Bhattarai , V.S. Bhopatkar , R. Bi , R.M. Bianchi , O. Biebel , D. Biedermann , R. Bielski ,K. Bierwagen , N.V. Biesuz , M. Biglietti , T.R.V. Billoud , M. Bindi , A. Bingul ,45. Bini , S. Biondi , C.J. Birch-sykes , M. Birman , T. Bisanz , J.P. Biswal ,D. Biswas , A. Bitadze , C. Bittrich , K. Bjørke , T. Blazek , I. Bloch , C. Blocker , A. Blue ,U. Blumenschein , G.J. Bobbink , V.S. Bobrovnikov , S.S. Bocchetta , D. Boerner ,D. Bogavac , A.G. Bogdanchikov , C. Bohm , V. Boisvert , P. Bokan , T. Bold ,A.E. Bolz , M. Bomben , M. Bona , J.S. Bonilla , M. Boonekamp , C.D. Booth ,A.G. Borbély , H.M. Borecka-Bielska , L.S. Borgna , A. Borisov , G. Borissov , D. Bortoletto ,D. Boscherini , M. Bosman , J.D. Bossio Sola , K. Bouaouda , J. Boudreau ,E.V. Bouhova-Thacker , D. Boumediene , A. Boveia , J. Boyd , D. Boye , I.R. Boyko ,A.J. Bozson , J. Bracinik , N. Brahimi , G. Brandt , O. Brandt , F. Braren , B. Brau ,J.E. Brau , W.D. Breaden Madden , K. Brendlinger , R. Brener , L. Brenner , R. Brenner ,S. Bressler , B. Brickwedde , D.L. Briglin , D. Britton , D. Britzger , I. Brock , R. Brock ,G. Brooijmans , W.K. Brooks , E. Brost , P.A. Bruckman de Renstrom , B. Brüers , D. Bruncko ,A. Bruni , G. Bruni , M. Bruschi , N. Bruscino , L. Bryngemark , T. Buanes , Q. Buat ,P. Buchholz , A.G. Buckley , I.A. Budagov , M.K. Bugge , F. Bührer , O. Bulekov ,B.A. Bullard , T.J. Burch , S. Burdin , C.D. Burgard , A.M. Burger , B. Burghgrave ,J.T.P. Burr , C.D. Burton , J.C. Burzynski , V. Büscher , E. Buschmann , P.J. Bussey ,J.M. Butler , C.M. Buttar , J.M. Butterworth , P. Butti , W. Buttinger , C.J. Buxo Vazquez ,A. Buzatu , A.R. Buzykaev , G. Cabras , S. Cabrera Urbán , F. Cadoux , D. Caforio ,H. Cai , V.M.M. Cairo , O. Cakir , N. Calace , P. Calafiura , G. Calderini , P. Calfayan ,G. Callea , L.P. Caloba , A. Caltabiano , S. Calvente Lopez , D. Calvet , S. Calvet ,T.P. Calvet , M. Calvetti , R. Camacho Toro , S. Camarda , D. Camarero Munoz ,P. Camarri , M.T. Camerlingo , D. Cameron , C. Camincher , S. Campana ,M. Campanelli , A. Camplani , V. Canale , A. Canesse , M. Cano Bret , J. Cantero ,T. Cao , Y. Cao , M.D.M. Capeans Garrido , M. Capua , R. Cardarelli , F. Cardillo ,G. Carducci , I. Carli , T. Carli , G. Carlino , B.T. Carlson , E.M. Carlson ,L. Carminati , R.M.D. Carney , S. Caron , E. Carquin , S. Carrá , G. Carratta ,J.W.S. Carter , T.M. Carter , M.P. Casado , A.F. Casha , E.G. Castiglia , F.L. Castillo ,L. Castillo Garcia , V. Castillo Gimenez , N.F. Castro , A. Catinaccio , J.R. Catmore ,A. Cattai , V. Cavaliere , V. Cavasinni , E. Celebi , F. Celli , K. Cerny , A.S. Cerqueira ,A. Cerri , L. Cerrito , F. Cerutti , A. Cervelli , S.A. Cetin , Z. Chadi , D. Chakraborty ,J. Chan , W.S. Chan , W.Y. Chan , J.D. Chapman , B. Chargeishvili , D.G. Charlton ,T.P. Charman , M. Chatterjee , C.C. Chau , S. Che , S. Chekanov , S.V. Chekulaev ,G.A. Chelkov , B. Chen , C. Chen , C.H. Chen , H. Chen , H. Chen , J. Chen , J. Chen ,J. Chen , S. Chen , S.J. Chen , X. Chen , Y. Chen , Y-H. Chen , H.C. Cheng , H.J. Cheng ,A. Cheplakov , E. Cheremushkina , R. Cherkaoui El Moursli , E. Cheu , K. Cheung ,T.J.A. Chevalérias , L. Chevalier , V. Chiarella , G. Chiarelli , G. Chiodini , A.S. Chisholm ,A. Chitan , I. Chiu , Y.H. Chiu , M.V. Chizhov , K. Choi , A.R. Chomont , Y.S. Chow ,L.D. Christopher , M.C. Chu , X. Chu , J. Chudoba , J.J. Chwastowski , L. Chytka ,D. Cieri , K.M. Ciesla , V. Cindro , I.A. Cioară , A. Ciocio , F. Cirotto , Z.H. Citron ,M. Citterio , D.A. Ciubotaru , B.M. Ciungu , A. Clark , M.R. Clark , P.J. Clark ,S.E. Clawson , C. Clement , Y. Coadou , M. Cobal , A. Coccaro , J. Cochran ,R. Coelho Lopes De Sa , S. Coelli , H. Cohen , A.E.C. Coimbra , B. Cole , A.P. Colijn ,J. Collot , P. Conde Muiño , S.H. Connell , I.A. Connelly , S. Constantinescu ,F. Conventi , A.M. Cooper-Sarkar , F. Cormier , K.J.R. Cormier , L.D. Corpe ,M. Corradi , E.E. Corrigan , F. Corriveau , M.J. Costa , F. Costanza , D. Costanzo ,G. Cowan , J.W. Cowley , J. Crane , K. Cranmer , R.A. Creager , S. Crépé-Renaudin ,F. Crescioli , M. Cristinziani , V. Croft , G. Crosetti , A. Cueto , T. Cuhadar Donszelmann ,46. Cui , A.R. Cukierman , W.R. Cunningham , S. Czekierda , P. Czodrowski ,M.M. Czurylo , M.J. Da Cunha Sargedas De Sousa , J.V. Da Fonseca Pinto , C. Da Via ,W. Dabrowski , F. Dachs , T. Dado , S. Dahbi , T. Dai , C. Dallapiccola , M. Dam ,G. D’amen , V. D’Amico , J. Damp , J.R. Dandoy , M.F. Daneri , M. Danninger , V. Dao ,G. Darbo , O. Dartsi , A. Dattagupta , T. Daubney , S. D’Auria , C. David , T. Davidek ,D.R. Davis , I. Dawson , K. De , R. De Asmundis , M. De Beurs , S. De Castro ,N. De Groot , P. de Jong , H. De la Torre , A. De Maria , D. De Pedis , A. De Salvo ,U. De Sanctis , M. De Santis , A. De Santo , J.B. De Vivie De Regie , D.V. Dedovich ,A.M. Deiana , J. Del Peso , Y. Delabat Diaz , D. Delgove , F. Deliot , C.M. Delitzsch ,M. Della Pietra , D. Della Volpe , A. Dell’Acqua , L. Dell’Asta , M. Delmastro ,C. Delporte , P.A. Delsart , D.A. DeMarco , S. Demers , M. Demichev , G. Demontigny ,S.P. Denisov , L. D’Eramo , D. Derendarz , J.E. Derkaoui , F. Derue , P. Dervan , K. Desch ,K. Dette , C. Deutsch , M.R. Devesa , P.O. Deviveiros , F.A. Di Bello , A. Di Ciaccio ,L. Di Ciaccio , W.K. Di Clemente , C. Di Donato , A. Di Girolamo , G. Di Gregorio ,B. Di Micco , R. Di Nardo , K.F. Di Petrillo , R. Di Sipio , C. Diaconu , F.A. Dias ,T. Dias Do Vale , M.A. Diaz , F.G. Diaz Capriles , J. Dickinson , M. Didenko , E.B. Diehl ,J. Dietrich , S. Díez Cornell , C. Diez Pardos , A. Dimitrievska , W. Ding , J. Dingfelder ,S.J. Dittmeier , F. Dittus , F. Djama , T. Djobava , J.I. Djuvsland , M.A.B. Do Vale ,M. Dobre , D. Dodsworth , C. Doglioni , J. Dolejsi , Z. Dolezal , M. Donadelli , B. Dong ,J. Donini , A. D’onofrio , M. D’Onofrio , J. Dopke , A. Doria , M.T. Dova , A.T. Doyle ,E. Drechsler , E. Dreyer , T. Dreyer , A.S. Drobac , D. Du , T.A. du Pree , Y. Duan ,F. Dubinin , M. Dubovsky , A. Dubreuil , E. Duchovni , G. Duckeck , O.A. Ducu , D. Duda ,A. Dudarev , A.C. Dudder , E.M. Duffield , M. D’uffizi , L. Duflot , M. Dührssen , C. Dülsen ,M. Dumancic , A.E. Dumitriu , M. Dunford , A. Duperrin , H. Duran Yildiz , M. Düren ,A. Durglishvili , D. Duschinger , B. Dutta , D. Duvnjak , G.I. Dyckes , M. Dyndal , S. Dysch ,B.S. Dziedzic , M.G. Eggleston , T. Eifert , G. Eigen , K. Einsweiler , T. Ekelof , H. El Jarrari ,V. Ellajosyula , M. Ellert , F. Ellinghaus , A.A. Elliot , N. Ellis , J. Elmsheuser , M. Elsing ,D. Emeliyanov , A. Emerman , Y. Enari , M.B. Epland , J. Erdmann , A. Ereditato ,P.A. Erland , M. Errenst , M. Escalier , C. Escobar , O. Estrada Pastor , E. Etzion , H. Evans ,M.O. Evans , A. Ezhilov , F. Fabbri , L. Fabbri , V. Fabiani , G. Facini ,R.M. Fakhrutdinov , S. Falciano , P.J. Falke , S. Falke , J. Faltova , Y. Fang , Y. Fang ,G. Fanourakis , M. Fanti , M. Faraj , A. Farbin , A. Farilla , E.M. Farina ,T. Farooque , S.M. Farrington , P. Farthouat , F. Fassi , P. Fassnacht , D. Fassouliotis ,M. Faucci Giannelli , W.J. Fawcett , L. Fayard , O.L. Fedin , W. Fedorko , A. Fehr ,M. Feickert , L. Feligioni , A. Fell , C. Feng , M. Feng , M.J. Fenton , A.B. Fenyuk ,S.W. Ferguson , J. Ferrando , A. Ferrante , A. Ferrari , P. Ferrari , R. Ferrari ,D.E. Ferreira de Lima , A. Ferrer , D. Ferrere , C. Ferretti , F. Fiedler , A. Filipčič ,F. Filthaut , K.D. Finelli , M.C.N. Fiolhais , L. Fiorini , F. Fischer , J. Fischer ,W.C. Fisher , T. Fitschen , I. Fleck , P. Fleischmann , T. Flick , B.M. Flierl , L. Flores ,L.R. Flores Castillo , F.M. Follega , N. Fomin , J.H. Foo , G.T. Forcolin , B.C. Forland ,A. Formica , F.A. Förster , A.C. Forti , E. Fortin , M.G. Foti , D. Fournier , H. Fox ,P. Francavilla , S. Francescato , M. Franchini , S. Franchino , D. Francis , L. Franco ,L. Franconi , M. Franklin , G. Frattari , A.N. Fray , P.M. Freeman , B. Freund ,W.S. Freund , E.M. Freundlich , D.C. Frizzell , D. Froidevaux , J.A. Frost , M. Fujimoto ,C. Fukunaga , E. Fullana Torregrosa , T. Fusayasu , J. Fuster , A. Gabrielli , A. Gabrielli ,S. Gadatsch , P. Gadow , G. Gagliardi , L.G. Gagnon , G.E. Gallardo , E.J. Gallas ,B.J. Gallop , R. Gamboa Goni , K.K. Gan , S. Ganguly , J. Gao , Y. Gao , Y.S. Gao ,47.M. Garay Walls , C. García , J.E. García Navarro , J.A. García Pascual , C. Garcia-Argos ,M. Garcia-Sciveres , R.W. Gardner , N. Garelli , S. Gargiulo , C.A. Garner , V. Garonne ,S.J. Gasiorowski , P. Gaspar , A. Gaudiello , G. Gaudio , P. Gauzzi , I.L. Gavrilenko ,A. Gavrilyuk , C. Gay , G. Gaycken , E.N. Gazis , A.A. Geanta , C.M. Gee , C.N.P. Gee ,J. Geisen , M. Geisen , C. Gemme , M.H. Genest , C. Geng , S. Gentile , S. George ,T. Geralis , L.O. Gerlach , P. Gessinger-Befurt , G. Gessner , S. Ghasemi ,M. Ghasemi Bostanabad , M. Ghneimat , A. Ghosh , A. Ghosh , B. Giacobbe , S. Giagu ,N. Giangiacomi , P. Giannetti , A. Giannini , G. Giannini , S.M. Gibson , M. Gignac ,D.T. Gil , B.J. Gilbert , D. Gillberg , G. Gilles , N.E.K. Gillwald , D.M. Gingrich ,M.P. Giordani , P.F. Giraud , G. Giugliarelli , D. Giugni , F. Giuli , S. Gkaitatzis ,I. Gkialas , E.L. Gkougkousis , P. Gkountoumis , L.K. Gladilin , C. Glasman , J. Glatzer ,P.C.F. Glaysher , A. Glazov , G.R. Gledhill , I. Gnesi , M. Goblirsch-Kolb , D. Godin ,S. Goldfarb , T. Golling , D. Golubkov , A. Gomes , R. Goncalves Gama ,R. Gonçalo , G. Gonella , L. Gonella , A. Gongadze , F. Gonnella , J.L. Gonski ,S. González de la Hoz , S. Gonzalez Fernandez , R. Gonzalez Lopez , C. Gonzalez Renteria ,R. Gonzalez Suarez , S. Gonzalez-Sevilla , G.R. Gonzalvo Rodriguez , L. Goossens ,N.A. Gorasia , P.A. Gorbounov , H.A. Gordon , B. Gorini , E. Gorini , A. Gorišek ,A.T. Goshaw , M.I. Gostkin , C.A. Gottardo , M. Gouighri , A.G. Goussiou , N. Govender ,C. Goy , I. Grabowska-Bold , E.C. Graham , J. Gramling , E. Gramstad , S. Grancagnolo ,M. Grandi , V. Gratchev , P.M. Gravila , F.G. Gravili , C. Gray , H.M. Gray , C. Grefe ,K. Gregersen , I.M. Gregor , P. Grenier , K. Grevtsov , C. Grieco , N.A. Grieser , A.A. Grillo ,K. Grimm , S. Grinstein , J.-F. Grivaz , S. Groh , E. Gross , J. Grosse-Knetter , Z.J. Grout ,C. Grud , A. Grummer , J.C. Grundy , L. Guan , W. Guan , C. Gubbels , J. Guenther ,A. Guerguichon , J.G.R. Guerrero Rojas , F. Guescini , D. Guest , R. Gugel , A. Guida ,T. Guillemin , S. Guindon , J. Guo , W. Guo , Y. Guo , Z. Guo , R. Gupta , S. Gurbuz ,G. Gustavino , M. Guth , P. Gutierrez , C. Gutschow , C. Guyot , C. Gwenlan ,C.B. Gwilliam , E.S. Haaland , A. Haas , C. Haber , H.K. Hadavand , A. Hadef , M. Haleem ,J. Haley , J.J. Hall , G. Halladjian , G.D. Hallewell , K. Hamano , H. Hamdaoui ,M. Hamer , G.N. Hamity , K. Han , L. Han , L. Han , S. Han , Y.F. Han , K. Hanagaki ,M. Hance , D.M. Handl , M.D. Hank , R. Hankache , E. Hansen , J.B. Hansen , J.D. Hansen ,M.C. Hansen , P.H. Hansen , E.C. Hanson , K. Hara , T. Harenberg , S. Harkusha ,P.F. Harrison , N.M. Hartman , N.M. Hartmann , Y. Hasegawa , A. Hasib , S. Hassani ,S. Haug , R. Hauser , L.B. Havener , M. Havranek , C.M. Hawkes , R.J. Hawkings ,S. Hayashida , D. Hayden , C. Hayes , R.L. Hayes , C.P. Hays , J.M. Hays , H.S. Hayward ,S.J. Haywood , F. He , Y. He , M.P. Heath , V. Hedberg , S. Heer , A.L. Heggelund ,C. Heidegger , K.K. Heidegger , W.D. Heidorn , J. Heilman , S. Heim , T. Heim ,B. Heinemann , J.J. Heinrich , L. Heinrich , J. Hejbal , L. Helary , A. Held , S. Hellesund ,C.M. Helling , S. Hellman , C. Helsens , R.C.W. Henderson , Y. Heng , L. Henkelmann ,A.M. Henriques Correia , H. Herde , Y. Hernández Jiménez , H. Herr , M.G. Herrmann ,T. Herrmann , G. Herten , R. Hertenberger , L. Hervas , T.C. Herwig , G.G. Hesketh ,N.P. Hessey , H. Hibi , S. Higashino , E. Higón-Rodriguez , K. Hildebrand , J.C. Hill ,K.K. Hill , K.H. Hiller , S.J. Hillier , M. Hils , I. Hinchliffe , F. Hinterkeuser , M. Hirose ,S. Hirose , D. Hirschbuehl , B. Hiti , O. Hladik , J. Hobbs , N. Hod , M.C. Hodgkinson ,A. Hoecker , D. Hohn , D. Hohov , T. Holm , T.R. Holmes , M. Holzbock , L.B.A.H. Hommels ,T.M. Hong , J.C. Honig , A. Hönle , B.H. Hooberman , W.H. Hopkins , Y. Horii , P. Horn ,L.A. Horyn , S. Hou , A. Hoummada , J. Howarth , J. Hoya , M. Hrabovsky , J. Hrdinka ,J. Hrivnac , A. Hrynevich , T. Hryn’ova , P.J. Hsu , S.-C. Hsu , Q. Hu , S. Hu , Y.F. Hu ,48.P. Huang , X. Huang , Y. Huang , Y. Huang , Z. Hubacek , F. Hubaut , M. Huebner ,F. Huegging , T.B. Huffman , M. Huhtinen , R. Hulsken , R.F.H. Hunter , P. Huo ,N. Huseynov , J. Huston , J. Huth , R. Hyneman , S. Hyrych , G. Iacobucci , G. Iakovidis ,I. Ibragimov , L. Iconomidou-Fayard , P. Iengo , R. Ignazzi , O. Igonkina , R. Iguchi ,T. Iizawa , Y. Ikegami , M. Ikeno , N. Ilic , F. Iltzsche , H. Imam , G. Introzzi ,M. Iodice , K. Iordanidou , V. Ippolito , M.F. Isacson , M. Ishino , W. Islam ,C. Issever , S. Istin , J.M. Iturbe Ponce , R. Iuppa , A. Ivina , J.M. Izen , V. Izzo ,P. Jacka , P. Jackson , R.M. Jacobs , B.P. Jaeger , V. Jain , G. Jäkel , K.B. Jakobi , K. Jakobs ,T. Jakoubek , J. Jamieson , K.W. Janas , R. Jansky , M. Janus , P.A. Janus , G. Jarlskog ,A.E. Jaspan , N. Javadov , T. Javůrek , M. Javurkova , F. Jeanneau , L. Jeanty , J. Jejelava ,P. Jenni , N. Jeong , S. Jézéquel , H. Ji , J. Jia , Z. Jia , H. Jiang , Y. Jiang , Z. Jiang ,S. Jiggins , F.A. Jimenez Morales , J. Jimenez Pena , S. Jin , A. Jinaru , O. Jinnouchi ,H. Jivan , P. Johansson , K.A. Johns , C.A. Johnson , E. Jones , R.W.L. Jones , S.D. Jones ,T.J. Jones , J. Jongmanns , J. Jovicevic , X. Ju , J.J. Junggeburth , A. Juste Rozas ,A. Kaczmarska , M. Kado , H. Kagan , M. Kagan , A. Kahn , C. Kahra , T. Kaji ,E. Kajomovitz , C.W. Kalderon , A. Kaluza , A. Kamenshchikov , M. Kaneda , N.J. Kang ,S. Kang , Y. Kano , J. Kanzaki , L.S. Kaplan , D. Kar , K. Karava , M.J. Kareem ,I. Karkanias , S.N. Karpov , Z.M. Karpova , V. Kartvelishvili , A.N. Karyukhin , E. Kasimi ,A. Kastanas , C. Kato , J. Katzy , K. Kawade , K. Kawagoe , T. Kawaguchi ,T. Kawamoto , G. Kawamura , E.F. Kay , S. Kazakos , V.F. Kazanin , J.M. Keaveney ,R. Keeler , J.S. Keller , E. Kellermann , D. Kelsey , J.J. Kempster , J. Kendrick , K.E. Kennedy ,O. Kepka , S. Kersten , B.P. Kerševan , S. Ketabchi Haghighat , M. Khader , F. Khalil-Zada ,M. Khandoga , A. Khanov , A.G. Kharlamov , T. Kharlamova , E.E. Khoda ,A. Khodinov , T.J. Khoo , G. Khoriauli , E. Khramov , J. Khubua , S. Kido , M. Kiehn ,E. Kim , Y.K. Kim , N. Kimura , A. Kirchhoff , D. Kirchmeier , J. Kirk , A.E. Kiryunin ,T. Kishimoto , D.P. Kisliuk , V. Kitali , C. Kitsaki , O. Kivernyk , T. Klapdor-Kleingrothaus ,M. Klassen , C. Klein , M.H. Klein , M. Klein , U. Klein , K. Kleinknecht , P. Klimek ,A. Klimentov , T. Klingl , T. Klioutchnikova , F.F. Klitzner , P. Kluit , S. Kluth , E. Kneringer ,E.B.F.G. Knoops , A. Knue , D. Kobayashi , M. Kobel , M. Kocian , T. Kodama , P. Kodys ,D.M. Koeck , P.T. Koenig , T. Koffas , N.M. Köhler , M. Kolb , I. Koletsou , T. Komarek ,T. Kondo , K. Köneke , A.X.Y. Kong , A.C. König , T. Kono , V. Konstantinides ,N. Konstantinidis , B. Konya , R. Kopeliansky , S. Koperny , K. Korcyl , K. Kordas ,G. Koren , A. Korn , I. Korolkov , E.V. Korolkova , N. Korotkova , O. Kortner , S. Kortner ,V.V. Kostyukhin , A. Kotsokechagia , A. Kotwal , A. Koulouris ,A. Kourkoumeli-Charalampidi , C. Kourkoumelis , E. Kourlitis , V. Kouskoura , R. Kowalewski ,W. Kozanecki , A.S. Kozhin , V.A. Kramarenko , G. Kramberger , D. Krasnopevtsev ,M.W. Krasny , A. Krasznahorkay , D. Krauss , J.A. Kremer , J. Kretzschmar , P. Krieger ,F. Krieter , A. Krishnan , M. Krivos , K. Krizka , K. Kroeninger , H. Kroha , J. Kroll ,J. Kroll , K.S. Krowpman , U. Kruchonak , H. Krüger , N. Krumnack , M.C. Kruse ,J.A. Krzysiak , A. Kubota , O. Kuchinskaia , S. Kuday , J.T. Kuechler , S. Kuehn , T. Kuhl ,V. Kukhtin , Y. Kulchitsky , S. Kuleshov , Y.P. Kulinich , M. Kuna , A. Kupco , T. Kupfer ,O. Kuprash , H. Kurashige , L.L. Kurchaninov , Y.A. Kurochkin , A. Kurova , M.G. Kurth ,E.S. Kuwertz , M. Kuze , A.K. Kvam , J. Kvita , T. Kwan , F. La Ruffa , C. Lacasta ,F. Lacava , D.P.J. Lack , H. Lacker , D. Lacour , E. Ladygin , R. Lafaye , B. Laforge ,T. Lagouri , S. Lai , I.K. Lakomiec , J.E. Lambert , S. Lammers , W. Lampl , C. Lampoudis ,E. Lançon , U. Landgraf , M.P.J. Landon , M.C. Lanfermann , V.S. Lang , J.C. Lange ,R.J. Langenberg , A.J. Lankford , F. Lanni , K. Lantzsch , A. Lanza , A. Lapertosa ,49.F. Laporte , T. Lari , F. Lasagni Manghi , M. Lassnig , V. Latonova , T.S. Lau ,A. Laudrain , A. Laurier , M. Lavorgna , S.D. Lawlor , M. Lazzaroni , B. Le ,E. Le Guirriec , A. Lebedev , M. LeBlanc , T. LeCompte , F. Ledroit-Guillon , A.C.A. Lee ,C.A. Lee , G.R. Lee , L. Lee , S.C. Lee , S. Lee , B. Lefebvre , H.P. Lefebvre , M. Lefebvre ,C. Leggett , K. Lehmann , N. Lehmann , G. Lehmann Miotto , W.A. Leight , A. Leisos ,M.A.L. Leite , C.E. Leitgeb , R. Leitner , D. Lellouch , K.J.C. Leney , T. Lenz , S. Leone ,C. Leonidopoulos , A. Leopold , C. Leroy , R. Les , C.G. Lester , M. Levchenko , J. Levêque ,D. Levin , L.J. Levinson , D.J. Lewis , B. Li , B. Li , C-Q. Li , F. Li , H. Li , H. Li ,J. Li , K. Li , L. Li , M. Li , Q. Li , Q.Y. Li , S. Li , X. Li , Y. Li , Z. Li ,Z. Li , Z. Li , Z. Liang , M. Liberatore , B. Liberti , A. Liblong , K. Lie , S. Lim ,C.Y. Lin , K. Lin , R.A. Linck , R.E. Lindley , J.H. Lindon , A. Linss , A.L. Lionti , E. Lipeles ,A. Lipniacka , T.M. Liss , A. Lister , J.D. Little , B. Liu , B.L. Liu , H.B. Liu , J.B. Liu ,J.K.K. Liu , K. Liu , M. Liu , M.Y. Liu , P. Liu , X. Liu , Y. Liu , Y. Liu , Y.L. Liu ,Y.W. Liu , M. Livan , A. Lleres , J. Llorente Merino , S.L. Lloyd , C.Y. Lo ,E.M. Lobodzinska , P. Loch , S. Loffredo , T. Lohse , K. Lohwasser , M. Lokajicek ,J.D. Long , R.E. Long , I. Longarini , L. Longo , K.A. Looper , I. Lopez Paz ,A. Lopez Solis , J. Lorenz , N. Lorenzo Martinez , A.M. Lory , P.J. Lösel , A. Lösle ,X. Lou , X. Lou , A. Lounis , J. Love , P.A. Love , J.J. Lozano Bahilo , M. Lu , Y.J. Lu ,H.J. Lubatti , C. Luci , F.L. Lucio Alves , A. Lucotte , F. Luehring , I. Luise ,L. Luminari , B. Lund-Jensen , M.S. Lutz , D. Lynn , H. Lyons , R. Lysak , E. Lytken ,F. Lyu , V. Lyubushkin , T. Lyubushkina , H. Ma , L.L. Ma , Y. Ma , D.M. Mac Donell ,G. Maccarrone , A. Macchiolo , C.M. Macdonald , J.C. Macdonald , J. Machado Miguens ,D. Madaffari , R. Madar , W.F. Mader , M. Madugoda Ralalage Don , N. Madysa , J. Maeda ,T. Maeno , M. Maerker , V. Magerl , N. Magini , J. Magro , D.J. Mahon , C. Maidantchik ,T. Maier , A. Maio , K. Maj , O. Majersky , S. Majewski , Y. Makida , N. Makovec ,B. Malaescu , Pa. Malecki , V.P. Maleev , F. Malek , D. Malito , U. Mallik , D. Malon ,C. Malone , S. Maltezos , S. Malyukov , J. Mamuzic , G. Mancini , I. Mandić ,L. Manhaes de Andrade Filho , I.M. Maniatis , J. Manjarres Ramos , K.H. Mankinen , A. Mann ,A. Manousos , B. Mansoulie , I. Manthos , S. Manzoni , A. Marantis , G. Marceca ,L. Marchese , G. Marchiori , M. Marcisovsky , L. Marcoccia , C. Marcon , M. Marjanovic ,Z. Marshall , M.U.F. Martensson , S. Marti-Garcia , C.B. Martin , T.A. Martin , V.J. Martin ,B. Martin dit Latour , L. Martinelli , M. Martinez , P. Martinez Agullo ,V.I. Martinez Outschoorn , S. Martin-Haugh , V.S. Martoiu , A.C. Martyniuk , A. Marzin ,S.R. Maschek , L. Masetti , T. Mashimo , R. Mashinistov , J. Masik , A.L. Maslennikov ,L. Massa , P. Massarotti , P. Mastrandrea , A. Mastroberardino , T. Masubuchi ,D. Matakias , A. Matic , N. Matsuzawa , P. Mättig , J. Maurer , B. Maček ,D.A. Maximov , R. Mazini , I. Maznas , S.M. Mazza , J.P. Mc Gowan , S.P. Mc Kee ,T.G. McCarthy , W.P. McCormack , E.F. McDonald , A.E. Mcdougall , J.A. Mcfayden ,G. Mchedlidze , M.A. McKay , K.D. McLean , S.J. McMahon , P.C. McNamara ,C.J. McNicol , R.A. McPherson , J.E. Mdhluli , Z.A. Meadows , S. Meehan , T. Megy ,S. Mehlhase , A. Mehta , B. Meirose , D. Melini , B.R. Mellado Garcia , J.D. Mellenthin ,M. Melo , F. Meloni , A. Melzer , E.D. Mendes Gouveia , A.M. Mendes Jacques Da Costa ,L. Meng , X.T. Meng , S. Menke , E. Meoni , S. Mergelmeyer , S.A.M. Merkt ,C. Merlassino , P. Mermod , L. Merola , C. Meroni , G. Merz , O. Meshkov ,J.K.R. Meshreki , J. Metcalfe , A.S. Mete , C. Meyer , J-P. Meyer , M. Michetti , R.P. Middleton ,L. Mijović , G. Mikenberg , M. Mikestikova , M. Mikuž , H. Mildner , A. Milic , C.D. Milke ,D.W. Miller , A. Milov , D.A. Milstead , R.A. Mina , A.A. Minaenko , I.A. Minashvili ,50.I. Mincer , B. Mindur , M. Mineev , Y. Minegishi , Y. Mino , L.M. Mir , M. Mironova ,K.P. Mistry , T. Mitani , J. Mitrevski , V.A. Mitsou , M. Mittal , O. Miu , A. Miucci ,P.S. Miyagawa , A. Mizukami , J.U. Mjörnmark , T. Mkrtchyan , M. Mlynarikova , T. Moa ,S. Mobius , K. Mochizuki , P. Mogg , S. Mohapatra , R. Moles-Valls , K. Mönig , E. Monnier ,A. Montalbano , J. Montejo Berlingen , M. Montella , M.M. Monti , F. Monticelli , S. Monzani ,N. Morange , A.L. Moreira De Carvalho , D. Moreno , M. Moreno Llácer ,C. Moreno Martinez , P. Morettini , M. Morgenstern , S. Morgenstern , D. Mori , M. Morii ,M. Morinaga , V. Morisbak , A.K. Morley , G. Mornacchi , A.P. Morris , L. Morvaj ,P. Moschovakos , B. Moser , M. Mosidze , T. Moskalets , P. Moskvitina , J. Moss ,E.J.W. Moyse , S. Muanza , J. Mueller , R.S.P. Mueller , D. Muenstermann , G.A. Mullier ,D.P. Mungo , J.L. Munoz Martinez , F.J. Munoz Sanchez , P. Murin , W.J. Murray ,A. Murrone , J.M. Muse , M. Muškinja , C. Mwewa , A.G. Myagkov , A.A. Myers ,G. Myers , J. Myers , M. Myska , B.P. Nachman , O. Nackenhorst , A.Nag Nag , K. Nagai ,K. Nagano , Y. Nagasaka , J.L. Nagle , E. Nagy , A.M. Nairz , Y. Nakahama , K. Nakamura ,T. Nakamura , H. Nanjo , F. Napolitano , R.F. Naranjo Garcia , R. Narayan , I. Naryshkin ,M. Naseri , T. Naumann , G. Navarro , J. Navarro-Gonzalez , P.Y. Nechaeva , F. Nechansky ,T.J. Neep , A. Negri , M. Negrini , C. Nellist , C. Nelson , M.E. Nelson , S. Nemecek ,M. Nessi , M.S. Neubauer , F. Neuhaus , M. Neumann , R. Newhouse , P.R. Newman ,C.W. Ng , Y.S. Ng , Y.W.Y. Ng , B. Ngair , H.D.N. Nguyen , T. Nguyen Manh , E. Nibigira ,R.B. Nickerson , R. Nicolaidou , D.S. Nielsen , J. Nielsen , M. Niemeyer , N. Nikiforou ,V. Nikolaenko , I. Nikolic-Audit , K. Nikolopoulos , P. Nilsson , H.R. Nindhito , A. Nisati ,N. Nishu , R. Nisius , I. Nitsche , T. Nitta , T. Nobe , D.L. Noel , Y. Noguchi , I. Nomidis ,M.A. Nomura , M. Nordberg , J. Novak , T. Novak , O. Novgorodova , R. Novotny , L. Nozka ,K. Ntekas , E. Nurse , F.G. Oakham , H. Oberlack , J. Ocariz , A. Ochi , I. Ochoa ,J.P. Ochoa-Ricoux , K. O’Connor , S. Oda , S. Odaka , S. Oerdek , A. Ogrodnik , A. Oh ,C.C. Ohm , H. Oide , M.L. Ojeda , H. Okawa , Y. Okazaki , M.W. O’Keefe , Y. Okumura ,A. Olariu , L.F. Oleiro Seabra , S.A. Olivares Pino , D. Oliveira Damazio , J.L. Oliver ,M.J.R. Olsson , A. Olszewski , J. Olszowska , Ö.O. Öncel , D.C. O’Neil , A.P. O’neill ,A. Onofre , P.U.E. Onyisi , H. Oppen , R.G. Oreamuno Madriz , M.J. Oreglia ,G.E. Orellana , D. Orestano , N. Orlando , R.S. Orr , V. O’Shea , R. Ospanov ,G. Otero y Garzon , H. Otono , P.S. Ott , G.J. Ottino , M. Ouchrif , J. Ouellette ,F. Ould-Saada , A. Ouraou , Q. Ouyang , M. Owen , R.E. Owen , V.E. Ozcan , N. Ozturk ,J. Pacalt , H.A. Pacey , K. Pachal , A. Pacheco Pages , C. Padilla Aranda , S. Pagan Griso ,G. Palacino , S. Palazzo , S. Palestini , M. Palka , P. Palni , C.E. Pandini ,J.G. Panduro Vazquez , P. Pani , G. Panizzo , L. Paolozzi , C. Papadatos , K. Papageorgiou ,S. Parajuli , A. Paramonov , C. Paraskevopoulos , D. Paredes Hernandez , S.R. Paredes Saenz ,B. Parida , T.H. Park , A.J. Parker , M.A. Parker , F. Parodi , E.W. Parrish , J.A. Parsons ,U. Parzefall , L. Pascual Dominguez , V.R. Pascuzzi , J.M.P. Pasner , F. Pasquali ,E. Pasqualucci , S. Passaggio , F. Pastore , P. Pasuwan , S. Pataraia , J.R. Pater ,A. Pathak , J. Patton , T. Pauly , J. Pearkes , B. Pearson , M. Pedersen , L. Pedraza Diaz ,R. Pedro , T. Peiffer , S.V. Peleganchuk , O. Penc , H. Peng , B.S. Peralva ,M.M. Perego , A.P. Pereira Peixoto , L. Pereira Sanchez , D.V. Perepelitsa , E. Perez Codina ,F. Peri , L. Perini , H. Pernegger , S. Perrella , A. Perrevoort , K. Peters , R.F.Y. Peters ,B.A. Petersen , T.C. Petersen , E. Petit , V. Petousis , A. Petridis , C. Petridou , P. Petroff ,F. Petrucci , M. Pettee , N.E. Pettersson , K. Petukhova , A. Peyaud , R. Pezoa ,L. Pezzotti , T. Pham , P.W. Phillips , M.W. Phipps , G. Piacquadio , E. Pianori ,A. Picazio , R.H. Pickles , R. Piegaia , D. Pietreanu , J.E. Pilcher , A.D. Pilkington ,51. Pinamonti , J.L. Pinfold , C. Pitman Donaldson , M. Pitt , L. Pizzimento , A. Pizzini ,M.-A. Pleier , V. Plesanovs , V. Pleskot , E. Plotnikova , P. Podberezko , R. Poettgen ,R. Poggi , L. Poggioli , I. Pogrebnyak , D. Pohl , I. Pokharel , G. Polesello , A. Poley ,A. Policicchio , R. Polifka , A. Polini , C.S. Pollard , V. Polychronakos , D. Ponomarenko ,L. Pontecorvo , S. Popa , G.A. Popeneciu , L. Portales , D.M. Portillo Quintero , S. Pospisil ,K. Potamianos , I.N. Potrap , C.J. Potter , H. Potti , T. Poulsen , J. Poveda , T.D. Powell ,G. Pownall , M.E. Pozo Astigarraga , A. Prades Ibanez , P. Pralavorio , M.M. Prapa , S. Prell ,D. Price , M. Primavera , M.L. Proffitt , N. Proklova , K. Prokofiev , F. Prokoshin ,S. Protopopescu , J. Proudfoot , M. Przybycien , D. Pudzha , A. Puri , P. Puzo ,D. Pyatiizbyantseva , J. Qian , Y. Qin , A. Quadt , M. Queitsch-Maitland , M. Racko ,F. Ragusa , G. Rahal , J.A. Raine , S. Rajagopalan , A. Ramirez Morales , K. Ran ,D.M. Rauch , F. Rauscher , S. Rave , B. Ravina , I. Ravinovich , J.H. Rawling , M. Raymond ,A.L. Read , N.P. Readioff , M. Reale , D.M. Rebuzzi , G. Redlinger , K. Reeves ,D. Reikher , A. Reiss , A. Rej , C. Rembser , A. Renardi , M. Renda , M.B. Rendel ,A.G. Rennie , S. Resconi , E.D. Resseguie , S. Rettie , B. Reynolds , E. Reynolds ,O.L. Rezanova , P. Reznicek , E. Ricci , R. Richter , S. Richter , E. Richter-Was ,M. Ridel , P. Rieck , O. Rifki , M. Rijssenbeek , A. Rimoldi , M. Rimoldi , L. Rinaldi ,T.T. Rinn , G. Ripellino , I. Riu , P. Rivadeneira , J.C. Rivera Vergara , F. Rizatdinova ,E. Rizvi , C. Rizzi , S.H. Robertson , M. Robin , D. Robinson , C.M. Robles Gajardo ,M. Robles Manzano , A. Robson , A. Rocchi , E. Rocco , C. Roda ,S. Rodriguez Bosca , A. Rodriguez Rodriguez , A.M. Rodríguez Vera , S. Roe , J. Roggel ,O. Røhne , R. Röhrig , R.A. Rojas , B. Roland , C.P.A. Roland , J. Roloff , A. Romaniouk ,M. Romano , N. Rompotis , M. Ronzani , L. Roos , S. Rosati , G. Rosin , B.J. Rosser ,E. Rossi , E. Rossi , E. Rossi , L.P. Rossi , L. Rossini , R. Rosten , M. Rotaru ,B. Rottler , D. Rousseau , G. Rovelli , A. Roy , D. Roy , A. Rozanov , Y. Rozen ,X. Ruan , T.A. Ruggeri , F. Rühr , A. Ruiz-Martinez , A. Rummler , Z. Rurikova ,N.A. Rusakovich , H.L. Russell , L. Rustige , J.P. Rutherfoord , E.M. Rüttinger , M. Rybar ,G. Rybkin , E.B. Rye , A. Ryzhov , J.A. Sabater Iglesias , P. Sabatini , L. Sabetta ,S. Sacerdoti , H.F-W. Sadrozinski , R. Sadykov , F. Safai Tehrani , B. Safarzadeh Samani ,M. Safdari , P. Saha , S. Saha , M. Sahinsoy , A. Sahu , M. Saimpert , M. Saito , T. Saito ,H. Sakamoto , D. Salamani , G. Salamanna , A. Salnikov , J. Salt , A. Salvador Salas ,D. Salvatore , F. Salvatore , A. Salvucci , A. Salzburger , J. Samarati , D. Sammel ,D. Sampsonidis , D. Sampsonidou , J. Sánchez , A. Sanchez Pineda , H. Sandaker ,C.O. Sander , I.G. Sanderswood , M. Sandhoff , C. Sandoval , D.P.C. Sankey , M. Sannino ,Y. Sano , A. Sansoni , C. Santoni , H. Santos , S.N. Santpur , A. Santra , K.A. Saoucha ,A. Sapronov , J.G. Saraiva , O. Sasaki , K. Sato , F. Sauerburger , E. Sauvan , P. Savard ,R. Sawada , C. Sawyer , L. Sawyer , I. Sayago Galvan , C. Sbarra , A. Sbrizzi ,T. Scanlon , J. Schaarschmidt , P. Schacht , D. Schaefer , L. Schaefer , S. Schaepe ,U. Schäfer , A.C. Schaffer , D. Schaile , R.D. Schamberger , E. Schanet , C. Scharf ,N. Scharmberg , V.A. Schegelsky , D. Scheirich , F. Schenck , M. Schernau , C. Schiavi ,L.K. Schildgen , Z.M. Schillaci , E.J. Schioppa , M. Schioppa , K.E. Schleicher ,S. Schlenker , K.R. Schmidt-Sommerfeld , K. Schmieden , C. Schmitt , S. Schmitt ,L. Schoeffel , A. Schoening , P.G. Scholer , E. Schopf , M. Schott , J.F.P. Schouwenberg ,J. Schovancova , S. Schramm , F. Schroeder , A. Schulte , H-C. Schultz-Coulon ,M. Schumacher , B.A. Schumm , Ph. Schune , A. Schwartzman , T.A. Schwarz ,Ph. Schwemling , R. Schwienhorst , A. Sciandra , G. Sciolla , M. Scornajenghi , F. Scuri ,F. Scutti , L.M. Scyboz , C.D. Sebastiani , P. Seema , S.C. Seidel , A. Seiden , B.D. Seidlitz ,52. Seiss , C. Seitz , J.M. Seixas , G. Sekhniaidze , S.J. Sekula , N. Semprini-Cesari , S. Sen ,C. Serfon , L. Serin , L. Serkin , M. Sessa , H. Severini , S. Sevova , F. Sforza ,A. Sfyrla , E. Shabalina , J.D. Shahinian , N.W. Shaikh , D. Shaked Renous , L.Y. Shan ,M. Shapiro , A. Sharma , A.S. Sharma , P.B. Shatalov , K. Shaw , S.M. Shaw , M. Shehade ,Y. Shen , A.D. Sherman , P. Sherwood , L. Shi , C.O. Shimmin , Y. Shimogama ,M. Shimojima , J.D. Shinner , I.P.J. Shipsey , S. Shirabe , M. Shiyakova , J. Shlomi ,A. Shmeleva , M.J. Shochet , J. Shojaii , D.R. Shope , S. Shrestha , E.M. Shrif , M.J. Shroff ,E. Shulga , P. Sicho , A.M. Sickles , E. Sideras Haddad , O. Sidiropoulou , A. Sidoti ,F. Siegert , Dj. Sijacki , M.Jr. Silva , M.V. Silva Oliveira , S.B. Silverstein , S. Simion ,R. Simoniello , C.J. Simpson-allsop , S. Simsek , P. Sinervo , V. Sinetckii , S. Singh ,M. Sioli , I. Siral , S.Yu. Sivoklokov , J. Sjölin , A. Skaf , E. Skorda , P. Skubic ,M. Slawinska , K. Sliwa , R. Slovak , V. Smakhtin , B.H. Smart , J. Smiesko , N. Smirnov ,S.Yu. Smirnov , Y. Smirnov , L.N. Smirnova , O. Smirnova , E.A. Smith , H.A. Smith ,M. Smizanska , K. Smolek , A. Smykiewicz , A.A. Snesarev , H.L. Snoek , I.M. Snyder ,S. Snyder , R. Sobie , A. Soffer , A. Søgaard , F. Sohns , C.A. Solans Sanchez ,E.Yu. Soldatov , U. Soldevila , A.A. Solodkov , A. Soloshenko , O.V. Solovyanov ,V. Solovyev , P. Sommer , H. Son , A. Sonay , W. Song , W.Y. Song , A. Sopczak ,A.L. Sopio , F. Sopkova , S. Sottocornola , R. Soualah , A.M. Soukharev , D. South ,S. Spagnolo , M. Spalla , M. Spangenberg , F. Spanò , D. Sperlich , T.M. Spieker ,G. Spigo , M. Spina , D.P. Spiteri , M. Spousta , A. Stabile , B.L. Stamas , R. Stamen ,M. Stamenkovic , A. Stampekis , E. Stanecka , B. Stanislaus , M.M. Stanitzki , M. Stankaityte ,B. Stapf , E.A. Starchenko , G.H. Stark , J. Stark , P. Staroba , P. Starovoitov , S. Stärz ,R. Staszewski , G. Stavropoulos , M. Stegler , P. Steinberg , A.L. Steinhebel , B. Stelzer ,H.J. Stelzer , O. Stelzer-Chilton , H. Stenzel , T.J. Stevenson , G.A. Stewart , M.C. Stockton ,G. Stoicea , M. Stolarski , S. Stonjek , A. Straessner , J. Strandberg , S. Strandberg ,M. Strauss , T. Strebler , P. Strizenec , R. Ströhmer , D.M. Strom , R. Stroynowski ,A. Strubig , S.A. Stucci , B. Stugu , J. Stupak , N.A. Styles , D. Su , W. Su , X. Su ,V.V. Sulin , M.J. Sullivan , D.M.S. Sultan , S. Sultansoy , T. Sumida , S. Sun , X. Sun ,C.J.E. Suster , M.R. Sutton , S. Suzuki , M. Svatos , M. Swiatlowski , S.P. Swift , T. Swirski ,A. Sydorenko , I. Sykora , M. Sykora , T. Sykora , D. Ta , K. Tackmann , J. Taenzer ,A. Taffard , R. Tafirout , E. Tagiev , R. Takashima , K. Takeda , T. Takeshita , E.P. Takeva ,Y. Takubo , M. Talby , A.A. Talyshev , K.C. Tam , N.M. Tamir , J. Tanaka , R. Tanaka ,S. Tapia Araya , S. Tapprogge , A. Tarek Abouelfadl Mohamed , S. Tarem , K. Tariq ,G. Tarna , G.F. Tartarelli , P. Tas , M. Tasevsky , E. Tassi , A. Tavares Delgado ,Y. Tayalati , A.J. Taylor , G.N. Taylor , W. Taylor , H. Teagle , A.S. Tee ,R. Teixeira De Lima , P. Teixeira-Dias , H. Ten Kate , J.J. Teoh , K. Terashi , J. Terron ,S. Terzo , M. Testa , R.J. Teuscher , S.J. Thais , N. Themistokleous , T. Theveneaux-Pelzer ,F. Thiele , D.W. Thomas , J.O. Thomas , J.P. Thomas , E.A. Thompson , P.D. Thompson ,E. Thomson , E.J. Thorpe , R.E. Ticse Torres , V.O. Tikhomirov , Yu.A. Tikhonov ,S. Timoshenko , P. Tipton , S. Tisserant , K. Todome , S. Todorova-Nova , S. Todt ,J. Tojo , S. Tokár , K. Tokushuku , E. Tolley , R. Tombs , K.G. Tomiwa , M. Tomoto ,L. Tompkins , P. Tornambe , E. Torrence , H. Torres , E. Torró Pastor , C. Tosciri ,J. Toth , D.R. Tovey , A. Traeet , C.J. Treado , T. Trefzger , F. Tresoldi , A. Tricoli ,I.M. Trigger , S. Trincaz-Duvoid , D.A. Trischuk , W. Trischuk , B. Trocmé , A. Trofymov ,C. Troncon , F. Trovato , L. Truong , M. Trzebinski , A. Trzupek , F. Tsai , J.C-L. Tseng ,P.V. Tsiareshka , A. Tsirigotis , V. Tsiskaridze , E.G. Tskhadadze , M. Tsopoulou ,I.I. Tsukerman , V. Tsulaia , S. Tsuno , D. Tsybychev , Y. Tu , A. Tudorache , V. Tudorache ,53.T. Tulbure , A.N. Tuna , S. Turchikhin , D. Turgeman , I. Turk Cakir , R.J. Turner , R. Turra ,P.M. Tuts , S. Tzamarias , E. Tzovara , K. Uchida , F. Ukegawa , G. Unal , M. Unal ,A. Undrus , G. Unel , F.C. Ungaro , Y. Unno , K. Uno , J. Urban , P. Urquijo , G. Usai ,Z. Uysal , V. Vacek , B. Vachon , K.O.H. Vadla , T. Vafeiadis , A. Vaidya , C. Valderanis ,E. Valdes Santurio , M. Valente , S. Valentinetti , A. Valero , L. Valéry , R.A. Vallance ,A. Vallier , J.A. Valls Ferrer , T.R. Van Daalen , P. Van Gemmeren , S. Van Stroud , I. Van Vulpen ,M. Vanadia , W. Vandelli , M. Vandenbroucke , E.R. Vandewall , A. Vaniachine ,D. Vannicola , R. Vari , E.W. Varnes , C. Varni , T. Varol , D. Varouchas , K.E. Varvell ,M.E. Vasile , G.A. Vasquez , F. Vazeille , D. Vazquez Furelos , T. Vazquez Schroeder , J. Veatch ,V. Vecchio , M.J. Veen , L.M. Veloce , F. Veloso , S. Veneziano , A. Ventura ,A. Verbytskyi , V. Vercesi , M. Verducci , C.M. Vergel Infante , C. Vergis , W. Verkerke ,A.T. Vermeulen , J.C. Vermeulen , C. Vernieri , P.J. Verschuuren , M.C. Vetterli ,N. Viaux Maira , T. Vickey , O.E. Vickey Boeriu , G.H.A. Viehhauser , L. Vigani ,M. Villa , M. Villaplana Perez , E.M. Villhauer , E. Vilucchi , M.G. Vincter , G.S. Virdee ,A. Vishwakarma , C. Vittori , I. Vivarelli , M. Vogel , P. Vokac , S.E. von Buddenbrock ,E. Von Toerne , V. Vorobel , K. Vorobev , M. Vos , J.H. Vossebeld , M. Vozak , N. Vranjes ,M. Vranjes Milosavljevic , V. Vrba , M. Vreeswijk , N.K. Vu , R. Vuillermet , I. Vukotic ,S. Wada , P. Wagner , W. Wagner , J. Wagner-Kuhr , S. Wahdan , H. Wahlberg , R. Wakasa ,V.M. Walbrecht , J. Walder , R. Walker , S.D. Walker , W. Walkowiak , V. Wallangen ,A.M. Wang , A.Z. Wang , C. Wang , C. Wang , F. Wang , H. Wang , H. Wang , J. Wang ,P. Wang , Q. Wang , R.-J. Wang , R. Wang , R. Wang , S.M. Wang , W.T. Wang , W. Wang ,W.X. Wang , Y. Wang , Z. Wang , C. Wanotayaroj , A. Warburton , C.P. Ward , R.J. Ward ,N. Warrack , A.T. Watson , M.F. Watson , G. Watts , B.M. Waugh , A.F. Webb , C. Weber ,M.S. Weber , S.A. Weber , S.M. Weber , A.R. Weidberg , J. Weingarten , M. Weirich ,C. Weiser , P.S. Wells , T. Wenaus , B. Wendland , T. Wengler , S. Wenig , N. Wermes ,M. Wessels , T.D. Weston , K. Whalen , A.M. Wharton , A.S. White , A. White , M.J. White ,D. Whiteson , B.W. Whitmore , W. Wiedenmann , C. Wiel , M. Wielers , N. Wieseotte ,C. Wiglesworth , L.A.M. Wiik-Fuchs , H.G. Wilkens , L.J. Wilkins , H.H. Williams ,S. Williams , S. Willocq , P.J. Windischhofer , I. Wingerter-Seez , E. Winkels , F. Winklmeier ,B.T. Winter , M. Wittgen , M. Wobisch , A. Wolf , R. Wölker , J. Wollrath , M.W. Wolter ,H. Wolters , V.W.S. Wong , N.L. Woods , S.D. Worm , B.K. Wosiek , K.W. Woźniak ,K. Wraight , S.L. Wu , X. Wu , Y. Wu , J. Wuerzinger , T.R. Wyatt , B.M. Wynne , S. Xella ,L. Xia , J. Xiang , X. Xiao , X. Xie , I. Xiotidis , D. Xu , H. Xu , H. Xu , L. Xu ,T. Xu , W. Xu , Y. Xu , Z. Xu , Z. Xu , B. Yabsley , S. Yacoob , D.P. Yallup ,N. Yamaguchi , Y. Yamaguchi , A. Yamamoto , M. Yamatani , T. Yamazaki , Y. Yamazaki ,J. Yan , Z. Yan , H.J. Yang , H.T. Yang , S. Yang , T. Yang , X. Yang , Y. Yang ,Z. Yang , W-M. Yao , Y.C. Yap , E. Yatsenko , H. Ye , J. Ye , S. Ye , I. Yeletskikh ,M.R. Yexley , E. Yigitbasi , P. Yin , K. Yorita , K. Yoshihara , C.J.S. Young , C. Young ,J. Yu , R. Yuan , X. Yue , M. Zaazoua , B. Zabinski , G. Zacharis , E. Zaffaroni ,J. Zahreddine , A.M. Zaitsev , T. Zakareishvili , N. Zakharchuk , S. Zambito , D. Zanzi ,S.V. Zeißner , C. Zeitnitz , G. Zemaityte , J.C. Zeng , O. Zenin , T. Ženiš , D. Zerwas ,M. Zgubič , B. Zhang , D.F. Zhang , G. Zhang , J. Zhang , Kaili. Zhang , L. Zhang ,L. Zhang , M. Zhang , R. Zhang , S. Zhang , X. Zhang , X. Zhang , Y. Zhang ,Z. Zhang , Z. Zhang , P. Zhao , Z. Zhao , A. Zhemchugov , Z. Zheng , D. Zhong , B. Zhou ,C. Zhou , H. Zhou , M.S. Zhou , M. Zhou , N. Zhou , Y. Zhou , C.G. Zhu , C. Zhu ,H.L. Zhu , H. Zhu , J. Zhu , Y. Zhu , X. Zhuang , K. Zhukov , V. Zhulanov ,D. Zieminska , N.I. Zimine , S. Zimmermann , Z. Zinonos , M. Ziolkowski , L. Živković ,54. Zobernig , A. Zoccoli , K. Zoch , T.G. Zorbas , R. Zou , L. Zwalinski . Department of Physics, University of Adelaide, Adelaide; Australia. Physics Department, SUNY Albany, Albany NY; United States of America. Department of Physics, University of Alberta, Edmonton AB; Canada. ( a ) Department of Physics, Ankara University, Ankara; ( b ) Istanbul Aydin University, Application andResearch Center for Advanced Studies, Istanbul; ( c ) Division of Physics, TOBB University of Economicsand Technology, Ankara; Turkey. LAPP, Université Grenoble Alpes, Université Savoie Mont Blanc, CNRS/IN2P3, Annecy; France. High Energy Physics Division, Argonne National Laboratory, Argonne IL; United States of America. Department of Physics, University of Arizona, Tucson AZ; United States of America. Department of Physics, University of Texas at Arlington, Arlington TX; United States of America. Physics Department, National and Kapodistrian University of Athens, Athens; Greece. Physics Department, National Technical University of Athens, Zografou; Greece. Department of Physics, University of Texas at Austin, Austin TX; United States of America. ( a ) Bahcesehir University, Faculty of Engineering and Natural Sciences, Istanbul; ( b ) Istanbul BilgiUniversity, Faculty of Engineering and Natural Sciences, Istanbul; ( c ) Department of Physics, BogaziciUniversity, Istanbul; ( d ) Department of Physics Engineering, Gaziantep University, Gaziantep; Turkey. Institute of Physics, Azerbaijan Academy of Sciences, Baku; Azerbaijan. Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology, Barcelona;Spain. ( a ) Institute of High Energy Physics, Chinese Academy of Sciences, Beijing; ( b ) Physics Department,Tsinghua University, Beijing; ( c ) Department of Physics, Nanjing University, Nanjing; ( d ) University ofChinese Academy of Science (UCAS), Beijing; China. Institute of Physics, University of Belgrade, Belgrade; Serbia. Department for Physics and Technology, University of Bergen, Bergen; Norway. Physics Division, Lawrence Berkeley National Laboratory and University of California, Berkeley CA;United States of America. Institut für Physik, Humboldt Universität zu Berlin, Berlin; Germany. Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University ofBern, Bern; Switzerland. School of Physics and Astronomy, University of Birmingham, Birmingham; United Kingdom. ( a ) Facultad de Ciencias y Centro de Investigaciónes, Universidad Antonio Nariño,Bogotá; ( b ) Departamento de Física, Universidad Nacional de Colombia, Bogotá, Colombia; Colombia. ( a ) INFN Bologna and Universita’ di Bologna, Dipartimento di Fisica; ( b ) INFN Sezione di Bologna; Italy. Physikalisches Institut, Universität Bonn, Bonn; Germany. Department of Physics, Boston University, Boston MA; United States of America. Department of Physics, Brandeis University, Waltham MA; United States of America. ( a ) Transilvania University of Brasov, Brasov; ( b ) Horia Hulubei National Institute of Physics and NuclearEngineering, Bucharest; ( c ) Department of Physics, Alexandru Ioan Cuza University of Iasi, Iasi; ( d ) NationalInstitute for Research and Development of Isotopic and Molecular Technologies, Physics Department,Cluj-Napoca; ( e ) University Politehnica Bucharest, Bucharest; ( f ) West University in Timisoara, Timisoara;Romania. ( a ) Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava; ( b ) Department ofSubnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Kosice; SlovakRepublic. Physics Department, Brookhaven National Laboratory, Upton NY; United States of America.55 Departamento de Física, Universidad de Buenos Aires, Buenos Aires; Argentina. California State University, CA; United States of America. Cavendish Laboratory, University of Cambridge, Cambridge; United Kingdom. ( a ) Department of Physics, University of Cape Town, Cape Town; ( b ) iThemba Labs, WesternCape; ( c ) Department of Mechanical Engineering Science, University of Johannesburg,Johannesburg; ( d ) University of South Africa, Department of Physics, Pretoria; ( e ) School of Physics,University of the Witwatersrand, Johannesburg; South Africa. Department of Physics, Carleton University, Ottawa ON; Canada. ( a ) Faculté des Sciences Ain Chock, Réseau Universitaire de Physique des Hautes Energies - UniversitéHassan II, Casablanca; ( b ) Faculté des Sciences, Université Ibn-Tofail, Kénitra; ( c ) Faculté des SciencesSemlalia, Université Cadi Ayyad, LPHEA-Marrakech; ( d ) Faculté des Sciences, Université MohamedPremier and LPTPM, Oujda; ( e ) Faculté des sciences, Université Mohammed V, Rabat; Morocco. CERN, Geneva; Switzerland. Enrico Fermi Institute, University of Chicago, Chicago IL; United States of America. LPC, Université Clermont Auvergne, CNRS/IN2P3, Clermont-Ferrand; France. Nevis Laboratory, Columbia University, Irvington NY; United States of America. Niels Bohr Institute, University of Copenhagen, Copenhagen; Denmark. ( a ) Dipartimento di Fisica, Università della Calabria, Rende; ( b ) INFN Gruppo Collegato di Cosenza,Laboratori Nazionali di Frascati; Italy. Physics Department, Southern Methodist University, Dallas TX; United States of America. Physics Department, University of Texas at Dallas, Richardson TX; United States of America. National Centre for Scientific Research "Demokritos", Agia Paraskevi; Greece. ( a ) Department of Physics, Stockholm University; ( b ) Oskar Klein Centre, Stockholm; Sweden. Deutsches Elektronen-Synchrotron DESY, Hamburg and Zeuthen; Germany. Lehrstuhl für Experimentelle Physik IV, Technische Universität Dortmund, Dortmund; Germany. Institut für Kern- und Teilchenphysik, Technische Universität Dresden, Dresden; Germany. Department of Physics, Duke University, Durham NC; United States of America. SUPA - School of Physics and Astronomy, University of Edinburgh, Edinburgh; United Kingdom. INFN e Laboratori Nazionali di Frascati, Frascati; Italy. Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg; Germany. II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen; Germany. Département de Physique Nucléaire et Corpusculaire, Université de Genève, Genève; Switzerland. ( a ) Dipartimento di Fisica, Università di Genova, Genova; ( b ) INFN Sezione di Genova; Italy. II. Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen; Germany. SUPA - School of Physics and Astronomy, University of Glasgow, Glasgow; United Kingdom. LPSC, Université Grenoble Alpes, CNRS/IN2P3, Grenoble INP, Grenoble; France. Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge MA; United States ofAmerica. ( a ) Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics,University of Science and Technology of China, Hefei; ( b ) Institute of Frontier and Interdisciplinary Scienceand Key Laboratory of Particle Physics and Particle Irradiation (MOE), Shandong University,Qingdao; ( c ) School of Physics and Astronomy, Shanghai Jiao Tong University, KLPPAC-MoE, SKLPPC,Shanghai; ( d ) Tsung-Dao Lee Institute, Shanghai; China. ( a ) Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg; ( b ) PhysikalischesInstitut, Ruprecht-Karls-Universität Heidelberg, Heidelberg; Germany. Faculty of Applied Information Science, Hiroshima Institute of Technology, Hiroshima; Japan. ( a ) Department of Physics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong; ( b ) Department of56hysics, University of Hong Kong, Hong Kong; ( c ) Department of Physics and Institute for Advanced Study,Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong; China. Department of Physics, National Tsing Hua University, Hsinchu; Taiwan. IJCLab, Université Paris-Saclay, CNRS/IN2P3, 91405, Orsay; France. Department of Physics, Indiana University, Bloomington IN; United States of America. ( a ) INFN Gruppo Collegato di Udine, Sezione di Trieste, Udine; ( b ) ICTP, Trieste; ( c ) DipartimentoPolitecnico di Ingegneria e Architettura, Università di Udine, Udine; Italy. ( a ) INFN Sezione di Lecce; ( b ) Dipartimento di Matematica e Fisica, Università del Salento, Lecce; Italy. ( a ) INFN Sezione di Milano; ( b ) Dipartimento di Fisica, Università di Milano, Milano; Italy. ( a ) INFN Sezione di Napoli; ( b ) Dipartimento di Fisica, Università di Napoli, Napoli; Italy. ( a ) INFN Sezione di Pavia; ( b ) Dipartimento di Fisica, Università di Pavia, Pavia; Italy. ( a ) INFN Sezione di Pisa; ( b ) Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa; Italy. ( a ) INFN Sezione di Roma; ( b ) Dipartimento di Fisica, Sapienza Università di Roma, Roma; Italy. ( a ) INFN Sezione di Roma Tor Vergata; ( b ) Dipartimento di Fisica, Università di Roma Tor Vergata, Roma;Italy. ( a ) INFN Sezione di Roma Tre; ( b ) Dipartimento di Matematica e Fisica, Università Roma Tre, Roma; Italy. ( a ) INFN-TIFPA; ( b ) Università degli Studi di Trento, Trento; Italy. Institut für Astro- und Teilchenphysik, Leopold-Franzens-Universität, Innsbruck; Austria. University of Iowa, Iowa City IA; United States of America. Department of Physics and Astronomy, Iowa State University, Ames IA; United States of America. Joint Institute for Nuclear Research, Dubna; Russia. ( a ) Departamento de Engenharia Elétrica, Universidade Federal de Juiz de Fora (UFJF), Juiz deFora; ( b ) Universidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro; ( c ) Universidade Federal deSão João del Rei (UFSJ), São João del Rei; ( d ) Instituto de Física, Universidade de São Paulo, São Paulo;Brazil. KEK, High Energy Accelerator Research Organization, Tsukuba; Japan. Graduate School of Science, Kobe University, Kobe; Japan. ( a ) AGH University of Science and Technology, Faculty of Physics and Applied Computer Science,Krakow; ( b ) Marian Smoluchowski Institute of Physics, Jagiellonian University, Krakow; Poland. Institute of Nuclear Physics Polish Academy of Sciences, Krakow; Poland. Faculty of Science, Kyoto University, Kyoto; Japan. Kyoto University of Education, Kyoto; Japan. Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, Fukuoka ;Japan. Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata; Argentina. Physics Department, Lancaster University, Lancaster; United Kingdom. Oliver Lodge Laboratory, University of Liverpool, Liverpool; United Kingdom. Department of Experimental Particle Physics, Jožef Stefan Institute and Department of Physics,University of Ljubljana, Ljubljana; Slovenia. School of Physics and Astronomy, Queen Mary University of London, London; United Kingdom. Department of Physics, Royal Holloway University of London, Egham; United Kingdom. Department of Physics and Astronomy, University College London, London; United Kingdom. Louisiana Tech University, Ruston LA; United States of America. Fysiska institutionen, Lunds universitet, Lund; Sweden. Centre de Calcul de l’Institut National de Physique Nucléaire et de Physique des Particules (IN2P3),Villeurbanne; France. Departamento de Física Teorica C-15 and CIAFF, Universidad Autónoma de Madrid, Madrid; Spain.57 Institut für Physik, Universität Mainz, Mainz; Germany.
School of Physics and Astronomy, University of Manchester, Manchester; United Kingdom.
CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille; France.
Department of Physics, University of Massachusetts, Amherst MA; United States of America.
Department of Physics, McGill University, Montreal QC; Canada.
School of Physics, University of Melbourne, Victoria; Australia.
Department of Physics, University of Michigan, Ann Arbor MI; United States of America.
Department of Physics and Astronomy, Michigan State University, East Lansing MI; United States ofAmerica.
B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk; Belarus.
Research Institute for Nuclear Problems of Byelorussian State University, Minsk; Belarus.
Group of Particle Physics, University of Montreal, Montreal QC; Canada.
P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow; Russia.
National Research Nuclear University MEPhI, Moscow; Russia.
D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow;Russia.
Fakultät für Physik, Ludwig-Maximilians-Universität München, München; Germany.
Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München; Germany.
Nagasaki Institute of Applied Science, Nagasaki; Japan.
Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya; Japan.
Department of Physics and Astronomy, University of New Mexico, Albuquerque NM; United States ofAmerica.
Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef,Nijmegen; Netherlands.
Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam;Netherlands.
Department of Physics, Northern Illinois University, DeKalb IL; United States of America. ( a ) Budker Institute of Nuclear Physics and NSU, SB RAS, Novosibirsk; ( b ) Novosibirsk State UniversityNovosibirsk; Russia.
Institute for High Energy Physics of the National Research Centre Kurchatov Institute, Protvino; Russia.
Institute for Theoretical and Experimental Physics named by A.I. Alikhanov of National ResearchCentre "Kurchatov Institute", Moscow; Russia.
Department of Physics, New York University, New York NY; United States of America.
Ochanomizu University, Otsuka, Bunkyo-ku, Tokyo; Japan.
Ohio State University, Columbus OH; United States of America.
Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman OK; UnitedStates of America.
Department of Physics, Oklahoma State University, Stillwater OK; United States of America.
Palacký University, RCPTM, Joint Laboratory of Optics, Olomouc; Czech Republic.
Institute for Fundamental Science, University of Oregon, Eugene, OR; United States of America.
Graduate School of Science, Osaka University, Osaka; Japan.
Department of Physics, University of Oslo, Oslo; Norway.
Department of Physics, Oxford University, Oxford; United Kingdom.
LPNHE, Sorbonne Université, Université de Paris, CNRS/IN2P3, Paris; France.
Department of Physics, University of Pennsylvania, Philadelphia PA; United States of America.
Konstantinov Nuclear Physics Institute of National Research Centre "Kurchatov Institute", PNPI, St.Petersburg; Russia. 58 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh PA; United States ofAmerica. ( a ) Laboratório de Instrumentação e Física Experimental de Partículas - LIP, Lisboa; ( b ) Departamento deFísica, Faculdade de Ciências, Universidade de Lisboa, Lisboa; ( c ) Departamento de Física, Universidade deCoimbra, Coimbra; ( d ) Centro de Física Nuclear da Universidade de Lisboa, Lisboa; ( e ) Departamento deFísica, Universidade do Minho, Braga; ( f ) Departamento de Física Teórica y del Cosmos, Universidad deGranada, Granada (Spain); ( g ) Dep Física and CEFITEC of Faculdade de Ciências e Tecnologia,Universidade Nova de Lisboa, Caparica; ( h ) Instituto Superior Técnico, Universidade de Lisboa, Lisboa;Portugal.
Institute of Physics of the Czech Academy of Sciences, Prague; Czech Republic.
Czech Technical University in Prague, Prague; Czech Republic.
Charles University, Faculty of Mathematics and Physics, Prague; Czech Republic.
Particle Physics Department, Rutherford Appleton Laboratory, Didcot; United Kingdom.
IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette; France.
Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz CA; UnitedStates of America. ( a ) Departamento de Física, Pontificia Universidad Católica de Chile, Santiago; ( b ) Universidad AndresBello, Department of Physics, Santiago; ( c ) Instituto de Alta Investigación, Universidad deTarapacá; ( d ) Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso; Chile.
Department of Physics, University of Washington, Seattle WA; United States of America.
Department of Physics and Astronomy, University of Sheffield, Sheffield; United Kingdom.
Department of Physics, Shinshu University, Nagano; Japan.
Department Physik, Universität Siegen, Siegen; Germany.
Department of Physics, Simon Fraser University, Burnaby BC; Canada.
SLAC National Accelerator Laboratory, Stanford CA; United States of America.
Physics Department, Royal Institute of Technology, Stockholm; Sweden.
Departments of Physics and Astronomy, Stony Brook University, Stony Brook NY; United States ofAmerica.
Department of Physics and Astronomy, University of Sussex, Brighton; United Kingdom.
School of Physics, University of Sydney, Sydney; Australia.
Institute of Physics, Academia Sinica, Taipei; Taiwan. ( a ) E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi; ( b ) HighEnergy Physics Institute, Tbilisi State University, Tbilisi; Georgia.
Department of Physics, Technion, Israel Institute of Technology, Haifa; Israel.
Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv; Israel.
Department of Physics, Aristotle University of Thessaloniki, Thessaloniki; Greece.
International Center for Elementary Particle Physics and Department of Physics, University of Tokyo,Tokyo; Japan.
Graduate School of Science and Technology, Tokyo Metropolitan University, Tokyo; Japan.
Department of Physics, Tokyo Institute of Technology, Tokyo; Japan.
Tomsk State University, Tomsk; Russia.
Department of Physics, University of Toronto, Toronto ON; Canada. ( a ) TRIUMF, Vancouver BC; ( b ) Department of Physics and Astronomy, York University, Toronto ON;Canada.
Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and AppliedSciences, University of Tsukuba, Tsukuba; Japan.
Department of Physics and Astronomy, Tufts University, Medford MA; United States of America.59 Department of Physics and Astronomy, University of California Irvine, Irvine CA; United States ofAmerica.
Department of Physics and Astronomy, University of Uppsala, Uppsala; Sweden.
Department of Physics, University of Illinois, Urbana IL; United States of America.
Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia - CSIC, Valencia; Spain.
Department of Physics, University of British Columbia, Vancouver BC; Canada.
Department of Physics and Astronomy, University of Victoria, Victoria BC; Canada.
Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg; Germany.
Department of Physics, University of Warwick, Coventry; United Kingdom.
Waseda University, Tokyo; Japan.
Department of Particle Physics, Weizmann Institute of Science, Rehovot; Israel.
Department of Physics, University of Wisconsin, Madison WI; United States of America.
Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische UniversitätWuppertal, Wuppertal; Germany.
Department of Physics, Yale University, New Haven CT; United States of America. a Also at Borough of Manhattan Community College, City University of New York, New York NY; UnitedStates of America. b Also at Centro Studi e Ricerche Enrico Fermi; Italy. c Also at CERN, Geneva; Switzerland. d Also at CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille; France. e Also at Département de Physique Nucléaire et Corpusculaire, Université de Genève, Genève;Switzerland. f Also at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona; Spain. g Also at Department of Financial and Management Engineering, University of the Aegean, Chios; Greece. h Also at Department of Physics and Astronomy, Michigan State University, East Lansing MI; UnitedStates of America. i Also at Department of Physics and Astronomy, University of Louisville, Louisville, KY; United States ofAmerica. j Also at Department of Physics, Ben Gurion University of the Negev, Beer Sheva; Israel. k Also at Department of Physics, California State University, East Bay; United States of America. l Also at Department of Physics, California State University, Fresno; United States of America. m Also at Department of Physics, California State University, Sacramento; United States of America. n Also at Department of Physics, King’s College London, London; United Kingdom. o Also at Department of Physics, St. Petersburg State Polytechnical University, St. Petersburg; Russia. p Also at Department of Physics, University of Fribourg, Fribourg; Switzerland. q Also at Dipartimento di Matematica, Informatica e Fisica, Università di Udine, Udine; Italy. r Also at Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow; Russia. s Also at Giresun University, Faculty of Engineering, Giresun; Turkey. t Also at Graduate School of Science, Osaka University, Osaka; Japan. u Also at Hellenic Open University, Patras; Greece. v Also at IJCLab, Université Paris-Saclay, CNRS/IN2P3, 91405, Orsay; France. w Also at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona; Spain. x Also at Institut für Experimentalphysik, Universität Hamburg, Hamburg; Germany. y Also at Institute for Mathematics, Astrophysics and Particle Physics, Radboud UniversityNijmegen/Nikhef, Nijmegen; Netherlands. z Also at Institute for Nuclear Research and Nuclear Energy (INRNE) of the Bulgarian Academy ofSciences, Sofia; Bulgaria. 60 a Also at Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Budapest;Hungary. ab Also at Institute of Particle Physics (IPP), Vancouver; Canada. ac Also at Institute of Physics, Azerbaijan Academy of Sciences, Baku; Azerbaijan. ad Also at Instituto de Fisica Teorica, IFT-UAM/CSIC, Madrid; Spain. ae Also at Joint Institute for Nuclear Research, Dubna; Russia. a f
Also at Louisiana Tech University, Ruston LA; United States of America. ag Also at Moscow Institute of Physics and Technology State University, Dolgoprudny; Russia. ah Also at National Research Nuclear University MEPhI, Moscow; Russia. ai Also at Physics Department, An-Najah National University, Nablus; Palestine. aj Also at Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg; Germany. ak Also at The City College of New York, New York NY; United States of America. al Also at TRIUMF, Vancouver BC; Canada. am Also at Universita di Napoli Parthenope, Napoli; Italy. an Also at University of Chinese Academy of Sciences (UCAS), Beijing; China. ∗∗