Mapping the material in the LHCb vertex locator using secondary hadronic interactions
M. Alexander, W. Barter, A. Bay, L.J. Bel, M. van Beuzekom, G. Bogdanova, S. Borghi, T.J.V. Bowcock, E. Buchanan, J. Buytaert, K. Carvalho Akiba, S. Chen, V. Coco, P. Collins, A. Crocombe, F. Da Cunha Marinho, E. Dall'Occo, S. De Capua, C.T. Dean, F. Dettori, D. Dossett, K. Dreimanis, G. Dujany, L. Eklund, T. Evans, M. Ferro-Luzzi, M. Gersabeck, T. Gershon, T. Hadavizadeh, J. Harrison, K. Hennessy, W. Hulsbergen, D. Hutchcroft, P. Ilten E. Jans, M. John, P. Kopciewicz, P. Koppenburg, G. Lafferty, T. Latham, A. Leflat, M.W. Majewski, R. McNulty, J. Mylroie-Smith, A. Oblakowska-Mucha, C. Parkes, A. Pearce, A. Poluektov, A. Pritchard, W. Qian, S. Redford, S. Richards, K. Rinnert, E. Rodrigues, G. Sarpis, M. Schiller, H. Schindler, M. Smith, N.A. Smith, T. Szumlak, J.J. Velthuis, V. Volkov, C. Wallace, H.M. Wark, A. Webber, M.R.J. Williams, M. Williams
PPreprint typeset in JINST style - HYPER VERSION
Mapping the material in the LHCb vertex locatorusing secondary hadronic interactions
M. Alexander , W. Barter , A. Bay , L.J. Bel , M. van Beuzekom , G. Bogdanova , S. Borghi ,T.J.V. Bowcock , E. Buchanan , J. Buytaert , K. Carvalho Akiba , S. Chen , V. Coco , P. Collins ,A. Crocombe , F. Da Cunha Marinho , E. Dall’Occo , S. De Capua , C.T. Dean , F. Dettori ,D. Dossett , a , K. Dreimanis , G. Dujany , L. Eklund , T. Evans , M. Ferro-Luzzi , M. Gersabeck ,T. Gershon , T. Hadavizadeh , J. Harrison , K. Hennessy , W. Hulsbergen , D. Hutchcroft , P. Ilten , b ∗ ,E. Jans , M. John , P. Kopciewicz , P. Koppenburg , G. Lafferty , T. Latham , A. Leflat , ,M.W. Majewski , R. McNulty , J. Mylroie-Smith , A. Oblakowska-Mucha , C. Parkes , A. Pearce ,A. Poluektov , A. Pritchard , W. Qian , S. Redford , S. Richards , K. Rinnert , E. Rodrigues ,G. Sarpis , M. Schiller , H. Schindler , M. Smith , N.A. Smith , T. Szumlak , J.J. Velthuis , V. Volkov ,C. Wallace , H.M. Wark , A. Webber , M.R.J. Williams , M. Williams ∗ . School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom European Organization for Nuclear Research (CERN), Geneva, Switzerland Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil Sezione INFN di Cagliari, Cagliari, Italy Department of Physics, University of Warwick, Coventry, United Kingdom LPNHE, Université Pierre et Marie Curie, Université Paris Diderot, CNRS/IN2P3, Paris, France Department of Physics, University of Oxford, Oxford, United Kingdom Massachusetts Institute of Technology, Cambridge, MA, United States AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science, Kraków, Poland School of Physics, University College Dublin, Dublin, Ireland University of Cincinnati, Cincinnati, OH, United States a Current address: School of Physics, The University of Melbourne, VIC 3010, Australia b Current address: School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom A BSTRACT : Precise knowledge of the location of the material in the LHCb vertex locator (VELO)is essential to reducing background in searches for long-lived exotic particles, and in identifyingjets that originate from beauty and charm quarks. Secondary interactions of hadrons produced inbeam-gas collisions are used to map the location of material in the VELO. Using this material map,along with properties of a reconstructed secondary vertex and its constituent tracks, a p -value canbe assigned to the hypothesis that the secondary vertex originates from a material interaction. Avalidation of this procedure is presented using photon conversions to dimuons. ∗ corresponding authors: [email protected], [email protected] a r X i v : . [ phy s i c s . i n s - d e t ] J un ontents
1. Introduction 12. Detector and Data Sets 23. Material Maps 44. Material Probability 85. Summary 9
1. Introduction
Precise knowledge of the location of the material in the LHCb vertex locator (VELO) [1] is essen-tial to reducing background in searches for long-lived exotic particles (see, e.g. , Refs. [2, 3]), andin identifying jets that originate from beauty and charm quarks [4]. The VELO aperture is smallerthan required by the LHC beams during injection; therefore, the VELO consists of two retractablehalves that close about the interaction region after the LHC beams are stable, resulting in fill-by-fillmovement of the VELO material. The location of the pp -collision region changes by O ( . ) from year to year, and changed by ≈ . e.g. , Ref. [7]). The typical resolution on thereconstructed vertex position for a secondary hadronic interaction is about 0.04 mm in r and 0.4 mmin z , which enables the construction of a high-precision map of the location of material in theVELO. Using this material map, along with properties of a reconstructed secondary vertex (SV)and its constituent tracks, a p -value can be assigned to the hypothesis that the SV originates froma material interaction. This approach was recently used to veto photon conversions to µ + µ − in asearch for dark photons at LHCb [8]. LHCb defines its coordinate system as follows: ˆ z is along the beam line, where positive z denotes the direction fromthe pp -interaction point into the LHCb detector; ˆ y is vertical upwards; and ˆ x is horizontal and defined such that thecoordinate system is right handed. Polar coordinates, r and φ , are also used in the xy plane. Many other experiments have employed alternative strategies for rejecting material-induced backgrounds in searchesfor long-lived particles, e.g. , see Ref. [9]. – 1 – igure 1.
From Ref. [1]: (top left) a photograph of one side of the VELO, taken during assembly, showingthe silicon sensors and readout hybrids; (top right) a schematic of both an r and φ sensor, showing the sensorstrips and routing lines; and (bottom) schematics showing the cross section of the xz plane at y =
0, wherethe r ( φ ) sensors are shown with solid blue (dashed red) lines, and an xy view of overlapping sensors in theclosed position. N.b. , the modules at positive (negative) x are known as the left or A-side (right or C-side). This analysis uses secondary interactions of hadrons produced in beam-gas collisions col-lected during special run periods where helium or neon gas was injected into the beam-crossingregion [10]. In such events, the LHC proton beams collide with the gas molecules producing pri-mary hadrons, which subsequently scatter off the VELO material producing secondary hadronsthat are detected by LHCb. Material interactions occur along the entire length of the VELO inbeam-gas events, rather than just near the pp -interaction region. A modified tracking configura-tion that makes no assumptions about the particle origin points along z is used to reconstruct theparticles produced in the secondary interactions. This article is structured as follows: the VELOdetector, beam-gas data sets, and track and vertex reconstruction algorithms are described in Sec. 2;in Sec. 3, the material map is presented; the procedure for obtaining material interaction p -valuesis discussed in Sec. 4; and Sec. 5 summarizes.
2. Detector and Data Sets
The LHCb detector is a single-arm spectrometer covering the forward pseudorapidity region of2 < η < b and c quarks, includes a high-precision charged-particle tracking system, two ring-imaging Cherenkovdetectors, electromagnetic and hadronic calorimeters, and a system of muon chambers. The LHCbcollaboration mostly collected pp -collision data at center-of-mass energies of 7 and 8 TeV in Run 1– 2 – [mm] y − − [ mm ] x − − LHCb [mm] y − − [ mm ] x − − LHCb
Figure 2.
Reconstructed SVs in the Run 2 data sample showing the xy plane integrated over z within theregion of the VELO that contains sensor modules. The left (right) panel shows the central (forward) VELOregion. The bins are 0 . × . and at 13 TeV in Run 2; however, special running periods at alternative energies, using heavy-ionbeams and gaseous targets have also been undertaken.The VELO is a silicon-microstrip detector that surrounds the pp -interaction region and pro-vides excellent vertex resolution (see Fig. 1). During physics data taking, the VELO sensors aremoved to within 7 mm of the beam, with the closest active regions only about 8 mm in the trans-verse plane from the pp collisions. This enables achieving a charged particle impact parameterresolution of 0.035 mm for a transverse momentum of p T ≈ z ) of 0.3 mm.These sensors are placed into 21 standard modules in r – φ pairs, where each r sensor providesa radial-coordinate measurement, each φ sensor provides an azimuthal-coordinate measurement,and the module location determines the z coordinate. Each half also has two additional modules,referred to as the pile-up system, that only contain an r sensor and are located in the most upstreampositions of the VELO. There is a slight overlap between the two VELO halves to ensure fullangular coverage and to assist in calibration of the detector. Each half is contained in an RF-box ,which provides an independent vacuum from the LHC machine vacuum. The beam-facing surfaceof the RF-boxes is the
RF-foil , a 0.3 mm thick AlMg sheet that is corrugated around the modulesto minimize the material traversed by charged particles. The RF-box and RF-foil shield the VELOsensors against RF pickup from the LHC beams, prevent impedance disruptions of the LHC beams,and protect the LHC machine vacuum.A beam-gas imaging system was proposed in Ref. [12], and developed and commissionedduring Run 1 [10] to enable making high-precision luminosity measurements [13]. This systemhas since been repurposed to allow LHCb to collect data as a fixed-gaseous-target experiment. Theanalysis presented here uses secondary interactions of hadrons produced in beam-gas collisionscollected during special run periods where helium or neon gas was injected into the beam-crossing– 3 – [mm] z − [ mm ] r ( s i gn e d ) − − LHCb
Figure 3.
Reconstructed SVs in the Run 1 data sample showing the zr plane integrated over φ , where apositive (negative) r value denotes that the SV is closest to material in the right (left) half of the VELO. Thebins are 0 . × N.b. , the inner-most RF-foil region is nearly semi-circular in the xy plane,which results in sharp edges at smaller r values; however, at large | y | values, the RF-foil is flat producingSVs at larger values of r which can easily be mistaken as background in the zr projection shown here. region. Several data samples are used from different running periods: data collected during pp running in 2011 and 2012 (Run 1) meant for luminosity studies, with beam energies of 3.5 and4.0 TeV, respectively; and data taken during a dedicated proton-helium run in 2016 (Run 2) with abeam energy of 4.0 TeV. Only one LHC beam has a nominally filled bunch slot in all events usedin this study. The data sets were collected using minimum bias triggers.Since the particles produced in secondary interactions in beam-gas events do not necessarilyoriginate from near the interaction point or the beam line, the tracks used in this analysis arereconstructed using a modified tracking configuration that makes no assumptions about the originsalong z of the particles. All reconstructed tracks are required to be of good quality and to have hitsin at least 3 r – φ sensor pairs. The SVs are reconstructed from 3 or more tracks and are requiredto be of good quality. Futhermore, the SVs are required to be inconsistent with originating froma primary beam-gas collision, and only events with exactly one SV are used. In total, the Run 1and Run 2 data samples contain 14M and 38M SVs, respectively. Figures 2 and 3 present somedisplays of the reconstructed SV locations.
3. Material Maps
The VELO closes around the beams at the beginning of each fill with a precision of O ( .
01 mm ) [1].As stated above, the location of the pp -collision region (beam spot) changes by O ( . ) fromyear to year, and changed by ≈ . z positions of the sensors are determined by fitting the observed SV z distributions neareach module location. In these fits, the SVs are required to have r > x > − . ( x < . ) for the left (right) VELO half. These requirements highly suppress contributionsfrom material interactions in the RF-foil and from beam-induced backgrounds. The fits estimatethe center-of-mass of each sensor in z which is stored as part of the material map. The sensors are0.3 mm thick and a material interaction can occur anywhere along the path of a particle traversinga sensor. This is accounted for in the material-interaction p -values by assigning an uncertainty tothe true origin point in the sensor. Furthermore, the sensors are tilted, i.e. not aligned at a single z value. This effect is small compared to the SV resolution; therefore, it is accounted for using anadditional uncertainty when determining the p -values, rather than being individually determinedfor each sensor. The precision of these SV-based fits in determining the z locations of the sensorsis estimated to be 0 .
03 mm by comparing the distance between the r -sensor and φ -sensor in each r – φ pair to the values determined by metrology during VELO construction.Since the manufacturing tolerance of the sensor wafers is only 0.05 mm, the nominal wafershapes in the transverse plane are used for the sensors; i.e. the shapes of the modules are not variedin this study, only their locations. The reference point used to define the x and y positions of eachsensor, which is taken to be the center of the module semi-circles nominally at x beam and y beam , isfitted to the observed xy positions using SVs near each sensor in z . Only SVs that are consistentwith originating from an interaction in a module are used in these fits. The xy location of eachmodule reference point is varied in order to maximize the vertex density that overlaps the modulelocation. The precision of these fits in determining the xy locations of the sensors is estimated tobe 0 .
03 mm (in each direction) by comparing the SV-based results to the high-precision software-based alignment locations.Figure 4 shows the differences in the x , y , and z locations of each module with respect tothe VELO survey specifications. The largest discrepancies observed in z are ≈ . (cid:46) . y positions are all found to be consistent with the survey values to ≈ . x [1]. These observed deviations fromthe survey specifications are known from the software alignment procedure and taken into accountduring the reconstruction, and reproducing them provides validation of the SV-based approach.The shape of the RF-foil in the xy -plane is roughly a semi-circle about the origin that transi-tions into straight lines that extend out away from the origin at fixed x values. The parametrizationemployed here describes these transitions using additional semi-circles (interpolation using bicubicsplines was also tried, but found to provide a worse description of the data). The xy distributionsof SVs are fit in 1 mm wide slices in z , where SVs consistent with originating from a module areremoved, and in each of the 1066 slices four parameters are determined. As with the modules,the thickness of the RF-foil is ignored when building the map, but accounted for as an uncertaintyin the true origin point when determining the material-interaction p -value. The z dependence of The resolution on the z positions of the SVs used in this study is ≈ . z position of a sensor at different values of r due to tilts is typically (cid:46) .
05 mm with the largest difference in z being ≈ .
15 mm, determined by the LHCb software-based alignment procedure which does account for tilt. Since the module shapes are fixed, moving the location of the reference point results in a translation in xy of theentire module. – 5 – [mm] z - f it [ mm ] - s u r v e y - LHCb x D y D z D Figure 4.
Differences in the sensor locations relative to the survey specifications. The observed deviationsare known from VELO alignment studies and accounted for during reconstruction. [mm] z - [ mm ] x - LHCb = 0 mm y MapSimulation
Figure 5.
Comparison between the RF-foil map at y = each RF-foil parameter is then fit to the following empirical functions: the y locations of all semi-circles are found to be well described by simple linear functions, while the remaining parametersare fit to a combination of sinusoidal and polynomial functions, except in the forward-most region, i.e. at large z , where dedicated functions are needed to capture additional structure in the RF-foil.Figure 5 shows an example comparison of the RF-foil map created here to the description of theRF-foil in the LHCb simulation. The simulation clearly uses a simplified shape—but also one thatfails to describe the sizable deviations from the design shape in the forward-most region.Figure 6 shows some example comparisons of the material map to the observed SV distribu-tions. Overall, the map describes the data well. There are some small discrepancies in the forward-most region, where some features of the RF-foil are not fully described; however, high precisionis not required in this region, since SVs reconstructed here are less precisely determined due tothe large separation between the modules at large z . Finally, given that the RF-foil is ≈ . z regions that are 1 mm wide, andthat its shape varies along the length of the VELO in ways that are not all fully captured by ourparametrization at all z values, an uncertainty of 0.5 mm is assigned to the RF-foil location in the xy plane when vetoing material interactions. – 6 – [mm] z - [ mm ] x - - LHCb = 0 mm y [mm] z [ mm ] x - - LHCb = 0 mm y [mm] y - [ mm ] x - LHCb = 34.4 mm z [mm] y - [ mm ] x - LHCb = 49.3 mm z Figure 6.
Example comparisons between the (filled bins) reconstructed SV locations and (red lines) the ma-terial map for: (top) x versus z near y = < z <
100 mmregion; (bottom left) x versus y near the left-half r sensor at z = . x versus y nearthe right-half φ sensor at z = . i.e. the red RF-foil curves do not display its thickness. – 7 – . Material Probability In this section, a method is presented that reports a p -value for the hypothesis that the true SVlocation is consistent with a point in space occupied by VELO material. The inputs used to de-termine this p -value are the 3-D location of the SV and its uncertainty, and the 3-D material mapwith the appropriate adjustments for the location of the detector during each fill. Several pos-sible metrics were considered, with the best performance achieved using the harmonic mean ofuncertainty-weighted material distances D = (cid:34) ∑ i = D − i (cid:35) − , (4.1)where each D i is defined as D i = min (cid:115)(cid:18) x i m − x sv σ x (cid:19) + (cid:18) y i m − y sv σ y (cid:19) + (cid:18) z i m − z sv σ z (cid:19) , (4.2)for a VELO material element described by { (cid:126) x m } , given an SV location (cid:126) x sv , and uncertainties ineach direction (cid:126) σ , which include contributions from both the material and SV locations. The sixmaterial elements considered are the sensors in each VELO half (two sensors), along with the RF-foil in each half where the positive and negative z directions from the SV z location are consideredseparately (four RF-foil elements). Each sensor is represented by its design shape in the xy planeand a z location with zero thickness. The minimum in the above equation considers the expressionin square brackets for every point on the sensor, taking the smallest value. For the RF-foil, theminima are found in a conceptually similar way, but 3-D numerical searches are required to findthem due to the complicated shape of the RF-foil.The expected D distribution can be obtained for any data sample as follows: reconstructedSVs in the data sample that are close to material can be repeatedly resampled, taking the closestmaterial point as the true origin and sampling the SV locations according to their uncertainties.Non-Gaussian effects are accounted for by taking the resampling distributions from simulation, i.e. the differences in the true and reconstructed SV locations are not assumed to follow Gaussian dis-tributions with widths given by the SV resolution. Instead these distributions are obtained from thefull LHCb simulation. This data-driven approach must be applied for each data sample, since the D distribution depends strongly on the SV resolution, which is correlated with the decay openingangle, number of decay products, and other decay-specific features.Figure 7 shows a validation of this procedure from a search for long-lived dark photons de-caying to dimuon final states [8]. The A (cid:48) → µ + µ − candidates are built from muons that are in-consistent with originating from the pp collision, satisfy stringent muon-identification criteria, andhave p T ( µ ) > . p ( µ ) >
10 GeV. To avoid potential bias in the SV locations and theiruncertainties, the following criteria are applied: the first two hits on each muon track are required The SV-fit χ values are required to be good, which highly suppresses the non-Gaussian contributions and miti-gates any potential mismodelling of these effects in the simulation. Additionally, non-Gaussian scattering effects aresuppressed even further in analyses that apply criteria to the consistency of the decay topology. – 8 – value] p [material log - - - F r ac ti on / . - - - - - - -
10 1
LHCb
Data conversion g ps = 1) A' ( t ps = 10) A' ( t Figure 7.
The normalized photon conversion p -value distribution obtained using a subsample of data froman LHCb long-lived dark-photon search [8]. The data are consistent with the photon-conversion hypoth-esis. Some example dark-photon distributions are also shown for lifetimes of 1 and 10 ps, showing goodseparation between potential exotic signals and photon conversions. to be in an r – φ sensor pair, the first hit on each track is required to be in the first VELO sensor inter-sected by its trajectory, the first hits on the two muons must be in the same sensor module, the twomuons cannot share more than 8 hits in the VELO to remove clones, and the SV is required to beupstream of the first hits on each muon track. The subsample shown in Fig. 7 uses only candidateswith an SV location at least 5 mm from the beam line and with m ( µ + µ − ) < .
25 GeV to suppressheavy-flavor and double-misidentified K S → π + π − backgrounds. The data are consistent with thephoton-conversion hypothesis. The search presented in Ref. [8] applied a mass-dependent criterionon D that reduced the contribution from conversions to a negligible level, while maintaining goodsignal efficiency. This procedure makes it possible to perform nearly background-free searchesfor many proposed types of long-lived exotic particles, greatly enhancing the physics discoverypotential c.f. simply removing SVs in predefined material regions.
5. Summary
In summary, a study of the LHCb VELO material based on secondary hadronic interactions waspresented, and a high-precision map of the VELO material was built. The analysis used secondaryinteractions of hadrons produced in beam-gas collisions collected during special run periods wherehelium or neon gas was injected into the beam-crossing region. Material interactions occur alongthe entire length of the VELO in such events, rather than just near the pp -interaction region. Usingthis material map, along with properties of a reconstructed SV and its constituent tracks, a p -valuecan be assigned to the hypothesis that the SV originates from a material interaction. This approachwas recently used to veto photon conversions to µ + µ − in a search for dark photons at LHCb [8].The procedure makes it possible to perform nearly background-free searches for many proposedtypes of long-lived exotic particles. – 9 – cknowledgments A special acknowledgement goes to all of our LHCb collaborators who contributed to obtainingthe results presented in this paper. Specifically, we thank Plamen Hopchev for help developingthe special reconstruction used in this study; and Yuri Guz, Christian Joram, and Rosen Matev forproviding useful feedback on this article. We express our gratitude to our colleagues in the CERNaccelerator departments for the excellent performance of the LHC. We thank the technical and ad-ministrative staff at the LHCb institutes. We also acknowledge support for the LHCb collaborationfrom CERN and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); MOSTand NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy);NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES and FASO(Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (United King-dom); NSF (USA). We acknowledge the computing resources that are provided by CERN, IN2P3(France), KIT and DESY (Germany), INFN (Italy), SURF (The Netherlands), PIC (Spain), GridPP(United Kingdom), RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania),CBPF (Brazil), PL-GRID (Poland) and OSC (USA). Individual LHCb groups or members havereceived support from AvH Foundation (Germany), EPLANET, Marie Skłodowska-Curie Actionsand ERC (European Union), ANR, Labex P2IO, ENIGMASS and OCEVU, and Région Auvergne-Rhône-Alpes (France), RFBR and Yandex LLC (Russia), GVA, XuntaGal and GENCAT (Spain),Herchel Smith Fund, the Royal Society, the English-Speaking Union and the Leverhulme Trust(United Kingdom).
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