Measurement of the CKM angle γ in B ± →D K ± and B ± →D π ± decays with D→ K 0 S h + h −
LHCb collaboration, R. Aaij, C. Abellán Beteta, T. Ackernley, B. Adeva, M. Adinolfi, H. Afsharnia, C.A. Aidala, S. Aiola, Z. Ajaltouni, S. Akar, J. Albrecht, F. Alessio, M. Alexander, A. Alfonso Albero, Z. Aliouche, G. Alkhazov, P. Alvarez Cartelle, S. Amato, Y. Amhis, L. An, L. Anderlini, A. Andreianov, M. Andreotti, F. Archilli, A. Artamonov, M. Artuso, K. Arzymatov, E. Aslanides, M. Atzeni, B. Audurier, S. Bachmann, M. Bachmayer, J.J. Back, S. Baker, P. Baladron Rodriguez, V. Balagura, W. Baldini, J. Baptista Leite, R.J. Barlow, S. Barsuk, W. Barter, M. Bartolini, F. Baryshnikov, J.M. Basels, G. Bassi, B. Batsukh, A. Battig, A. Bay, M. Becker, F. Bedeschi, I. Bediaga, A. Beiter, V. Belavin, S. Belin, V. Bellee, K. Belous, I. Belov, I. Belyaev, G. Bencivenni, E. Ben-Haim, A. Berezhnoy, R. Bernet, D. Berninghoff, H.C. Bernstein, C. Bertella, E. Bertholet, A. Bertolin, C. Betancourt, F. Betti, M.O. Bettler, Ia. Bezshyiko, S. Bhasin, J. Bhom, L. Bian, M.S. Bieker, S. Bifani, P. Billoir, M. Birch, F.C.R. Bishop, A. Bizzeti, M. Bjørn, M.P. Blago, T. Blake, F. Blanc, S. Blusk, D. Bobulska, V. Bocci, J.A. Boelhauve, O. Boente Garcia, T. Boettcher, A. Boldyrev, A. Bondar, N. Bondar, S. Borghi, M. Borisyak, M. Borsato, J.T. Borsuk, S.A. Bouchiba, T.J.V. Bowcock, et al. (886 additional authors not shown)
EEUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-EP-2020-175LHCb-PAPER-2020-01916 October 2020
Measurement of the CKM angle γ in B ± → DK ± and B ± → Dπ ± decays with D → K h + h − LHCb collaboration † Abstract
A measurement of CP -violating observables is performed using the decays B ± → DK ± and B ± → Dπ ± , where the D meson is reconstructed in one of theself-conjugate three-body final states K π + π − and K K + K − (commonly denoted K h + h − ). The decays are analysed in bins of the D -decay phase space, leadingto a measurement that is independent of the modelling of the D -decay amplitude.The observables are interpreted in terms of the CKM angle γ . Using a data samplecorresponding to an integrated luminosity of 9 fb − collected in proton-proton colli-sions at centre-of mass energies of 7, 8, and 13 TeV with the LHCb experiment, γ is measured to be (cid:0) . +5 . − . (cid:1) ◦ . The hadronic parameters r DKB , r DπB , δ DKB , and δ DπB ,which are the ratios and strong-phase differences of the suppressed and favoured B ± decays, are also reported. Submitted to JHEP © † Authors are listed at the end of this paper. a r X i v : . [ h e p - e x ] O c t i Introduction
In the framework of the Standard Model, CP violation can be described by the anglesand lengths of the Unitarity Triangle constructed from elements of the CKM matrix [1, 2].The angle γ ≡ arg ( − V ud V ∗ ub /V cd V ∗ cb ), has particularly interesting features. It is the onlyCKM angle that can be measured in decays including only tree-level processes, and isexperimentally accessible through the interference of b → cus and b → ucs (and CP -conjugate) decay amplitudes. In addition, there are negligible theoretical uncertaintieswhen interpreting the measured observables in terms of γ [3]. Hence, in the absence ofunknown physics effects at tree level, a precision measurement of γ provides a StandardModel benchmark that can be compared with indirect determinations from other CKM-matrix observables more likely to be affected by physics beyond the Standard Model [4].Such comparisons are currently limited by the precision of direct measurements of γ ,which is about 5 ◦ [5, 6] dominated by LHCb results.Decays such as B ± → DK ± , where D represents a superposition of D and D states,are used to observe the effects of interference between b → cus and b → ucs (and CP -conjugate) decay amplitudes. The interference arises when the decay channel of the D meson is common to both D and D mesons. The B ± → DK ± decay has beenstudied extensively with a wide range of D -meson final states [7–11]. The exact choiceof observables from each of these analyses is dependent on the method that is mostappropriate for the D decay used [12–20]. The methods can be extended to a variety ofdifferent B -decay modes [8, 21–25].This paper presents a model-independent study of the decay modes B ± → DK ± and B ± → Dπ ± where the chosen D decays are the self-conjugate decays D → K π + π − and D → K K + K − (denoted D → K h + h − ). The analysis of the B ± → DK ± , D → K h + h − decay chain is powerful due to the rich resonance structure of the D -decay modes, as hasbeen described in Refs. [17–19]. The data used in this analysis were accumulated withthe LHCb detector over the period 2011–2018 in pp collisions at energies of √ s =7, 8, 13TeV, corresponding to a total integrated luminosity of approximately 9 fb − .The presence of interference leads to differences in the phase-space distributions of D decays from reconstructed B + and B − decays. In order to interpret any observed differencein the context of the angle γ , knowledge of the strong phase of the D decay amplitude,and how it varies over phase space, is required. An attractive model-independent approachmakes use of direct measurements of the strong-phase difference between D and D decays, averaged over regions of the phase space [17, 26, 27]. Quantum correlated pairs of D mesons produced in decays of ψ (3770) give direct access to the strong-phase differences.These have been measured by the CLEO collaboration [28], and more recently the BESIIIcollaboration [29–31]. Measurements using the inputs in Ref. [28] have been used bythe LHCb [10, 21, 32] and Belle [33, 34] collaborations. An alternate method is to use anamplitude model of the D decay to determine the strong-phase variation [35–37]. Theseparation of data into binned regions of the Dalitz plot leads to a loss of statisticalsensitivity in comparison to using an amplitude model. However, the advantage of usingthe direct strong-phase measurements resides in the model-independent nature of thesystematic uncertainties. Where the direct strong-phase measurements are used, there isonly a systematic uncertainty associated with the finite precision of such measurements.Conversely, systematic uncertainties associated with determining a phase from an ampli-tude model are difficult to evaluate, as common approaches to amplitude-model building1iolate the optical theorem [38]. Therefore, the loss in statistical precision is compensatedby reliability in the evaluation of the systematic uncertainty, which is increasingly impor-tant as the overall precision on the CKM angle γ improves. The analysis approach is laidout in Sect. 2, while Sect. 3 describes the LHCb detector used to collect the data sample,and Sect. 4 summarises the selection criteria. The measurement is based on a two-step fitprocedure covered in Sect. 5, where the fit to the invariant-mass distribution is detailed,and Sect. 6, which describes how the CP observables are determined. The systematicuncertainties are reported in Sect. 7, and the results are interpreted to determine thevalue of γ in Section 8. Finally, the conclusions are presented in Sect. 9. The sum of the favoured and suppressed contributions to the B − → DK − amplitude canbe written as A B ( m − , m ) ∝ A D ( m − , m ) + r DKB e i ( δ DKB − γ ) A D ( m − , m ) , (1)where A D ( m − , m ) is the D → K h + h − decay amplitude, and A D ( m − , m ) is the D → K h + h − decay amplitude. The hadronic parameters r DKB and δ DKB are the ratioof the magnitudes of the amplitudes of B − → D K − and B − → D K − and the strong-phase difference between them, respectively. Finally, the position of the decay in theDalitz plot is defined by m − and m , which are the squared invariant masses of the K h − and K h + particle combinations, respectively. The equivalent expression for thecharge-conjugated decay B + → DK + is obtained by making the substitutions γ → − γ and A D ( m − , m ) ↔ A D ( m − , m ).The D -decay phase space is partitioned into 2 × N bins labelled from i = −N to i = + N (excluding zero), symmetric around m − = m such that if ( m − , m ) is in bin i then ( m , m − ) is in bin − i . The bins for which m − > m are defined to have positivevalues of i . The strong-phase difference between the D - and D -decay amplitudes ata given point on the Dalitz plot is denoted as δ D ( m − , m ). The cosine of δ D ( m − , m )weighted by the D -decay amplitude and averaged over bin i is written as c i [17], and isgiven by c i ≡ (cid:82) i dm − dm | A D ( m − , m ) || A D ( m , m − ) | cos [ δ D ( m − , m ) − δ D ( m , m − )] (cid:113)(cid:82) i dm − dm | A D ( m − , m ) | (cid:82) i dm − dm | A D ( m , m − ) | , (2)where the integrals are evaluated over bin i . An analogous expression can be written for s i , which is the sine of the strong-phase difference weighted by the decay amplitude andaveraged over the bin phase space.The expected yield of B − decays in bin i is found by integrating the square of theamplitude given in Eq. (1) over the region of phase space defined by the i th bin. The effectsof charm mixing and CP violation are ignored, as is the presence of CP violation andmatter regeneration in the neutral K decays. These effects are expected to have a smallimpact [39, 40] on the distribution of events on the Dalitz plot. Selection requirements For historical reasons, this convention defines positive bins in the opposite manner to that used todetermine the charm strong-phase differences in D → K h + h − decays. η ( m − , m ). At LHCb the typical efficiency variation over phase space for a D → K h + h − decay from a region of high efficiency to low efficiency is approximately 60% [21]. Thefractional yield of pure D decays in bin i in the presence of this efficiency profile isdenoted F i , given by F i = (cid:82) i dm − dm | A D ( m − , m ) | η ( m − , m ) (cid:80) j (cid:82) j dm − dm | A D ( m − , m ) | η ( m − , m ) , (3)where the sum in the denominator is over all Dalitz plot bins, indexed by j . Neglecting CP violation in these charm decays, the charge-conjugate amplitudes satisfy the relation A D ( m − , m ) = A D ( m , m − ), and therefore F i = F − i , where F i is the fractional yield of D decays to bin i . The physics parameters of interest, r DKB , δ DKB , and γ , are translatedinto four CP -violating observables [41] that are measured in this analysis and are the realand imaginary parts of the ratio of the suppressed and favoured B decay amplitudes, x DK ± ≡ r DKB cos( δ DKB ± γ ) and y DK ± ≡ r DKB sin( δ DKB ± γ ) . (4)Using the relations c i = c − i and s i = − s − i the B + ( B − ) yields, N + ( N − ), in bin i and − i are given by N ++ i = h B + (cid:104) F − i + (cid:16)(cid:0) x DK + (cid:1) + (cid:0) y DK + (cid:1) (cid:17) F + i + 2 (cid:112) F i F − i (cid:0) x DK + c + i − y DK + s + i (cid:1)(cid:105) ,N + − i = h B + (cid:104) F + i + (cid:16)(cid:0) x DK + (cid:1) + (cid:0) y DK + (cid:1) (cid:17) F − i + 2 (cid:112) F i F − i (cid:0) x DK + c + i + y DK + s + i (cid:1)(cid:105) ,N − + i = h B − (cid:104) F + i + (cid:16)(cid:0) x DK − (cid:1) + (cid:0) y DK − (cid:1) (cid:17) F − i + 2 (cid:112) F i F − i (cid:0) x DK − c + i + y DK − s + i (cid:1)(cid:105) ,N −− i = h B − (cid:104) F − i + (cid:16)(cid:0) x DK − (cid:1) + (cid:0) y DK − (cid:1) (cid:17) F + i + 2 (cid:112) F i F − i (cid:0) x DK − c + i − y DK − s + i (cid:1)(cid:105) , (5)where h B + and h B − are normalisation constants. The value of r DKB is allowed to bedifferent for each charge and is constructed from either ( r DKB ) = (cid:0) x DK + (cid:1) + (cid:0) y DK + (cid:1) or( r DKB ) = (cid:0) x DK − (cid:1) + (cid:0) y DK − (cid:1) . The normalisation constants can be written as a functionof γ , analogous to the global asymmetries studied in decays where the D meson decaysto a CP eigenstate [8]. However, not only is this global asymmetry expected to be smallsince the CP -even content of the D → K π + π − and D → K K + K − decay modes is closeto 0.5, it is also expected to be heavily biased due to the effects of K CP violation [40]on total yields. Therefore the global asymmetry is ignored and the loss of information isminimal. An advantage of this approach is that the normalisation constants h B + and h B − are independent of each other, and will implicitly contain the effects of the productionasymmetry of B ± mesons in pp collisions and the detection asymmetries of the chargedkaon from the B decay. This leads to a CP -violation measurement that is free of systematicuncertainties associated to these effects.The system of equations provides 4 N observables and 4 + 2 N unknowns, assuming thatthe available measurements of c i and s i are used. This is solvable for N ≥
2, but in practicethe simultaneous fit of the F i , x DK ± , and y DK ± parameters leads to large uncertainties onthe CP observables, and hence some external knowledge of the F i parameters is desirable.The F i parameters could be computed from simulation and an amplitude model, but thesystematic uncertainties associated with the LHCb simulation would be significant. Recent3nalyses [10, 32] have used the semileptonic decay B → D ∗ µν , where the flavour-taggedyields of D mesons are corrected for the differences in selection between the semileptonicchannel and the signal mode. However, with the increased signal yields, the uncertaintydue to this necessary correction will be approximately half the statistical uncertainty onthe measurement presented in this paper, and therefore a different method is adopted.The B ± → Dπ ± decay mode is expected to have F i parameters that are the sameas those for B ± → DK ± if a similar selection is applied due to the common topologyand the ability to use same signatures in the detector to select the candidates. The B ± → Dπ ± decay is expected to exhibit CP violation through the interference of b → cud and b → ucd transitions, analogous to the B ± → DK ± decay but suppressed by oneorder of magnitude [42]. Further effects from K CP violation and matter regenerationhave been recently shown to have only a small impact on the distribution over the Dalitzplot [40], in contrast to their impact on the global asymmetry. Therefore the B ± → Dπ ± channel can be used to determine the F i parameters if the small level of CP violation inthe B ± decay is accounted for.Pseudoexperiments are performed in which the two B -decay modes are fit togetherassuming common F i parameters. Independent x ± and y ± observables are required forthe two B decay modes due to different values of the hadronic parameters, r B and δ B .The value of r B in B ± → DK ± is approximately 0 .
1, and it is expected that it will be afactor 20 smaller in B ± → Dπ ± decays [42]. The yields of B ± → Dπ ± are described by aset of equations analogous to Eq. (5), with the substitutions x DK ± → x Dπ ± and y DK ± → y Dπ ± .An analysis that simultaneously measures the F i , x DK ± , y DK ± , x Dπ ± , and y Dπ ± parametersis found to be stable only if r DπB > .
03. At the expected value r DπB = 0 .
005 the fitis unstable due to high correlations between the F i and x Dπ ± and y Dπ ± . Therefore analternate parameterisation [43,44] is introduced, which utilises the fact that γ is a commonparameter, and that the CP violation in B ± → Dπ ± decays can therefore be described bythe addition of a single complex variable ξ Dπ = (cid:18) r DπB r DKB (cid:19) exp (cid:0) iδ DπB − iδ DKB (cid:1) , (6)and in terms of x Dπξ ≡ Re( ξ Dπ ) and y Dπξ ≡ Im( ξ Dπ ), the (cid:0) x Dπ ± , y Dπ ± (cid:1) parameters are givenby x Dπ ± = x Dπξ x DK ± − y Dπξ y DK ± , y Dπ ± = x Dπξ y DK ± + y Dπξ x DK ± . (7)With this parameterisation, the simultaneous fit to x DK ± , y DK ± , x Dπξ , y Dπξ (the CP observ-ables) and F i parameters is stable for all values of r DπB . The simultaneous fit of B ± → Dπ ± and B ± → DK ± candidates has two advantages. Firstly, the extraction of F i in thismanner is expected to have negligible associated systematic uncertainty, and reduces signif-icantly the reliance on simulation. Secondly, the CP -violating observables in B ± → Dπ ± using other D -decay modes [8, 9] are not routinely included in the γ combination of allresults because they allow for two solutions of (cid:0) r DπB , δ
DπB (cid:1) , which makes the statisticalinterpretation of the full B ± → Dh ± combination problematic [45]. The measurement inthe B ± → Dπ ± , D → K h + h − decays has the potential to resolve this redundancy, andallow for a more straightforward inclusion of all B ± → Dπ ± results in the combination.A small disadvantage is that the measurement of γ will incorporate information fromboth B ± → DK ± and B ± → Dπ ± decay modes and the contribution of each cannot be4 igure 1: Binning schemes for (left) D → K π + π − decays and (right) D → K K + K − decays.The diagonal line separates the positive and negative bins, where the positive bins are in theregion in which m − > m is satisfied. disentangled. However, since the size of contribution from the B ± → Dπ ± decay to theprecision is expected to be negligible in comparison to that from the B ± → DK ± decay,this is considered an acceptable compromise.The measurements of c i and s i are available in four different 2 × D → K π + π − decay. This analysis uses the scheme called the optimal binning,where the bins have been chosen to optimise the statistical sensitivity to γ , as described inRef. [28]. The optimisation was performed assuming a strong-phase difference distributionas predicted by the BaBar model presented in Ref. [46]. For the K K + K − final state,three choices of binning schemes are available, containing 2 ×
2, 2 ×
3, and 2 × D → K K + K − decay mode is dominated by the intermediate K φ and K a (980) states which are CP -odd and CP -even, respectively, and the narrow K φ resonance is encapsulated within the second bin of the 2 × × D → K K + K − decaymode. The measurements of c i and s i are not biased by the use of a specific amplitudemodel in defining the bin boundaries. The choice of the model only affects this analysisto the extent that a poor model description of the underlying decay would result in areduced statistical sensitivity of the γ measurement. The binning choices for the twodecay modes are shown in Fig. 1.Measurements of the c i and s i parameters in the optimal binning scheme for the D → K π + π − decay and in the 2 × D → K K + K − decay areavailable from both the CLEO and BESIII collaborations. A combination of results fromboth collaborations is presented in Ref. [30] and Ref. [31] for the D → K π + π − and D → K K + K − decays, respectively. The combinations are used within this analysis.5 LHCb Detector
The LHCb detector [48, 49] is a single-arm forward spectrometer covering thepseudorapidity range 2 < η <
5, designed for the study of particles containing b or c quarks. The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region, a large-area silicon-stripdetector located upstream of a dipole magnet with a bending power of about 4 Tm, andthree stations of silicon-strip detectors and straw drift tubes placed downstream of themagnet. The tracking system provides a measurement of the momentum, p , of chargedparticles with a relative uncertainty that varies from 0.5% at low momentum to 1.0% at200 GeV/ c . The minimum distance of a track to a primary vertex (PV), the impact param-eter (IP), is measured with a resolution of (15 + 29 /p T ) µ m, where p T is the componentof the momentum transverse to the beam, in GeV/ c . Different types of charged hadronsare distinguished using information from two ring-imaging Cherenkov detectors. Photons,electrons and hadrons are identified by a calorimeter system consisting of scintillating-padand preshower detectors, an electromagnetic and a hadronic calorimeter. Muons areidentified by a system composed of alternating layers of iron and multiwire proportionalchambers. The online event selection is performed by a trigger, which consists of ahardware stage, based on information from the calorimeter and muon systems, followedby a software stage, which applies a full event reconstruction. The events considered inthe analysis are triggered at the hardware level when either one of the final-state tracks ofthe signal decay deposits enough energy in the calorimeter system, or when one of theother particles in the event, not reconstructed as part of the signal candidate, fulfils anytrigger requirement. At the software stage, it is required that at least one particle shouldhave high p T and high χ , where χ is defined as the difference in the primary vertex fit χ with and without the inclusion of that particle. A multivariate algorithm [50] is usedto identify secondary vertices consistent with being a two-, three-, or four-track b -hadrondecay. The PVs are fitted with and without the B candidate tracks, and the PV thatgives the smallest χ is associated with the B candidate.Simulation is required to model the invariant-mass distributions of the signal andbackground contributions and determine the selection efficiencies of the background relativeto the signal decay modes. It is also used to provide an approximation for the efficiencyvariations over the phase space of the D decay for systematic studies. In the simulation, pp collisions are generated using Pythia [51] with a specific LHCb configuration [52].Decays of unstable particles are described by
EvtGen [53], in which final-state radiationis generated using
Photos [54]. The decays D → K π + π − and D → K K + K − aregenerated uniformly over phase space. The interaction of the generated particles with thedetector, and its response, are implemented using the Geant4 toolkit [55] as describedin Ref. [56]. With the exception of the signal decay, the simulated event is reused multipletimes [57]. Some subdominant backgrounds are generated with a fast simulation [58] thatcan mimic the geometric acceptance and tracking efficiency of the LHCb detector as wellas the dynamics of the decay. 6
Selection
The selection closely follows that of Ref. [10]. Decays of K → π + π − are reconstructed intwo different ways: the first involving K mesons that decay early enough for the pions tobe reconstructed in the vertex detector; and the second containing K that decay latersuch that track segments of the pions cannot be formed in the vertex detector. The firstand second types of reconstructed K decays are referred to as long and downstream candidates, respectively. The long candidates have the best mass, momentum and vertexresolution, but approximately two-thirds of the signal candidates belong to the downstream category.The D meson candidates are built by combining a K candidate with two tracksassigned either the pion or kaon hypothesis. A B candidate is then formed by combiningthe D meson candidate with a further track. At each stage of combination, selectionrequirements are placed to ensure good quality vertices, and K and D candidate invariant-masses are required to be close to their nominal mass [59]. Mutually exclusive particleidentification (PID) requirements are placed on the companion track from the B decayto separate B ± → DK ± and B ± → Dπ ± candidates, where the companion refers to thefinal state π ± or K ± meson produced in the B ± → Dh ± decay. PID requirements are alsoplaced on the charged decay products of the D meson to reduce combinatorial background.A series of selection requirements are placed on the candidates to remove background fromother B meson decays. A background from B ± → Dh ± decays where the D meson decaysto either π + π − π + π − or K + K − π + π − is rejected by requiring that the long K candidatesdecay a significant distance from the D vertex. Similarly, the D meson is required to havetravelled a significant distance from the B vertex to suppress B decays with the samefinal state, but where there is no intermediate D meson decay. Semileptonic decays of thetype D → K ∗− l + ν , where charge-conjugate decays are implied, can be reconstructed as D → K h + h − with expected contamination rates of the order of a percent. To suppresselectron to pion misidentification, a veto is placed on the pion from the D decay that hasthe opposite charge with respect to the companion particle, if the PID response suggests itis an electron. To suppress the similar muonic background, it is required that the chargedtrack from the D decay has no corresponding activity in the muon detector. This vetoalso suppresses signal decays where the pion or kaon meson decays before reaching themuon detector. Therefore, it is applied on both charged tracks from the D decay, as theseevents have a worse resolution on the Dalitz plot, which is undesirable. Finally, the samerequirement is placed on the companion track to suppress B → Dµν decays.The large remaining combinatorial background is suppressed through the use of aboosted decision tree (BDT) [60, 61] multivariate classifier. The BDT is trained onsimulated signal events. The background training sample is obtained from the far uppersideband of the m ( Dh ± ) mass distribution between 5800-7000 MeV/ c , in order to providea sample independent from the data which will be used in the fit to determine the CP observables. A separate BDT is trained for B decays containing long or downstream K candidates. The input variables given to each BDT include momenta of the B , D ,and companion particles, the absolute and relative positions of decay vertices, as well asparameters that quantify the fit quality in the reconstruction; the parameter set is identicalto the one used in the previous LHCb measurement and listed in detail in Ref. [10]. TheBDT has been proven not to bias the m ( Dh ± ) distribution. A series of pseudoexperimentsare run to find the threshold values for the two BDTs which provide the best sensitivity7 igure 2: Dalitz plot for D decays of (left) B + → DK + and (right) B − → DK − candidatesin the signal region, in the (top) D → K π + π − and (bottom) D → K K + K − channels. Thehorizontal and vertical axes are interchanged between the B + and B − decay plots to aidvisualisation of the CP asymmetries between the two distributions. to γ . This requirement rejects approximately 98% of the combinatorial background thatsurvives all other selection requirements, while having an efficiency of approximately 93%in simulated B ± → DK ± decays. The selection applied to B ± → DK ± and B ± → Dπ ± candidates is identical between the two decay modes with the exception of the PIDrequirement on the companion track.A signal region is defined as within 30 MeV/ c of the B -meson mass [59]. The phase-space distributions for candidates in this range are shown in the Dalitz plots of Fig. 2for B ± → DK ± candidates. The data are split by the final state of the D decay and bythe charge of the B meson. Small differences between the phase-space distributions in B + → DK + and B − → DK − decays are visible in the K π + π − final state. DK and Dπ invariant-mass spectra The analysis uses a two-stage strategy to determine the CP observables. First, an extendedmaximum-likelihood fit to the invariant-mass spectrum of all selected B ± candidates in8
200 5400 5600 5800 m ( DK ± ) [MeV/ c ]0100200300400500600 LHCb C a nd i d a t e s / ( M e V / c ) B ± → DK ± B ± → Dπ ± B → D ∗ ( → D [ π ∓ ]) K ± B ± → D ∗ ( → D [ π ]) K ± B ± → D ∗ ( → D [ γ ]) K ± B ± → D [ π ] K ± B s → D [ π ± ] K ∓ Part. reco. mis-IDCombinatorialData m ( Dπ ± ) [MeV/ c ]02000400060008000 LHCb C a nd i d a t e s / ( M e V / c ) B ± → Dπ ± B ± → DK ± B → D ∗ ( → D [ π ∓ ]) π ± B ± → D ∗ ( → D [ π ]) π ± B ± → D ∗ ( → D [ γ ]) π ± B ± → D [ π ] π ± CombinatorialData m ( DK ± ) [MeV/ c ]0200400600800100012001400 LHCb C a nd i d a t e s / ( M e V / c ) B ± → DK ± B ± → Dπ ± B → D ∗ ( → D [ π ∓ ]) K ± B ± → D ∗ ( → D [ π ]) K ± B ± → D ∗ ( → D [ γ ]) K ± B ± → D [ π ] K ± B s → D [ π ± ] K ∓ Part. reco. mis-IDCombinatorialData m ( Dπ ± ) [MeV/ c ]025005000750010000125001500017500 LHCb C a nd i d a t e s / ( M e V / c ) B ± → Dπ ± B ± → DK ± B → D ∗ ( → D [ π ∓ ]) π ± B ± → D ∗ ( → D [ π ]) π ± B ± → D ∗ ( → D [ γ ]) π ± B ± → D [ π ] π ± CombinatorialData
Figure 3: Invariant mass distributions for the (left) B ± → DK ± channel and (right) B ± → Dπ ± channel with D → K π + π − . The top (bottom) plots show data where the K candidate is long ( downstream ). A particle within square brackets in the legend denotes the particle that has notbeen reconstructed. the mass range 5080 to 5800 MeV/ c is performed, with no partition of the D phase space.This fit is referred to as the global fit. The global fit is used to determine the signal andbackground component parameterisations, which are subsequently used in a second stagewhere the data are split by B charge and partitioned into the Dalitz plot bins to determinethe CP observables.The invariant mass distributions of the selected B ± candidates are shown for D → K π + π − and D → K K + K − candidates in Figs. 3 and 4, respectively, together withthe results of the global fit superimposed. The invariant mass is kinematically constrainedthrough a fit imposed on the full B ± decay chain [62]. The D and K candidates areconstrained to their known masses [59] and the B ± candidate momentum vector is requiredto point towards the associated PV. The data sample is split into 8 categories dependingon the reconstructed B decay, D decay mode, and K category, since the latter exhibitsslightly different mass resolutions. The fit is performed simultaneously for all categoriesin order to allow parameters to be shared.The peaks centered around 5280 MeV/ c correspond to the signal B ± → DK ± and B ± → Dπ ± candidates. The parameterisation for the signal invariant-mass shape isdetermined from simulation; the invariant-mass distribution is modelled with a sum of9
200 5400 5600 5800 m ( DK ± ) [MeV/ c ]020406080100 LHCb C a nd i d a t e s / ( M e V / c ) B ± → DK ± B ± → Dπ ± B → D ∗ ( → D [ π ∓ ]) K ± B ± → D ∗ ( → D [ π ]) K ± B ± → D ∗ ( → D [ γ ]) K ± B ± → D [ π ] K ± B s → D [ π ± ] K ∓ Part. reco. mis-IDCombinatorialData m ( Dπ ± ) [MeV/ c ]020040060080010001200 LHCb C a nd i d a t e s / ( M e V / c ) B ± → Dπ ± B ± → DK ± B → D ∗ ( → D [ π ∓ ]) π ± B ± → D ∗ ( → D [ π ]) π ± B ± → D ∗ ( → D [ γ ]) π ± B ± → D [ π ] π ± CombinatorialData m ( DK ± ) [MeV/ c ]050100150200 LHCb C a nd i d a t e s / ( M e V / c ) B ± → DK ± B ± → Dπ ± B → D ∗ ( → D [ π ∓ ]) K ± B ± → D ∗ ( → D [ π ]) K ± B ± → D ∗ ( → D [ γ ]) K ± B ± → D [ π ] K ± B s → D [ π ± ] K ∓ Part. reco. mis-IDCombinatorialData m ( Dπ ± ) [MeV/ c ]05001000150020002500 LHCb C a nd i d a t e s / ( M e V / c ) B ± → Dπ ± B ± → DK ± B → D ∗ ( → D [ π ∓ ]) π ± B ± → D ∗ ( → D [ π ]) π ± B ± → D ∗ ( → D [ γ ]) π ± B ± → D [ π ] π ± CombinatorialData
Figure 4: Invariant mass distributions for the (left) B ± → DK ± channel and (right) B ± → Dπ ± channel with D → K K + K − . The top (bottom) plots show data where the K candidate is long ( downstream ). A particle within square brackets in the legend denotes the particle that hasnot been reconstructed. the probability density function (PDF) for a Gaussian distribution, f G ( m | m B , σ ), anda modified Gaussian PDF that is used to account for the radiative tail and the widerresolution of signal events that are poorly reconstructed. The modified Gaussian has theform f MG ( m | m B , σ, α L , α R , β ) ∝ exp (cid:104) − ∆ m (1+ β ∆ m )2 σ + α L ∆ m (cid:105) , ∆ m = m − m B < (cid:104) − ∆ m (1+ β ∆ m )2 σ + α R ∆ m (cid:105) , ∆ m = m − m B > , , (8)which is Gaussian when ∆ m (cid:28) σ /α L/R or ∆ m (cid:29) β − (with widths of σ and (cid:112) α L/R /β ,respectively), with an exponential-like transition that is able to model the effect of theexperimental resolution of LHCb. Thus, the signal PDF has the form f signal ( m | m B , σ, α L , α R , β, k ) = k · f MG ( m | m B , σ, α L , α R , β )+ (1 − k ) · f G ( m | m B , σ ) (9)The values of the tail parameters ( α L , α R , β ) and k are fixed from simulation and arecommon for the two D decays (which is possible due to the applied kinematic constraints)10ut different for each B decay and type of K candidate. The signal mass, m B , isdetermined in data and is the same for all categories. The width, σ , of the signal PDFis determined by the data and allowed to be different for each B decay and type of K candidate. The width is narrower in B ± → DK ± decays compared to B ± → Dπ ± decays due to the smaller free energy in the decay. The width is approximately 3%narrower in decays with long K candidates. The signal yield is determined in each ofthe categories where the candidates are reconstructed as B ± → Dπ ± . The signal yieldin the corresponding category where the candidates are reconstructed as B ± → DK ± isdetermined by multiplying the B ± → Dπ ± yield by the parameters B × (cid:15) . The parameter B corresponds to the ratio of the branching fractions for B ± → DK ± and B ± → Dπ ± decays, while the correction factor, (cid:15) , takes into account the ratio of PID and selectionefficiencies, and is determined for each pair of B ± → DK ± and B ± → Dπ ± categories.The parameter B is shared across all categories and is found to be consistent with Ref. [59].To the right of the B ± → DK ± peak there is a visible contribution from B ± → Dπ ± decays that are reconstructed as B ± → DK ± decays. The corresponding contribution inthe B ± → Dπ ± category is minimal due to the smaller branching fraction of B ± → DK ± ,but is accounted for in the fit. The rates of these cross-feed backgrounds are fixed from PIDefficiencies determined in calibration data, which is reweighted to match the momentumand pseudorapidity distributions of the companion track of the signal. A data-drivenapproach is used to determine the PDF of B ± → Dπ ± decays that are reconstructed as B ± → DK ± candidates, as described in Ref. [10]. The same procedure is implemented todetermine the PDF of B ± → DK ± decays reconstructed as B ± → Dπ ± candidates.The background observed at invariant masses smaller than the signal peak are candi-dates that originate from other B -meson decays where not all decay products have beenreconstructed. Due to the selected invariant-mass range it is only necessary to consider B meson decays where a single photon or pion has not been reconstructed. This backgroundtype is split into three sources; the first where the candidate originates from a B ± or B meson, referred to as partially reconstructed background, the second where the candidateoriginates from a B s meson, and the third where the candidate originates from a B ± or B and furthermore one of the reconstructed tracks is assigned the kaon hypothesis, whenthe true particle is a pion. The latter type of background appears in the B ± → DK ± candidates and is referred to as misidentified partially reconstructed background. Thecorresponding type of background is not modelled in the B ± → Dπ ± candidates, since itis suppressed due to the branching fractions involved and the majority is removed by thelower invariant-mass requirement.There are contributions from B → D ∗± h ∓ and B ± → D ∗ h ± decays in all categories,where the pion or the photon originating from the D ∗ meson is not reconstructed. Theinvariant-mass distributions of these decays depend on the spin and mass of the missingparticle as described in Ref. [25]. The parameters of these shapes are determined fromsimulation, with the exception of a free parameter in the fit to characterise the resolution.The decays B ± , → Dπ ± π , ∓ contribute to the B ± → Dπ ± candidates where one ofthe pions from the B decay is not reconstructed. The shape of this background isdetermined from simulated B ± → Dρ ± and B → Dρ decays. The decays B ± → DK ± π and B → DK + π − contribute to the B ± → DK ± candidates where the pion is notreconstructed. The invariant-mass distribution for these events is based on the amplitudemodel of B → DK + π − decays [63]. The model is used to generate four-vectors ofthe decay products, which are smeared to account for the LHCb detector resolution.11he invariant mass is then calculated omitting the particle that is not reconstructed,and this distribution is subsequently fit to determine the fixed distribution for the fit.The same shape is used for the B ± → DK ± π decay as the corresponding amplitudemodel is not available. Finally, the B ± → DK ± candidates also have a contributionfrom B s → D π + K − decays where the pion is not reconstructed. The shape of thiscontribution is determined in a similar manner to that of B → DK + π − decays using the B s → D π + K − amplitude model determined in Ref. [64].The yield of the partially reconstructed background is a floating parameter in each B ± → Dπ ± sample and related to the yield in the corresponding B ± → DK ± samplevia the floating parameter B L and correction factors from PID and selection efficiencies.Analogously to the signal-yield parameterisation, B L is a single parameter, common to allcategories, but in this case has no direct physical meaning. The relative yield of B ± → D ∗ ( → D [ γ ]) π ± and B → D ∗ ( → D [ π ∓ ]) π ± decays, where the particle within the squarebrackets is the one not reconstructed, are fixed from branching fractions [59], and selectionefficiencies determined from simulation. The fractional yields of B ± → D ∗ ( → D [ γ ]) π ± ,and B ± , → D [ π ,π ∓ ] π ± decays are determined in the fit and are constrained to be thesame for each B ± → Dπ ± sample. Due to the lower yields in the B ± → DK ± categoryand presence of additional backgrounds, the relative fractions of the various B ± and B components are all fixed using information from branching fractions [59] and selectionefficiencies from simulation. The yield of the B s → D π + K − decays is fixed relative to theyield of B ± → Dπ ± decays in the corresponding category using branching fractions [59],the fragmentation fraction [65], and relative selection efficiencies.The shapes for the misidentified partially reconstructed backgrounds are determinedfrom simulation, weighted by the PID efficiencies from calibration data. The yield of thesebackgrounds are determined from the partially reconstructed yields in the B ± → Dπ ± candidates, and the relative selection efficiencies, which include the PID efficiencies fromcalibration data and the selection efficiency due to requiring the reconstructed invariantmass to be above 5080 MeV/ c . The final component of background is combinatorial whichis parameterised by an exponential function. The yield and slope of this background ineach category are free parameters. The yields of the different signals and backgroundtypes are integrated in the signal region 5249–5309 MeV/ c and reported in Table 1. The B ± → DK ± yields in categories of different D decay and type of K candidate haveuncertainties that are smaller than their Poisson uncertainty since they are determinedusing the value of B , which is measured from all B ± → DK ± candidates. CP observables To determine the CP observables the data are divided into 16 categories ( B decay, B charge, D decay, type of K candidate) and then further split into each Dalitz plot bin.A simultaneous fit to the invariant-mass distribution is performed in all categories andDalitz plot bins. The mass shape parameters are all fixed from the global mass fit. Thelower limit of the invariant mass is increased to 5150 MeV/ c to remove a large fraction ofthe partially reconstructed background. The composition of the remaining backgroundis determined from the global fit described in Sect. 5. The signal yield in each bin isparameterised using Eq. (5) or the analogous set of expressions for B ± → Dπ ± . Theseequations are normalised such that the parameters h B ± represent the total observed signal12 able 1: The signal and background yields in the region m B ∈ [5249 , c as obtainedin the fit. For the B ± → DK ± candidates, the yield of the partially reconstructed backgroundincludes the contributions from B s decays and misidentified partially reconstructed backgrounds. Reconstructed as: B ± → DK ± B ± → Dπ ± D decay Component long downstream long downstream D → K π + π − B ± → DK ± ±
41 8735 ±
89 182 ± ± B ± → Dπ ± ± ± ±
240 124786 ± ± ± ± ± ±
36 458 ±
60 392 ±
66 1142 ± D → K K + K − B ± → DK ± ± ±
15 29 ± ± B ± → Dπ ± ± ± ±
92 17863 ± ± ± ± ± ±
13 75 ±
20 127 ±
32 288 ± yield in each category, and these are measured independently.The parameters x DK ± , y DK ± , x Dπξ , and y Dπξ are free parameters in the fit and commonto the K and D decay categories. The parameters c i and s i are fixed to those determinedfrom the combination of BESIII and CLEO data in Ref. [30] for the D → K π + π − decaysand in Ref. [31] for the D → K K + K − decays. The F i parameters for each D decay aredetermined in the fit; separate sets of F i parameters are determined for the two types of K candidates because the efficiency profile over the Dalitz plot differs between the K selections. Since the F i parameters must satisfy the constraints (cid:80) i F i = 1 , F i ∈ [0 , F i parameters are reparameterised as a series of recursive fractions withparameters, R i , determined in the fit. The relation between the F i and R i parameters isgiven by F i = R i , i = −NR i (cid:81) j
05 0 .
00 0 .
05 0 . x DK − . − . . . . y D K γB + B − LHCb − . − .
05 0 . x Dπξ − . . . y D π ξ LHCb
Figure 5: Confidence levels at 68.2 % and 95.5 % probability for (left, blue) ( x DK ± + , y DK ± + ),(left, red) ( x DK ± − , y DK ± − ), and (right, green) ( x Dπ ± ξ , y Dπ ± ξ ) as measured in B ± → DK ± and B ± → Dπ ± decays with a profile likelihood scan. The black dots show the central values by a Gaussian function and are found to have mean and width consistent with 0 and 1,respectively.The results for x DK ± , y DK ± , x Dπξ , and y Dπξ are presented in Fig. 5 along with theirlikelihood contours, where only statistical uncertainties are considered. The two vectorsdefined by the origin and the end-point coordinates ( x DK − , y DK − ) and ( x DK + , y DK + ) give thevalues for r DKB for B − and B + decays. The signature for CP violation is that these vectorsmust have non-zero length and have a non-zero opening angle between them, since thisangle is equal to 2 γ , as illustrated on the figure. Therefore, the data exhibit unambiguousfeatures of CP violation as expected. The relation between the hadronic parameters in B ± → Dπ ± and B ± → DK ± decays is also illustrated in Fig 5, where the vector definedby the coordinates ( x Dπξ , y Dπξ ) is the relative magnitude of r B between the two decay modes.It is consistent with the expectation of 5% [42].A series of cross checks is carried out by performing separate fits by splitting the datasample into data-taking periods by year, type of K candidate, D -decay, and magnetpolarity. The results are consistent between the datasets. As an additional cross check, thetwo-stage fit procedure is repeated with a number of different selections applied to the data.Of particular interest are the alternative selections that significantly affect the presence ofspecific backgrounds: the fits where the value of the BDT threshold value is varied todecrease the level of combinatorial background and those where the choice of PID selectionis changed to result in a substantially lower level of misidentified B ± → Dπ ± decays andmisidentified partially reconstructed background in the B ± → DK ± candidates. Thevariations in the central values for the CP observables are consistent within the statisticaluncertainty associated with the change in the data sample.In order to assess the goodness of fit and to demonstrate that the equations involvingthe CP parameters provide a good description of the signal yields in data, an alternative fitis performed where the signal yield in each B ± → DK ± and B ± → Dπ ± bin is measuredindependently. These yields are compared with those predicted from the values of14 i − . . . . . . ( N −− i − N ++ i ) / ( N −− i + N ++ i ) K S π + π − K S K + K − LHCb B ± → DK ± -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 -2 -1 1 2Effective bin i − . − . − . − . . . . ( N −− i − N ++ i ) / ( N −− i + N ++ i ) K S π + π − K S K + K − LHCb B ± → Dπ ± Figure 6: The bin-by-bin asymmetries ( N −− i − N ++ i ) / ( N −− i + N ++ i ) for each Dalitz-plot bin numberfor (left) B ± → DK ± decays and (right) B ± → Dπ ± decays. The prediction from the centralvalues of the CP -violation observables is shown with a solid line and the asymmetries obtainedin fits with independent bin yields are shown with the error bars. The predicted asymmetries ina fit that does not allow for CP violation are shown with a dotted line. The vertical dashed lineseparates the K π + π − and K K + K − bins on the horizontal axis. ( x DK ± , y DK ± ) in the default fit and a high level of agreement is found. In order to visualisethe observed CP violation, the asymmetry, ( N −− i − N ++ i ) / ( N −− i + N ++ i ), is computed for effective bin pairs , defined to comprise bin i for a B + decay and bin − i for a B − decay.Figure 6 shows the obtained asymmetries and those predicted by the values of the CP observables obtained in the fit. A further fit that does not allow for CP violation is carriedout by imposing the conditions x DK + = x DK − , y DK + = y DK − . This determines the predictedasymmetry arising from detector and production effects. In the B ± → DK ± sample the CP violation is clearly visible as the data are inconsistent with the CP -conserved hypothesis.The predicted asymmetries in the B ± → Dπ ± decay are an order of magnitude smaller.The data in this analysis cannot distinguish between the CP -violating and CP -conservingpredictions for B ± → Dπ ± due to the relatively large statistical uncertainties. Systematic uncertainties on the measurements of the CP observables are evaluated andare presented in Table 2. The limited precision on ( c i , s i ) coming from the combinedBESIII and CLEO [30, 31] results induces uncertainties on the CP parameters. Theseuncertainties are evaluated by fitting the data multiple times, each time with different ( c i , s i ) values sampled according to their experimental uncertainties and correlations. Theresulting standard deviation of each distribution of the CP observables is assigned as thesystematic uncertainty. The size of the systematic uncertainty is notably much smallerthan the corresponding uncertainty in Ref. [10] due to the improvement in the knowledgeof these strong-phase parameters [30, 31].The non-uniform efficiency profile over the Dalitz plot means that the values of ( c i , s i ) The detailed output of this study is available as supplemental material to this paper at [publisher willinsert URL], and provides sufficient information to determine the correlation between this uncertaintyand the corresponding uncertainties of future γ measurements that also rely on the same strong-phasemeasurements. able 2: Overview of all sources of uncertainty, σ , on x DK ± , y DK ± , x Dπξ , and y Dπξ . All uncertaintiesare quoted × − . Source σ ( x DK − ) σ ( y DK − ) σ ( x DK + ) σ ( y DK + ) σ ( x Dπξ ) σ ( y Dπξ )Statistical 0.96 1.14 0.96 1.20 1.99 2.34Strong-phase inputs 0.23 0.35 0.18 0.28 0.14 0.18Efficiency correction of ( c i , s i ) 0.11 0.05 0.05 0.10 0.08 0.09Mass-shape parameters 0.05 0.08 0.03 0.08 0.16 0.17Mass-shape bin dependence 0.05 0.07 0.04 0.08 0.07 0.09Part. reco. physics effects 0.04 0.10 0.15 0.05 0.10 0.09 CP violation of K D mixing 0.04 0.01 0.00 0.02 0.02 0.01PID efficiencies 0.03 0.03 0.01 0.05 0.02 0.02Fixed yield ratios 0.05 0.06 0.03 0.06 0.02 0.02Dalitz-bin migration 0.04 0.08 0.08 0.11 0.18 0.10Bias correction 0.04 0.03 0.02 0.04 0.09 0.05Small backgrounds 0.11 0.16 0.13 0.12 0.08 0.13Total LHCb-related uncertainty 0.20 0.25 0.24 0.26 0.32 0.54Total systematic uncertainty 0.31 0.43 0.30 0.38 0.35 0.57 appropriate for this analysis can differ from those measured in Refs. [30, 31], whichcorrespond to the case where there is no variation in efficiency over the Dalitz plot.Amplitude models from Refs. [47, 66] are used to calculate the values of c i and s i bothwith and without the efficiency profiles determined from simulation. The shift in the c i and s i values is taken as an estimate of the size of this effect. Pseudoexperiments aregenerated assuming the shifted c i and s i values and fit with the default values of c i and s i . The mean bias of each CP observable is assigned as a systematic uncertainty. Theassumption that the relative variation of efficiency over the Dalitz plot is the same inselected B ± → DK ± and B ± → Dπ ± candidates is verified in simulated samples of similarsize to the B ± → Dπ ± yields observed in data. No statistically significant difference isobserved and no systematic uncertainty is assigned.The uncertainties from the fixed invariant-mass shapes determined in the global fitare propagated to the CP observables through a resampling method [67]. The followingprocedure, which takes into account the fact that some parameters are determined insimulation and others in data, is carried out a hundred times. First, the simulated decaysthat were used to determine the nominal mass shape parameters are each resampled withreplacement and fit to determine an alternative set of parameters. Then, the final datasetis resampled with replacement and the global fit is repeated using the alternative fixedshape parameters, to determine alternative values for the parameters that are determinedfrom real data. Finally, the CP fit is performed using the alternative invariant-massparameterisations, without resampling the final dataset. The standard deviation of the CP observables obtained via this procedure is taken as the systematic uncertainty due tothe fixed parameterisation.The PID efficiencies are varied within their uncertainties in the global and CP fit andthe standard deviation of the CP parameters is taken as the systematic uncertainty. Asimilar method is used to determine the uncertainties due to the fixed fractions between16ifferent partially reconstructed backgrounds where the uncertainties on the fixed fractionsare those from the branching fractions [59] and the selection efficiencies.The CP fit assumes the same mass shape for each component in each Dalitz plot bin.For the signal and cross-feed backgrounds the shapes are redetermined in each bin using thesame procedures described in Sect. 5. The variance is very small due to weak correlationsbetween phase-space coordinates and particle kinematics. The combinatorial slope can alsovary from bin to bin, as the relative rate of combinatorial background with and without areal D meson will not be constant. The size of this effect is determined through the studyof the high invariant-mass sideband where only combinatorial background contributes.Pseudodata are generated where this variation in mass shape across the Dalitz plot bins isreplicated for signal, cross-feed and combinatorial backgrounds, and the generated samplesare fit with the default fit assumptions of the same shape in each bin. The mean bias isassigned as the systematic uncertainty.The partially reconstructed background shape is also expected to vary in each bin,however the leading source of this effect is due to the individual components of thisbackground having a different distribution over the Dalitz plot. Some partially recon-structed backgrounds will be distributed as D ( D ) → D → K h + h − for reconstructed B − ( B + ) candidates, while others will be distributed as a D – D admixture dependingon the relevant CP -violation parameters. Pseudodata are generated, where the D -decayphase-space distributions for B ± → D ∗ K ± and B ± → DK ∗ + background events arebased on the CP parameters reported in Ref. [68]. No CP violation is introduced intothe partially reconstructed background in the B ± → Dπ ± samples since it is expected tobe small, and the B → Dρ background is treated as an equal mix of D and D sinceeither pion can be reconstructed. The generated pseudodata are fitted with the default fitand the mean bias is assigned as the systematic uncertainty.Systematic uncertainties are assigned for small residual backgrounds that contaminatethe data sample but are not accounted for in the fit. Their impact is assessed bygenerating pseudoexperiments that contain these backgrounds and are fit with the defaultmodel. The mean bias is assigned as the uncertainty. One source of background is from Λ b → Dpπ − decays where the pion is not reconstructed and the proton is misidentified asa kaon. This background is modelled as a D -like contribution in B − decays, and has anexpected yield of 0.5% of the B ± → DK ± signal. A further, even smaller, background is Λ b → Λ + c ( → pK π + π − ) π − decays where the π + meson in the Λ + c decay is missed, and the p reconstructed as the π + from the D -decay. The effective distribution of the reconstructed D meson is unknown and is assigned to be D -like in B − decays to be conservative. Themass shapes and rates of these backgrounds are determined from simulation. Anothersource of background comes from residual B → Dµν decays, where the rate (less than0.2 % relative to the signal mode, after the applied veto) and shape are determined fromsimulation with PID efficiencies from calibration data. The residual semileptonic D decaybackground has a rate of less than 0.1% of signal and the distribution of these eventson the Dalitz plot is determined through a simplified simulation [58] taking into accountvarious K ∗ mesons. Finally, a small peaking background from B ± → D ( → K ± π ∓ ) K π ± decays where the kaon is reconstructed as the companion and the other particles areassigned to the D decay is considered. The yield of this background is determined tobe 0.5% of the signal yield in B ± → DK ± by a data driven study of the invariant-massdistribution of switched tracks. The distribution on the Dalitz plot is determined throughthe simplified simulation [58] where different K ∗± → K π ± resonances are generated.17he main effect of migration from one Dalitz plot bin to another is implicitly taken intoaccount by using the data to determine the F i , which thus include the effects of the net binmigration. However, a small effect arises because of the differences in the distributions ofthe B ± → DK ± and B ± → Dπ ± decays due to the differing hadronic decay parameters.To investigate this, data points are generated according to the amplitude model in Ref. [66]with CP observables consistent with expectation [5, 68]. To smear these data points on theDalitz plot, an event is selected from full LHCb simulation and the difference in m and m − between its true and reconstructed quantities is applied to the data point in order todetermine its reconstructed bin. The difference between true and reconstructed quantitiesis multiplied by a factor of 1.2 to account for differences in resolution between data andsimulation. Pseudoexperiments are generated based on the expected reconstructed yieldsin each bin and fit with a nominal fit where the c i and s i parameters are determined bythe amplitude model [66]. The mean bias in the CP violation parameters is taken as thesystematic uncertainty, which is small.The impact of ignoring the CP violation and matter effects in K decays is determinedthrough generating pseudoexperiments taking into account all these effects as detailedin Ref. [40], where LHCb simulation is used to obtain the K lifetime acceptance andmomentum distribution. The size of the bias found is consistent with those expectedfrom Ref. [40], where it was also predicted that the relative uncertainties on B ± → Dπ ± observables are be expected to be larger than for B ± → DK ± observables. This is foundto be true, but even the most significant uncertainty, on y Dπξ , is an order of magnitudesmaller than the corresponding statistical uncertainty. The effect of ignoring charm mixingis expected to be minimal, given that the first-order effects are inherently taken intoaccount when the F i parameters are measured as a part of the fit [39]. This is verifiedby generating pseudoexperiments that include charm mixing and fitting them with thenominal fit.In previous studies, a bias correction has been necessary when similar measurementshave been performed with lower signal yields [10] leading to some fit instabilities. Inthis case, the higher yields have resulted in a bias that is of negligible size and henceno correction is applied. Nonetheless, the uncertainty on the biases are assigned as thesystematic uncertainties.In general, all the systematic uncertainties are small in comparison to the statisticaluncertainties. There is no dominant source of systematic uncertainty for all CP observables,however the description of backgrounds, either those not modelled or the modelling ofthe partially reconstructed backgrounds are some of the larger sources. The uncertaintyattributed to the precision of the strong-phase measurements is of similar size to the totalLHCb-related systematic uncertainty. 18 Interpretation
The CP observables are measured to be x DK − = ( 5 . ± . ± . ± . × − ,y DK − = ( 6 . ± . ± . ± . × − ,x DK + = ( − . ± . ± . ± . × − ,y DK + = ( − . ± . ± . ± . × − ,x Dπξ = ( − . ± . ± . ± . × − ,y Dπξ = ( 0 . ± . ± . ± . × − , (11)where the first uncertainty is statistical, the second arises from systematic effects in themethod or detector considerations, and the third from external inputs of strong-phasemeasurements from the combination of CLEO and BESIII [28, 30] results. The correlationmatrices for each source of uncertainty are available in the appendices in Tables 3-5.The CP observables are interpreted in terms of the underlying physics parameters γ , and r B and δ B for each B ± decay mode. The interpretation is done via a maximumlikelihood fit using a frequentist treatment as described in Ref. [45]. The solution for thephysics parameters has a two-fold ambiguity as the equations are invariant under thesimultaneous substitutions γ → γ + 180 ◦ and δ B → δ B + 180 ◦ . The solution that satisfies0 < γ < ◦ is chosen, and leads to γ = (68 . +5 . − . ) ◦ ,r DK ± B = 0 . +0 . − . ,δ DK ± B = (118 . +5 . − . ) ◦ ,r Dπ ± B = 0 . ± . ,δ Dπ ± B = (291 +24 − ) ◦ . (12)Pseudoexperiments are carried out to confirm that the value of γ is extracted withoutbias. This is the most precise single measurement of γ to date. The result is consistentwith the indirect determination γ = (cid:0) . +0 . − . (cid:1) ◦ [6]. The confidence limits for γ areillustrated in Fig. 7, while Fig. 8 shows the two-dimensional confidence regions obtainedfor the ( γ , r B ) and ( r B , δ B ) parameter combinations. The results for γ , r DKB ,and δ DKB are consistent with their current world averages [5, 6] which include the LHCb resultsobtained with the 2011–2016 data. The knowledge of r DπB and δ DπB from other sourcesis limited, with the combination of many observables presented in Ref. [45] providingtwo possible solutions. The results here have a single solution, and favour a centralvalue that is consistent with the expectation for r DπB , given the value of r DKB and CKMelements [42]. This is likely to remove the two-solution aspect in future combinationsof γ and associated hadronic parameters. The low value of r DπB means that the directcontribution to γ from B ± → Dπ ± decays in this measurement is minimal. However theability to use this decay mode to determine the efficiency has approximately halved thetotal LHCb related experimental systematic uncertainty in comparison to Ref. [10]. Thenew inputs from the BESIII collaboration have led to the strong-phase related uncertaintyon γ to be approximately 1 ◦ , which is a significant reduction compared to the propagateduncertainty when only CLEO measurements were available.19 C L -
50 60 70 80 90 ] (cid:176) [ g LHCb
Figure 7: Confidence limits for the CKM angle γ obtained using the method described inRef. [45].
50 60 70 80 90 ] (cid:176) [ g D K B r LHCb
100 110 120 130 140 150 ] (cid:176) [ DKB d D K B r LHCb
50 60 70 80 90 ] (cid:176) [ g p D B r LHCb
200 250 300 350 ] (cid:176) [ p DB d p D B r LHCb
Figure 8: The 68 % and 95 % confidence regions for combinations of the physics parameters( γ, r
DKB , δ
DKB , r
DπB , δ
DπB ) obtained using the methods described in Ref. [45]. Conclusions
In summary, the decays B ± → DK ± and B ± → Dπ ± with D → K π + π − or D → K K + K − obtained from the full LHCb dataset collected to date, correspondingto an integrated luminosity of 9 fb − , have been analysed to determine the CKM angle γ . The sensitivity to γ comes almost entirely from B ± → DK ± decays where the sig-nal yields of reconstructed events are approximately 13600 (1900) in the D → K π + π − ( D → K K + K − ) decay modes. The B ± → Dπ ± data is primarily used to control effectsdue to selection and reconstruction of the data, which leads to small experimental sys-tematic uncertainties. The analysis is performed in bins of the D -decay Dalitz plot anda combination of measurements performed by the CLEO and BESIII collaborations pre-sented in Refs. [30, 31] are used to provide input on the D -decay strong-phase parameters( c i , s i ). Such an approach allows the analysis to be free from model-dependent assumptionson the strong-phase variation across the Dalitz plot. The analysis also determines thehadronic parameters r B and δ B for each B ± decay mode. Those of the B ± → DK ± decayare consistent with current averages, and those of the B ± → Dπ ± decay are obtained withthe best precision to date, and have not previously been measured using these D -decaymodes. The CKM angle γ is determined to be γ = (68 . +5 . − . ) ◦ , where the result is limitedby statistical uncertainties. This is the most precise measurement of γ from a singleanalysis, and supersedes the results in Refs. [10, 32]. Acknowledgements
We express our gratitude to our colleagues in the CERN accelerator departments for theexcellent performance of the LHC. We thank the technical and administrative staff at theLHCb institutes. We acknowledge support from CERN and from the national agencies:CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST and NSFC (China); CNRS/IN2P3(France); BMBF, DFG and MPG (Germany); INFN (Italy); NWO (Netherlands); MNiSWand NCN (Poland); MEN/IFA (Romania); MSHE (Russia); MICINN (Spain); SNSFand SER (Switzerland); NASU (Ukraine); STFC (United Kingdom); DOE NP and NSF(USA). We acknowledge the computing resources that are provided by CERN, IN2P3(France), KIT and DESY (Germany), INFN (Italy), SURF (Netherlands), PIC (Spain),GridPP (United Kingdom), RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID (Poland) and OSC (USA). We are indebtedto the communities behind the multiple open-source software packages on which wedepend. Individual groups or members have received support from AvH Foundation(Germany); EPLANET, Marie Sk(cid:32)lodowska-Curie Actions and ERC (European Union);A*MIDEX, ANR, Labex P2IO and OCEVU, and R´egion Auvergne-Rhˆone-Alpes (France);Key Research Program of Frontier Sciences of CAS, CAS PIFI, Thousand Talents Program,and Sci. & Tech. Program of Guangzhou (China); RFBR, RSF and Yandex LLC (Russia);GVA, XuntaGal and GENCAT (Spain); the Royal Society and the Leverhulme Trust(United Kingdom). 21 ppendicesA Correlation matrices
The correlations matrices for the measured observables are shown in Tables 3–5 for thestatistical uncertainties, the experimental systematic uncertainties, and the strong-phase-related uncertainties, respectively. 22 able 3: Statistical uncertainties, σ , and correlation matrix for x DK ± , y DK ± , x Dπξ , and y Dπξ . Uncertainty ( × − ) x DK − y DK − x DK + y DK + x Dπξ y Dπξ σ .
96 1 .
14 0 .
98 1 .
23 1 .
99 2 . x DK − y DK − x DK + y DK + x Dπξ y Dπξ x DK − − . − .
013 0 .
019 0 . − . y DK − − . − .
010 0 .
097 0 . x DK + . − .
108 0 . y DK + − . − . x Dπξ . y Dπξ Table 4: Total LHCb-related systematic uncertainties, σ , for x DK ± , y DK ± , x Dπξ , and y Dπξ , and thecorresponding correlation matrix.
Uncertainty ( × − ) x DK − y DK − x DK + y DK + x Dπξ y Dπξ σ .
20 0 .
25 0 .
24 0 .
26 0 .
32 0 . x DK − y DK − x DK + y DK + x Dπξ y Dπξ x DK − .
864 0 .
734 0 .
897 0 .
349 0 . y DK − .
874 0 .
903 0 .
408 0 . x DK + .
771 0 .
563 0 . y DK + .
507 0 . x Dπξ . y Dπξ able 5: Systematic uncertainties, σ , for x DK ± , y DK ± , x Dπξ , and y Dπξ due to strong-phase inputs,the corresponding correlation matrix.
Uncertainty ( × − ) x DK − y DK − x DK + y DK + x Dπξ y Dπξ σ .
23 0 .
35 0 .
18 0 .
28 0 .
14 0 . x DK − y DK − x DK + y DK + x Dπξ y Dπξ x DK − − . − .
490 0 .
322 0 .
189 0 . y DK − . − . − . − . x DK + .
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Denysenko , D. Derkach , O. Deschamps , F. Desse ,F. Dettori ,f , B. Dey , P. Di Nezza , S. Didenko , L. Dieste Maronas , H. Dijkstra ,V. Dobishuk , A.M. Donohoe , F. Dordei , M. Dorigo ,w , A.C. dos Reis , L. Douglas ,A. Dovbnya , A.G. Downes , K. Dreimanis , M.W. Dudek , L. Dufour , V. Duk ,P. Durante , J.M. Durham , D. Dutta , M. Dziewiecki , A. Dziurda , A. Dzyuba ,S. Easo , U. Egede , V. Egorychev , S. Eidelman ,v , S. Eisenhardt , S. Ek-In ,L. Eklund , S. Ely , A. Ene , E. Epple , S. Escher , J. Eschle , S. Esen , T. Evans ,A. Falabella , J. Fan , Y. Fan , B. Fang , N. Farley , S. Farry , D. Fazzini ,j , P. Fedin ,M. F´eo , P. Fernandez Declara , A. Fernandez Prieto , J.M. Fernandez-tenllado Arribas ,F. Ferrari ,e , L. Ferreira Lopes , F. Ferreira Rodrigues , S. Ferreres Sole , M. Ferrillo ,M. Ferro-Luzzi , S. Filippov , R.A. Fini , M. Fiorini ,g , M. Firlej , K.M. Fischer ,C. Fitzpatrick , T. Fiutowski , F. Fleuret ,b , M. Fontana , F. Fontanelli ,i , R. Forty , . Franco Lima , M. Franco Sevilla , M. Frank , E. Franzoso , G. Frau , C. Frei ,D.A. Friday , J. Fu , Q. Fuehring , W. Funk , E. Gabriel , T. Gaintseva ,A. Gallas Torreira , D. Galli ,e , S. Gallorini , S. Gambetta , Y. Gan , M. Gandelman ,P. Gandini , Y. Gao , M. Garau , L.M. Garcia Martin , P. Garcia Moreno ,J. Garc´ıa Pardi˜nas , B. Garcia Plana , F.A. Garcia Rosales , L. Garrido , D. Gascon ,C. Gaspar , R.E. Geertsema , D. Gerick , L.L. Gerken , E. Gersabeck , M. Gersabeck ,T. Gershon , D. Gerstel , Ph. Ghez , V. Gibson , M. Giovannetti ,k , A. Giovent`u ,P. Gironella Gironell , L. Giubega , C. Giugliano ,g , K. Gizdov , E.L. Gkougkousis ,V.V. Gligorov , C. G¨obel , E. Golobardes , D. Golubkov , A. Golutvin , , A. Gomes ,a ,S. Gomez Fernandez , F. Goncalves Abrantes , M. Goncerz , G. Gong , P. Gorbounov ,I.V. Gorelov , C. Gotti ,j , E. Govorkova , J.P. Grabowski , R. Graciani Diaz ,T. Grammatico , L.A. Granado Cardoso , E. Graug´es , E. Graverini , G. Graziani ,A. Grecu , L.M. Greeven , P. Griffith , L. Grillo , S. Gromov , L. Gruber ,B.R. Gruberg Cazon , C. Gu , M. Guarise , P. A. G¨unther , E. Gushchin , A. Guth ,Y. Guz , , T. Gys , T. Hadavizadeh , G. Haefeli , C. Haen , J. Haimberger ,S.C. Haines , T. Halewood-leagas , P.M. Hamilton , Q. Han , X. Han , T.H. Hancock ,S. Hansmann-Menzemer , N. Harnew , T. Harrison , C. Hasse , M. Hatch , J. He ,M. Hecker , K. Heijhoff , K. Heinicke , A.M. Hennequin , K. Hennessy , L. Henry , ,J. Heuel , A. Hicheur , D. Hill , M. Hilton , S.E. Hollitt , P.H. Hopchev , J. Hu , J. Hu ,W. Hu , W. Huang , X. Huang , W. Hulsbergen , R.J. Hunter , M. Hushchyn ,D. Hutchcroft , D. Hynds , P. Ibis , M. Idzik , D. Ilin , P. Ilten , A. Inglessi ,A. Ishteev , K. Ivshin , R. Jacobsson , S. Jakobsen , E. Jans , B.K. Jashal ,A. Jawahery , V. Jevtic , M. Jezabek , F. Jiang , M. John , D. Johnson , C.R. Jones ,T.P. Jones , B. Jost , N. Jurik , S. Kandybei , Y. Kang , M. Karacson , J.M. Kariuki ,N. Kazeev , M. Kecke , F. Keizer , , M. Kenzie , T. Ketel , B. Khanji , A. Kharisova ,S. Kholodenko , K.E. Kim , T. Kirn , V.S. Kirsebom , O. Kitouni , S. Klaver ,K. Klimaszewski , S. Koliiev , A. Kondybayeva , A. Konoplyannikov , P. Kopciewicz ,R. Kopecna , P. Koppenburg , M. Korolev , I. Kostiuk , , O. Kot , S. Kotriakhova , ,P. Kravchenko , L. Kravchuk , R.D. Krawczyk , M. Kreps , F. Kress , S. Kretzschmar ,P. Krokovny ,v , W. Krupa , W. Krzemien , W. Kucewicz ,l , M. Kucharczyk ,V. Kudryavtsev ,v , H.S. Kuindersma , G.J. Kunde , T. Kvaratskheliya , D. Lacarrere ,G. Lafferty , A. Lai , A. Lampis , D. Lancierini , J.J. Lane , R. Lane , G. Lanfranchi ,C. Langenbruch , J. Langer , O. Lantwin , , T. Latham , F. Lazzari ,t , R. Le Gac ,S.H. Lee , R. Lef`evre , A. Leflat , S. Legotin , O. Leroy , T. Lesiak , B. Leverington ,H. Li , L. Li , P. Li , X. Li , Y. Li , Y. Li , Z. Li , X. Liang , T. Lin , R. Lindner ,V. Lisovskyi , R. Litvinov , G. Liu , H. Liu , S. Liu , X. Liu , A. Loi , J. Lomba Castro ,I. Longstaff , J.H. Lopes , G. Loustau , G.H. Lovell , Y. Lu , D. Lucchesi ,m , S. Luchuk ,M. Lucio Martinez , V. Lukashenko , Y. Luo , A. Lupato , E. Luppi ,g , O. Lupton ,A. Lusiani ,r , X. Lyu , L. Ma , S. Maccolini ,e , F. Machefert , F. Maciuc , V. Macko ,P. Mackowiak , S. Maddrell-Mander , O. Madejczyk , L.R. Madhan Mohan , O. Maev ,A. Maevskiy , D. Maisuzenko , M.W. Majewski , S. Malde , B. Malecki , A. Malinin ,T. Maltsev ,v , H. Malygina , G. Manca ,f , G. Mancinelli , R. Manera Escalero ,D. Manuzzi ,e , D. Marangotto ,o , J. Maratas ,u , J.F. Marchand , U. Marconi ,S. Mariani , ,h , C. Marin Benito , M. Marinangeli , P. Marino , J. Marks ,P.J. Marshall , G. Martellotti , L. Martinazzoli ,j , M. Martinelli ,j , D. Martinez Santos ,F. Martinez Vidal , A. Massafferri , M. Materok , R. Matev , A. Mathad , Z. Mathe ,V. Matiunin , C. Matteuzzi , K.R. Mattioli , A. Mauri , E. Maurice ,b , J. Mauricio ,M. Mazurek , M. McCann , L. Mcconnell , T.H. Mcgrath , A. McNab , R. McNulty ,J.V. Mead , B. Meadows , C. Meaux , G. Meier , N. Meinert , D. Melnychuk ,S. Meloni ,j , M. Merk , , A. Merli , L. Meyer Garcia , M. Mikhasenko , D.A. Milanes , . Millard , M. Milovanovic , M.-N. Minard , L. Minzoni ,g , S.E. Mitchell , B. Mitreska ,D.S. Mitzel , A. M¨odden , R.A. Mohammed , R.D. Moise , T. Momb¨acher , I.A. Monroy ,S. Monteil , M. Morandin , G. Morello , M.J. Morello ,r , J. Moron , A.B. Morris ,A.G. Morris , R. Mountain , H. Mu , F. Muheim , M. Mukherjee , M. Mulder ,D. M¨uller , K. M¨uller , C.H. Murphy , D. Murray , P. Muzzetto , P. Naik , T. Nakada ,R. Nandakumar , T. Nanut , I. Nasteva , M. Needham , I. Neri ,g , N. Neri ,o ,S. Neubert , N. Neufeld , R. Newcombe , T.D. Nguyen , C. Nguyen-Mau , E.M. Niel ,S. Nieswand , N. Nikitin , N.S. Nolte , C. Nunez , A. Oblakowska-Mucha , V. Obraztsov ,D.P. O’Hanlon , R. Oldeman ,f , C.J.G. Onderwater , A. Ossowska ,J.M. Otalora Goicochea , T. Ovsiannikova , P. Owen , A. Oyanguren , B. Pagare ,P.R. Pais , T. Pajero , ,r , A. Palano , M. Palutan , Y. Pan , G. Panshin ,A. Papanestis , M. Pappagallo ,d , L.L. Pappalardo ,g , C. Pappenheimer , W. Parker ,C. Parkes , C.J. Parkinson , B. Passalacqua , G. Passaleva , A. Pastore , M. Patel ,C. Patrignani ,e , C.J. Pawley , A. Pearce , A. Pellegrino , M. Pepe Altarelli ,S. Perazzini , D. Pereima , P. Perret , K. Petridis , A. Petrolini ,i , A. Petrov ,S. Petrucci , M. Petruzzo , A. Philippov , L. Pica , M. Piccini , B. Pietrzyk ,G. Pietrzyk , M. Pili , D. Pinci , J. Pinzino , F. Pisani , A. Piucci , Resmi P.K ,V. Placinta , S. Playfer , J. Plews , M. Plo Casasus , F. Polci , M. Poli Lener ,M. Poliakova , A. Poluektov , N. Polukhina ,c , I. Polyakov , E. Polycarpo , G.J. Pomery ,S. Ponce , A. Popov , D. Popov , , S. Popov , S. Poslavskii , K. Prasanth ,L. Promberger , C. Prouve , V. Pugatch , A. Puig Navarro , H. Pullen , G. Punzi ,n ,W. Qian , J. Qin , R. Quagliani , B. Quintana , N.V. Raab , R.I. Rabadan Trejo ,B. Rachwal , J.H. Rademacker , M. Rama , M. Ramos Pernas , M.S. Rangel ,F. Ratnikov , , G. Raven , M. Reboud , F. Redi , F. Reiss , C. Remon Alepuz , Z. Ren ,V. Renaudin , R. Ribatti , S. Ricciardi , D.S. Richards , K. Rinnert , P. Robbe ,A. Robert , G. Robertson , A.B. Rodrigues , E. Rodrigues , J.A. Rodriguez Lopez ,A. Rollings , P. Roloff , V. Romanovskiy , M. Romero Lamas , A. Romero Vidal ,J.D. Roth , M. Rotondo , M.S. Rudolph , T. Ruf , J. Ruiz Vidal , A. Ryzhikov ,J. Ryzka , J.J. Saborido Silva , N. Sagidova , N. Sahoo , B. Saitta ,f ,D. Sanchez Gonzalo , C. Sanchez Gras , C. Sanchez Mayordomo , R. Santacesaria ,C. Santamarina Rios , M. Santimaria , E. Santovetti ,k , D. Saranin , G. Sarpis ,M. Sarpis , A. Sarti , C. Satriano ,q , A. Satta , M. Saur , D. Savrina , , H. Sazak ,L.G. Scantlebury Smead , S. Schael , M. Schellenberg , M. Schiller , H. Schindler ,M. Schmelling , T. Schmelzer , B. Schmidt , O. Schneider , A. Schopper , M. Schubiger ,S. Schulte , M.H. Schune , R. Schwemmer , B. Sciascia , A. Sciubba , S. Sellam ,A. Semennikov , M. Senghi Soares , A. Sergi , , N. Serra , J. Serrano , L. Sestini ,A. Seuthe , P. Seyfert , D.M. Shangase , M. Shapkin , I. Shchemerov , L. Shchutska ,T. Shears , L. Shekhtman ,v , Z. Shen , V. Shevchenko , E.B. Shields ,j , E. Shmanin ,J.D. Shupperd , B.G. Siddi , R. Silva Coutinho , G. Simi , S. Simone ,d , I. Skiba ,g ,N. Skidmore , T. Skwarnicki , M.W. Slater , J.C. Smallwood , J.G. Smeaton ,A. Smetkina , E. Smith , M. Smith , A. Snoch , M. Soares , L. Soares Lavra ,M.D. Sokoloff , F.J.P. Soler , A. Solovev , I. Solovyev , F.L. Souza De Almeida ,B. Souza De Paula , B. Spaan , E. Spadaro Norella ,o , P. Spradlin , F. Stagni , M. Stahl ,S. Stahl , P. Stefko , O. Steinkamp , , S. Stemmle , O. Stenyakin , H. Stevens ,S. Stone , M.E. Stramaglia , M. Straticiuc , D. Strekalina , S. Strokov , F. Suljik ,J. Sun , L. Sun , Y. Sun , P. Svihra , P.N. Swallow , K. Swientek , A. Szabelski ,T. Szumlak , M. Szymanski , S. Taneja , Z. Tang , T. Tekampe , F. Teubert ,E. Thomas , K.A. Thomson , M.J. Tilley , V. Tisserand , S. T’Jampens , M. Tobin ,S. Tolk , L. Tomassetti ,g , D. Torres Machado , D.Y. Tou , M. Traill , M.T. Tran ,E. Trifonova , C. Trippl , A. Tsaregorodtsev , G. Tuci ,n , A. Tully , N. Tuning , . Ukleja , D.J. Unverzagt , A. Usachov , A. Ustyuzhanin , , U. Uwer , A. Vagner ,V. Vagnoni , A. Valassi , G. Valenti , N. Valls Canudas , M. van Beuzekom ,H. Van Hecke , E. van Herwijnen , C.B. Van Hulse , M. van Veghel , R. Vazquez Gomez ,P. Vazquez Regueiro , C. V´azquez Sierra , S. Vecchi , J.J. Velthuis , M. Veltri ,p ,A. Venkateswaran , M. Veronesi , M. Vesterinen , D. Vieira , M. Vieites Diaz ,H. Viemann , X. Vilasis-Cardona , E. Vilella Figueras , P. Vincent , G. Vitali ,A. Vollhardt , D. Vom Bruch , A. Vorobyev , V. Vorobyev ,v , N. Voropaev , R. Waldi ,J. Walsh , C. Wang , J. Wang , J. Wang , J. Wang , J. Wang , M. Wang , R. Wang ,Y. Wang , Z. Wang , D.R. Ward , H.M. Wark , N.K. Watson , S.G. Weber ,D. Websdale , C. Weisser , B.D.C. Westhenry , D.J. White , M. Whitehead ,D. Wiedner , G. Wilkinson , M. Wilkinson , I. Williams , M. Williams , ,M.R.J. Williams , F.F. Wilson , W. Wislicki , M. Witek , L. Witola , G. Wormser ,S.A. Wotton , H. Wu , K. Wyllie , Z. Xiang , D. Xiao , Y. Xie , H. Xing , A. Xu , J. Xu ,L. Xu , M. Xu , Q. Xu , Z. Xu , Z. Xu , D. Yang , Y. Yang , Z. Yang , Z. Yang , Y. Yao ,L.E. Yeomans , H. Yin , J. Yu , X. Yuan , O. Yushchenko , K.A. Zarebski ,M. Zavertyaev ,c , M. Zdybal , O. Zenaiev , M. Zeng , D. Zhang , L. Zhang , S. Zhang ,Y. Zhang , Y. Zhang , A. Zhelezov , Y. Zheng , X. Zhou , Y. Zhou , X. Zhu ,V. Zhukov , , J.B. Zonneveld , S. Zucchelli ,e , D. Zuliani , G. Zunica . Centro Brasileiro de Pesquisas F´ısicas (CBPF), Rio de Janeiro, Brazil Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil Center for High Energy Physics, Tsinghua University, Beijing, China School of Physics State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing,China University of Chinese Academy of Sciences, Beijing, China Institute Of High Energy Physics (IHEP), Beijing, China Institute of Particle Physics, Central China Normal University, Wuhan, Hubei, China Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy, France Universit´e Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France Ijclab, Orsay, France LPNHE, Sorbonne Universit´e, Paris Diderot Sorbonne Paris Cit´e, CNRS/IN2P3, Paris, France I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany Fakult¨at Physik, Technische Universit¨at Dortmund, Dortmund, Germany Max-Planck-Institut f¨ur Kernphysik (MPIK), Heidelberg, Germany Physikalisches Institut, Ruprecht-Karls-Universit¨at Heidelberg, Heidelberg, Germany School of Physics, University College Dublin, Dublin, Ireland INFN Sezione di Bari, Bari, Italy INFN Sezione di Bologna, Bologna, Italy INFN Sezione di Ferrara, Ferrara, Italy INFN Sezione di Firenze, Firenze, Italy INFN Laboratori Nazionali di Frascati, Frascati, Italy INFN Sezione di Genova, Genova, Italy INFN Sezione di Milano-Bicocca, Milano, Italy INFN Sezione di Milano, Milano, Italy INFN Sezione di Cagliari, Monserrato, Italy Universita degli Studi di Padova, Universita e INFN, Padova, Padova, Italy INFN Sezione di Pisa, Pisa, Italy INFN Sezione di Roma Tor Vergata, Roma, Italy INFN Sezione di Roma La Sapienza, Roma, Italy Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam,Netherlands Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Krak´ow, Poland AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science,Krak´ow, Poland National Center for Nuclear Research (NCBJ), Warsaw, Poland Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania Petersburg Nuclear Physics Institute NRC Kurchatov Institute (PNPI NRC KI), Gatchina, Russia Institute of Theoretical and Experimental Physics NRC Kurchatov Institute (ITEP NRC KI), Moscow,Russia Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS), Moscow, Russia Yandex School of Data Analysis, Moscow, Russia Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia Institute for High Energy Physics NRC Kurchatov Institute (IHEP NRC KI), Protvino, Russia,Protvino, Russia ICCUB, Universitat de Barcelona, Barcelona, Spain Instituto Galego de F´ısica de Altas Enerx´ıas (IGFAE), Universidade de Santiago de Compostela,Santiago de Compostela, Spain Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia - CSIC, Valencia, Spain European Organization for Nuclear Research (CERN), Geneva, Switzerland Institute of Physics, Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne, Switzerland Physik-Institut, Universit¨at Z¨urich, Z¨urich, Switzerland NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine University of Birmingham, Birmingham, United Kingdom H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom Department of Physics, University of Warwick, Coventry, United Kingdom STFC Rutherford Appleton Laboratory, Didcot, United Kingdom School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom Imperial College London, London, United Kingdom Department of Physics and Astronomy, University of Manchester, Manchester, United Kingdom Department of Physics, University of Oxford, Oxford, United Kingdom Massachusetts Institute of Technology, Cambridge, MA, United States University of Cincinnati, Cincinnati, OH, United States University of Maryland, College Park, MD, United States Los Alamos National Laboratory (LANL), Los Alamos, United States Syracuse University, Syracuse, NY, United States School of Physics and Astronomy, Monash University, Melbourne, Australia, associated to
Pontif´ıcia Universidade Cat´olica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to
Physics and Micro Electronic College, Hunan University, Changsha City, China, associated to
Guangdong Provencial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South ChinaNormal University, Guangzhou, China, associated to
School of Physics and Technology, Wuhan University, Wuhan, China, associated to
Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia, associated to
Universit¨at Bonn - Helmholtz-Institut f¨ur Strahlen und Kernphysik, Bonn, Germany, associated to
Institut f¨ur Physik, Universit¨at Rostock, Rostock, Germany, associated to
INFN Sezione di Perugia, Perugia, Italy, associated to
Van Swinderen Institute, University of Groningen, Groningen, Netherlands, associated to
Universiteit Maastricht, Maastricht, Netherlands, associated to
National Research Centre Kurchatov Institute, Moscow, Russia, associated to
National University of Science and Technology “MISIS”, Moscow, Russia, associated to
National Research University Higher School of Economics, Moscow, Russia, associated to
National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
DS4DS, La Salle, Universitat Ramon Llull, Barcelona, Spain, associated to