Measurement of the CKM angle γ using B ± →D K ± with D→ K 0 S π + π − , K 0 S K + K − decays
LHCb collaboration, R. Aaij, B. Adeva, M. Adinolfi, C.A. Aidala, Z. Ajaltouni, S. Akar, P. Albicocco, J. Albrecht, F. Alessio, M. Alexander, A. Alfonso Albero, S. Ali, G. Alkhazov, P. Alvarez Cartelle, A.A. Alves Jr, S. Amato, S. Amerio, Y. Amhis, L. An, L. Anderlini, G. Andreassi, M. Andreotti, J.E. Andrews, R.B. Appleby, F. Archilli, P. d'Argent, J. Arnau Romeu, A. Artamonov, M. Artuso, K. Arzymatov, E. Aslanides, M. Atzeni, S. Bachmann, J.J. Back, S. Baker, V. Balagura, W. Baldini, A. Baranov, R.J. Barlow, S. Barsuk, W. Barter, F. Baryshnikov, V. Batozskaya, B. Batsukh, V. Battista, A. Bay, J. Beddow, F. Bedeschi, I. Bediaga, A. Beiter, L.J. Bel, N. Beliy, V. Bellee, N. Belloli, K. Belous, I. Belyaev, E. Ben-Haim, G. Bencivenni, S. Benson, S. Beranek, A. Berezhnoy, R. Bernet, D. Berninghoff, E. Bertholet, A. Bertolin, C. Betancourt, F. Betti, M.O. Bettler, M. van Beuzekom, Ia. Bezshyiko, S. Bhasin, J. Bhom, L. Bian, S. Bifani, P. Billoir, A. Birnkraut, A. Bizzeti, M. Bjørn, M.P. Blago, T. Blake, F. Blanc, S. Blusk, D. Bobulska, V. Bocci, O. Boente Garcia, T. Boettcher, A. Bondar, N. Bondar, S. Borghi, M. Borisyak, M. Borsato, F. Bossu, M. Boubdir, T.J.V. Bowcock, C. Bozzi, S. Braun, M. Brodski, J. Brodzicka, D. Brundu, et al. (724 additional authors not shown)
EEUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-EP-2018-135LHCb-PAPER-2018-01721 September 2018
Measurement of the CKM angle γ using B ± → DK ± with D → K S π + π − , K S K + K − decays LHCb collaboration † Abstract
A binned Dalitz plot analysis of B ± → DK ± decays, with D → K S π + π − and D → K S K + K − , is used to perform a measurement of the CP -violating observables x ± and y ± , which are sensitive to the Cabibbo-Kobayashi-Maskawa angle γ . The analysis isperformed without assuming any D decay model, through the use of information onthe strong-phase variation over the Dalitz plot from the CLEO collaboration. Usinga sample of proton-proton collision data collected with the LHCb experiment in2015 and 2016, and corresponding to an integrated luminosity of 2.0 fb − , the valuesof the CP violation parameters are found to be x − = (9 . ± . ± . ± . × − , y − = (2 . ± . ± . ± . × − , x + = ( − . ± . ± . ± . × − , and y + = ( − . ± . ± . ± . × − . The first uncertainty is statistical, thesecond is systematic, and the third is due to the uncertainty on the strong-phasemeasurements. These values are used to obtain γ = (cid:0) +11 − (cid:1) ◦ , r B = 0 . +0 . − . ,and δ B = (101 ± ◦ , where r B is the ratio between the suppressed and favoured B -decay amplitudes and δ B is the corresponding strong-interaction phase difference.This measurement is combined with the result obtained using 2011 and 2012 datacollected with the LHCb experiment, to give γ = (cid:0) +10 − (cid:1) ◦ , r B = 0 . ± . δ B = (110 ± ◦ . Published in JHEP (2018) 2018: 176. c (cid:13) † Authors are listed at the end of this paper. a r X i v : . [ h e p - e x ] S e p i Introduction
The Standard Model (SM) description of CP violation [1,2] can be tested by overconstrain-ing the angles of the Unitarity Triangle. The Cabibbo-Kobayashi-Maskawa (CKM) angle γ ≡ arg( − V ud V ∗ ub /V cd V ∗ cb ) is experimentally accessible through the interference between¯ b → ¯ cu ¯ s and ¯ b → ¯ uc ¯ s transitions. It is the only CKM angle easily accessible in tree-levelprocesses and it can be measured with negligible uncertainty from theory [3]. Hence, inthe absence of new physics effects at tree level, a precision measurement of γ provides aSM benchmark that can be compared with other CKM-matrix observables more likelyto be affected by physics beyond the SM. Such comparisons are currently limited by theuncertainty on direct measurements of γ , which is about 5 ◦ [4] and is driven by the LHCbaverage.The effects of interference between ¯ b → ¯ cu ¯ s and ¯ b → ¯ uc ¯ s transitions can be probedby studying CP -violating observables in B ± → DK ± decays, where D represents a D or a D meson reconstructed in a final state that is common to both [5–7]. This decaymode has been studied at LHCb with a wide range of D -meson final states to measureobservables with sensitivity to γ [8–11]. In addition to these studies, other B decays havealso been used with a variety of techniques to determine γ [12–15].This paper presents a model-independent study of the decay mode B ± → DK ± , using D → K S π + π − and D → K S K + K − decays (denoted D → K S h + h − decays). The analysisutilises pp collision data accumulated with LHCb in 2015 and 2016 at a centre-of-massenergy of √ s = 13 TeV and corresponding to a total integrated luminosity of 2 . − . Theresult is combined with the result obtained by LHCb with the same analysis technique,using data collected in 2011 and 2012 (Run 1) at centre-of-mass energies of √ s = 7 TeVand √ s = 8 TeV [9].The sensitivity to γ is obtained by comparing the distributions in the Dalitz plots of D → K S h + h − decays from reconstructed B + and B − mesons [6, 7]. For this comparison,the variation of the strong-phase difference between D and D decay amplitudes withinthe Dalitz plot needs to be known. An attractive, model-independent, approach makes useof direct measurements of the strong-phase variation over bins of the Dalitz plot [6, 16, 17].The strong phase can be directly accessed by exploiting the quantum correlation of D D pairs from ψ (3770) decays. Such measurements have been performed by theCLEO collaboration [18] and have been used by the LHCb [9] and Belle [19] collaborationsto measure γ in B ± → DK ± decays, and have also been used to study B → DK ∗ decays [20, 21]. An alternative method relies on amplitude models of D → K S h + h − decays, determined from flavour-tagged D → K S h + h − decays, to predict the strong-phasevariation over the Dalitz plot. This method has been used for a variety of B decays [22–28].The separation of data into binned regions of the Dalitz plot leads to a loss ofstatistical sensitivity in comparison to using an amplitude model [16, 17]. However, theadvantage of using the direct strong-phase measurements resides in the model-independentnature of the systematic uncertainties. Where the direct strong-phase measurementsare used, there is only a systematic uncertainty associated with the finite precision ofsuch measurements. Conversely, systematic uncertainties associated with determininga phase from an amplitude model are difficult to evaluate, as common approaches toamplitude-model building break the optical theorem [29]. Therefore, the loss in statisticalprecision is compensated by reliability in the evaluation of the systematic uncertainty,which is increasingly important as the overall precision on the CKM angle γ improves.1 Overview of the analysis
The amplitude of the decay B − → DK − , D → K S h + h − can be written as a sum of thefavoured B − → D K − and suppressed B − → D K − contributions as A B ( m − , m ) ∝ A D ( m − , m ) + r B e i ( δ B − γ ) A D ( m − , m ) , (1)where m − and m are the squared invariant masses of the K S h − and K S h + particlecombinations, respectively, that define the position of the decay in the Dalitz plot, A D ( m − , m ) is the D → K S h + h − decay amplitude, and A D ( m − , m ) the D → K S h + h − decay amplitude. The parameter r B is the ratio of the magnitudes of the B − → D K − and B − → D K − amplitudes, while δ B is their strong-phase difference. The equivalentexpression for the charge-conjugated decay B + → DK + is obtained by making thesubstitutions γ → − γ and A D ( m − , m ) ↔ A D ( m − , m ). Neglecting CP violation incharm decays, the charge-conjugated amplitudes satisfy the relation A D ( m − , m ) = A D ( m , m − ).The D -decay Dalitz plot 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 . By convention, the positive values of i correspond to bins forwhich m − > m . The strong-phase difference between the D and D -decay amplitudesat a 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 [6], 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 the phase space of bin i . An analogous expressioncan be written for s i , which is the sine of the strong-phase difference weighted by thedecay amplitude and averaged over the bin phase space. The values of c i and s i have beendirectly measured by the CLEO collaboration, exploiting quantum-correlated D D pairsproduced at the ψ (3770) resonance [18].The measurements of c i and s i are available in four different 2 × D → K S π + π − decay. This analysis uses the ‘optimal binning’ scheme where the binshave been chosen to optimise the statistical sensitivity to γ , as described in Ref. [18]. Theoptimisation was performed assuming a strong-phase difference distribution as predictedby the BaBar model presented in Ref. [23]. For the K S K + K − final state, three choicesof binning schemes are available, containing 2 ×
2, 2 ×
3, and 2 × × D → K S K + K − mode. The same choice of bins was used in the LHCb Run 1 analysis [9].The measurements of c i and s i are not biased by the use of a specific amplitude modelin defining the bin boundaries. The choice of the model only affects this analysis to theextent that a poor model description of the underlying decay would result in a reducedstatistical sensitivity of the γ measurement. The binning choices for the two decay modesare shown in Fig. 1.The physics parameters of interest, r B , δ B , and γ , are translated into four CP obser-vables [22] that are measured in this analysis. These observables are defined as x ± ≡ r B cos( δ B ± γ ) and y ± ≡ r B sin( δ B ± γ ) . (3)2 c / [GeV +2 m ] c / [ G e V - m | B i n nu m b e r | c / [GeV +2 m ] c / [ G e V - m | B i n nu m b e r | Figure 1: Binning schemes for (left) D → K S π + π − decays and (right) D → K S 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. It follows from Eq. (1) that the expected numbers of B + and B − decays in bin i , N + i and N − i , are given by N + ± i = h B + (cid:104) F ∓ i + ( x + y ) F ± i + 2 (cid:112) F i F − i ( x + c ± i − y + s ± i ) (cid:105) ,N −± i = h B − (cid:104) F ± i + ( x − + y − ) F ∓ i + 2 (cid:112) F i F − i ( x − c ± i + y − s ± i ) (cid:105) , (4)where F i are the fractions of decays in bin i of the D → K S h + h − Dalitz plot, and h B ± arenormalisation factors, which can be different for B + and B − due to production, detection,and CP asymmetries. In this measurement, the integrated yields are not used to provideinformation on x ± and y ± , and so the analysis is insensitive to such effects. From Eq. (4)it is seen that studying the distribution of candidates over the D → K S h + h − Dalitz plotgives access to the x ± and y ± observables. The detector and selection requirements placedon the data lead to a non-uniform efficiency over the Dalitz plot, which affects the F i parameters. The efficiency profile for the signal candidates is denoted as η ( m − , m ). Theparameters F i can then be expressed as 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 ) . (5)The values of F i are determined from the control decay mode ( ) B → D ∗± µ ∓ ( ) ν µ X , wherethe D ∗− meson decays to D π − and the D meson decays to either the K S π + π − or K S K + K − final state. The symbol X indicates other particles which may be producedin the decay but are not reconstructed. Samples of simulated events are used to correctfor the small differences in efficiency arising through unavoidable differences in selecting ( ) B → D ∗± µ ∓ ( ) ν µ X and B ± → DK ± decays, as discussed further in Sect. 5.In addition to B ± → DK ± and ( ) B → D ∗± µ ∓ ( ) ν µ X candidates, B ± → Dπ ± decaysare selected. These provide an important control sample that is used to constrain the3nvariant-mass shape of the B ± → DK ± signal, as well as to determine the yield of B ± → Dπ ± decays misidentified as B ± → DK ± candidates. Note that this channel is notoptimal for determining the values of F i as the small level of CP violation in the decayleads to a significant systematic uncertainty, as was reported in Ref. [30]. This uncertaintyis eliminated when using the flavour-specific semileptonic decay, in favour of a smallersystematic uncertainty associated with efficiency differences.The effect of D – D mixing was ignored in the above discussion. If the parameters F i are obtained from ( ) B → D ∗± µ ∓ ( ) ν µ X , where the D ∗− decays to D π − , D – D mixing hasbeen shown to lead to a bias of approximately 0 . ◦ in the γ determination [31], which isnegligible for the current analysis. The effects of CP violation in the neutral kaon systemand of the different nuclear interaction cross-sections for K and K mesons are discussedin Sect. 7, where a systematic uncertainty is assigned. The LHCb detector [32, 33] 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 polarity of the dipole magnet is reversed periodically throughout data-taking.The tracking system provides a measurement of momentum, p , of charged particles withrelative uncertainty that varies from 0.5% at low momentum to 1.0% at 200 GeV /c . Theminimum distance of a track to a primary vertex (PV), the impact parameter (IP), is mea-sured with a resolution of (15 + 29 /p T ) µ m, where p T is the component of the momentumtransverse to the beam, in GeV /c . Different types of charged hadrons are distinguishedusing information from two ring-imaging Cherenkov detectors. Photons, electrons, andhadrons are identified by a calorimeter system consisting of scintillating-pad and preshowerdetectors, an electromagnetic calorimeter and a hadronic calorimeter. Muons are identifiedby a system composed of alternating layers of iron and multiwire proportional chambers.The online event selection is performed by a trigger, which consists of a hardware stagebased on information from the calorimeter and muon systems, followed by a softwarestage, which applies a full event reconstruction. At the hardware trigger stage, events arerequired to have a muon with high p T or a hadron, photon or electron with high transverseenergy in the calorimeters. For hadrons, the transverse energy threshold is 3.5 GeV. Thesoftware trigger requires a two-, three- or four-track secondary vertex with a significantdisplacement from any primary pp interaction vertex. At least one charged particle musthave transverse momentum p T > . /c and be inconsistent with originating froma PV. A multivariate algorithm [34] is used for the identification of secondary verticesconsistent with the decay of a b hadron. Small changes in the trigger thresholds weremade throughout both years of data taking.In the simulation, pp collisions are generated using Pythia
EvtGen [37],in which final-state radiation is generated using
Photos [38]. The interaction of thegenerated particles with the detector, and its response, are implemented using the
Geant4 B ± → DK ± and B ± → Dπ ± decays Decays of K S mesons to the π + π − final state are reconstructed in two categories, thefirst containing K S mesons that decay early enough for the pions to be reconstructedin the vertex detector and the second containing K S mesons that decay later such thattrack segments of the pions cannot be formed in the vertex detector. These categories arereferred to as long and downstream , respectively. The candidates in the long category havebetter mass, momentum and vertex resolution than those in the downstream category.Hereinafter, B ± candidates are denoted long or downstream depending on which categoryof K S candidate they contain.For many of the quantities used in the selection and analysis of the data, a kinematicfit [41] is imposed on the full B ± decay chain. Depending on the quantity being calculated,the D and K S candidates may be constrained to have their known masses [42], as describedbelow. The fit also constrains the B ± candidate momentum vector to point towards theassociated PV, defined as the PV for which the candidate has the smallest IP significance.These constraints improve the resolution of the calculated quantities, and thus helpimprove separation between signal and background decays. Furthermore, it improves theresolution on the Dalitz plot coordinates and ensures that all candidates lie within thekinematically allowed D → K S h + h − phase space.The D ( K S ) candidates are required to be within 25 MeV /c (15 MeV /c ) of theirknown mass [42]. These requirements are placed on masses obtained using kinematicfits in which all constraints are applied except for that on the mass under consideration.Combinatorial background is primarily suppressed through the use of a boosted decisiontree (BDT) multivariate classifier [43, 44]. The BDT is trained on simulated signal eventsand background taken from the high B ± mass sideband (5800–7000 MeV /c ). SeparateBDTs are trained for the long and downstream categories.Each BDT uses the same set of variables: the χ of the kinematic fit of the whole decaychain; p and p T of the companion, D , and B ± after the kinematic refit (here and in thefollowing, companion refers to the final state π ± or K ± meson produced in the B ± → Dh ± decay); the vertex quality of the K S , D , and B ± candidates; the distance of closestapproach between tracks forming the D and B ± vertices; the cosine of the angle betweenthe momentum vector and the vector between the production and decay vertices of a givenparticle, for each of the K S , D , and B ± candidates; the minimum and maximum values ofthe χ of the pions from both the D and K S decays, where χ is defined as the differencein χ of the PV fit with and without the considered particle; the χ for the companion, K S , D , and B ± candidates; the B ± flight-distance significance; the radial distance fromthe beamline to the D and B ± -candidate vertices; and a B ± isolation variable , which isdesigned to ensure the B ± candidate is well isolated from other tracks in the event. The B ± isolation variable is the asymmetry between the p T of the signal candidate and thesum of the p T of other tracks in the event that lie within a distance of 1.5 in η – φ space,where φ is the azimuthal angle measured in radians. Candidates in the data samples thathave a BDT output value below a threshold are rejected. An optimal threshold value isdetermined for each of the two BDTs, using a series of pseudoexperiments to obtain the5alues that provide the best sensitivity to x ± and y ± . Across all B ± → DK ± channelsthis requirement is found to reject 99.1 % of the combinatorial background in the high B mass sideband that survives all other requirements, while having an efficiency of 92.4 %on simulated B ± → DK ± signal samples.Particle identification (PID) requirements are placed on the companion to separate B ± → DK ± and B ± → Dπ ± candidates, and on the charged decay products of the D meson to remove cross-feed between different D → K S h + h − decays. To ensure goodcontrol of the PID performance it is required that information from the RICH detectorsis present. To remove background from D → π + π − π + π − or D → π + π − K + K − decays,long K S candidates are required to have travelled a significant distance from the D vertex.This requirement is not necessary for downstream candidates. Similarly, the D decayvertex is required be significantly displaced from the B ± decay vertex in order to removecharmless B ± decays.The Dalitz plots for B ± → DK ± candidates in a narrow region of ±
25 MeV /c aroundthe B ± mass are shown in Fig. 2, for both D → K S h + h − final states samples. Separateplots are shown for B + and B − decays. The Dalitz coordinates are calculated from thekinematic fit with all mass constraints applied.In order to determine the parameterisation of the signal and background componentsthat are used in the fit of partitioned regions of the Dalitz plot described in Sect. 6, anextended maximum likelihood fit to the invariant-mass distributions of the B ± candidatesis performed, in which the B + and B − candidates in all of the Dalitz bins are combined.The invariant mass of each B ± candidate is calculated using the results of a kinematic fitin which the D and K S masses are constrained to their known values. The sample is splitinto B ± → DK ± and B ± → Dπ ± candidates, by D decay mode and by K S category. Inorder to allow sharing of some parameters, the fit is performed simultaneously for all ofthe above categories. The projections of the fit and the invariant-mass distributions of theselected B ± candidates are shown in Figs. 3 and 4 for D → K S π + π − and D → K S K + K − candidates, respectively. The fit range is between 5080 MeV /c and 5800 MeV /c in the B ± candidate invariant mass.The peaks corresponding to actual B ± → DK ± and B ± → Dπ ± candidates are fittedwith a sum of two Crystal Ball [45] functions, which are parameterised asCB( m, µ, σ, α, n ) ∝ (cid:40) exp (cid:104) − (cid:0) m − µσ (cid:1) (cid:105) if ( m − µ ) /σ > − αA (cid:0) B − m − µσ (cid:1) − n otherwise, (6)where α >
0, and A = (cid:16) nα (cid:17) n exp[ − α / , (7) B = nα − α . (8)The sum is implemented such that the Crystal Ball functions have tails pointing in eitherdirection. They share a common width, σ , and mean, µ . In practice, the signal probabilitydensity function (PDF) is defined as f signal ( m, µ, σ, α L , n L , α R , n R , f CB )= f CB · CB( m, µ, σ, α L , n L ) + (1 − f CB ) · CB( m, µ, − σ, α R , n R ) . (9)6 /c ) [GeV + p K ( m ] / c ) [ G e V - p S K ( m LHCb ] /c ) [GeV - p K ( m ] / c ) [ G e V + p S K ( m LHCb ] /c ) [GeV + K K ( m ] / c ) [ G e V - K S K ( m LHCb ] /c ) [GeV - K K ( m ] / c ) [ G e V + K S K ( m LHCb
Figure 2: Dalitz plots of long and downstream (left) B + → DK + and (right) B − → DK − candi-dates for (top) D → K S π + π − and (bottom) D → K S K + K − decays in which the reconstructedinvariant mass of the B ± candidate is in a region of ±
25 MeV /c around the B ± mass. Thenarrow region is chosen to obtain high purity, as no background subtraction has been made.The Dalitz coordinates are calculated using the results of a kinematic fit in which the D and K S masses are constrained to their known values. The blue lines show the kinematic boundaries ofthe decays. The tail parameters, n L , R and α L , R , are fixed from simulation, while the other parametersare left as free parameters in the fit. Separate tail parameters, f CB , and σ are used forlong and downstream candidates. Different widths are used for the B ± → DK ± and B ± → Dπ ± channels, with their ratio r σ = σ DK /σ Dπ shared between all categories. Themean is shared among all categories. The yield of B ± → Dπ ± decays in each K S and D -meson decay category, N cat ( B ± → Dπ ± ), is determined in the fit. Instead of fittingthe yield of B ± → DK ± decays directly in each category, it is determined from the B ± → Dπ ± yield in the corresponding category and the ratio R ≡ N cat ( B ± → DK ± ) ε catPID ( B ± → DK ± ) (cid:30) N cat ( B ± → Dπ ± ) ε catPID ( B ± → Dπ ± ) , (10)7 c ) [MeV/ – KD ( m ) c C a nd i d a t e s / ( . M e V / – KD fi – B – p D fi – B CombinatorialPart. reco.
LHCb ] c ) [MeV/ – p D ( m ) c C a nd i d a t e s / ( . M e V / – KD fi – B – p D fi – B CombinatorialPart. reco.
LHCb ] c ) [MeV/ – KD ( m ) c C a nd i d a t e s / ( . M e V / – KD fi – B – p D fi – B CombinatorialPart. reco.
LHCb ] c ) [MeV/ – p D ( m ) c C a nd i d a t e s / ( . M e V / – KD fi – B – p D fi – B CombinatorialPart. reco.
LHCb
Figure 3: Invariant-mass distributions of (left) B ± → DK ± and (right) B ± → Dπ ± candidates,with D → K S π + π − , shown separately for the (top) long and (bottom) downstream K S categories.Fit results, including the signal component and background components due to misidentifiedcompanions, partially reconstructed decays and combinatorial background, are also shown. which is a free parameter in the fit. The category-dependent PID efficiencies, ε catPID ( B ± → Dh ± ), are taken into account, so that a single R parameter can be sharedbetween all categories in the fit. How these efficiencies are obtained is described below.As the parameter R is efficiency corrected, it is equal to the ratio of branching fractionsbetween the B ± → DK ± and B ± → Dπ ± decay modes. The measured ratio is found tobe R = (7 . ± .
14) %, where the uncertainty is statistical only, and this is consistentwith the expected value of (7 . ± .
4) % [42].The background consists of random track combinations, partially reconstructed B decays, and B ± → Dh ± decays in which the companion has been misidentified. Therandom track combinations are modelled by an exponential PDF. The slopes of theexponentials are free parameters in the fit to the data. These slopes are independent foreach of the B ± → Dπ ± categories, while they are shared for the B ± → DK ± categoriesto improve the stability of the fit. When these slopes are allowed to be independent, thefit returns results that are statistically compatible.In the B ± → DK ± sample there is a clear contribution from B ± → Dπ ± decaysin which the companion particle is misidentified as a kaon by the RICH system. The8 c ) [MeV/ – KD ( m ) c C a nd i d a t e s / ( . M e V / – KD fi – B – p D fi – B CombinatorialPart. reco.
LHCb ] c ) [MeV/ – p D ( m ) c C a nd i d a t e s / ( . M e V / – KD fi – B – p D fi – B CombinatorialPart. reco.
LHCb ] c ) [MeV/ – KD ( m ) c C a nd i d a t e s / ( . M e V / – KD fi – B – p D fi – B CombinatorialPart. reco.
LHCb ] c ) [MeV/ – p D ( m ) c C a nd i d a t e s / ( . M e V / – KD fi – B – p D fi – B CombinatorialPart. reco.
LHCb
Figure 4: Invariant-mass distributions of (left) B ± → DK ± and (right) B ± → Dπ ± candidates,with D → K S K + K − , shown separately for the (top) long and (bottom) downstream K S categories. Fit results, including the signal component and background components due tomisidentified companions, partially reconstructed decays and combinatorial background, are alsoshown. rate for B ± → DK ± decays to be misidentified and placed in the B ± → Dπ ± sampleis much lower due to the reduced branching fraction. Nevertheless, this contribution isstill accounted for in the fit. The yields of these backgrounds are fixed in the fit, usingknowledge of misidentification efficiencies and the fitted yields of reconstructed decayswith the correct particle hypothesis. The misidentification efficiencies are obtained fromlarge samples of D ∗± → ( ) D π ± , ( ) D → K ∓ π ± decays. These decays are selected usingonly kinematic variables in order to provide pure samples of K ∓ and π ± that are unbiasedin the PID variables. The PID efficiency is parameterised as a function of the companionmomentum and pseudorapidity, and the charged-particle multiplicity in the event. Thecalibration sample is weighted so that the distribution of these variables matches that ofthe candidates in the signal region of the B ± sample, thereby ensuring that the measuredPID performance is representative for the samples used in this measurement. The efficiencyto identify a kaon correctly is found to be approximately 86 %, while that for a pionis approximately 97 %. The PDFs of the backgrounds due to misidentified companionparticles are determined using data. As an example, consider the case of true B ± → Dπ ± B ± → DK ± candidates. The sPlot method [46] is used on the B ± → Dπ ± sample in order to isolate the contribution from the signal decays. The B ± invariant mass is then calculated using the kaon mass hypothesis for the companionpion, and weighting by PID efficiencies in order to properly reproduce the kinematicproperties of pions misidentified as kaons in the signal B ± → DK ± sample. The weighteddistribution is fitted with a sum of two Crystal Ball shapes. The fitted parameters aresubsequently fixed in the fit to the B ± invariant-mass spectrum, with the procedureapplied separately for long and downstream candidates. An analogous approach is usedto determine the shape of the misidentified B ± → DK ± contribution in the B ± → Dπ ± sample.Partially reconstructed b -hadron decays contaminate the sample predominantly atinvariant masses smaller than that of the signal peak. These decays contain an unrecon-structed pion or photon, which predominantly comes from an intermediate resonance.There are contributions from B → D ∗± h ∓ and B ± → D ∗ h ± decays in all channels(denoted as B → D ∗ h ± decays), while B ± → Dρ ± and B ± → DK ∗± decays contributeto the B ± → Dπ ± and B ± → DK ± channels, respectively. In the B ± → DK ± channelsthere is also a contribution from B s → D π + K − ( B s → D π − K + ) decays where thecharged pion is not reconstructed. The invariant-mass distributions of these backgroundsdepend on the spin and mass of the missing particle, as described in Ref. [47]. Theshape of the background from B s decays is based on the results of Ref. [48]. Additionally,each of the above backgrounds of B ± → Dπ ± decays can contribute in the B ± → DK ± channels if the pion is misidentified. The inverse contribution is negligible and is neglected.The shapes for the decays in which a pion is misidentified as a kaon are parameterisedwith semi-empirical PDFs formed from sums of Gaussian and error functions. The pa-rameters of these backgrounds are fixed to the results of fits to data from two-body D decays [47], where they were obtained with a much larger data sample. However, thewidth of the resolution function and a shift along the B ± mass are allowed to differ inorder to accommodate small differences between the D decay modes.In each of the B ± → Dπ ± channels, the total yield of the partially reconstructedbackground is fitted independently. The relative amount of each B → D ∗ π ∓ mode isfixed from efficiencies obtained from simulation and known branching fractions, while thefraction of B ± → Dρ ± decays is left free. In the B ± → DK ± channels, the yield of the B s → D π + K − background is fixed relative to the corresponding B ± → Dπ ± yield, usingefficiencies from simulation and the known branching fraction. The total yield of theremaining partially reconstructed backgrounds is expressed via a single fraction, R low DK/Dπ ,relative the B ± → Dπ ± yields. It is free in the fit, and common to all channels aftertaking into account the different particle-identification efficiencies. The relative amountof each B → D ∗ K ∓ mode is fixed using efficiencies from simulation and known branchingfractions, while the fraction of B ± → DK ∗± decays is fixed using the results of Ref. [47].The yields of the partially reconstructed modes with a companion pion misidentified as akaon are fixed via the known PID efficiencies, based on the fitted yield of the partiallyreconstructed backgrounds in the corresponding B ± → Dπ ± channel.In the B ± → Dπ ± channels, a total signal yield of approximately 56 100 (7750) isfound in the signal region 5249–5319 MeV /c of the D → K S π + π − ( D → K S K + K − )channel, 31 % (32 %) of which are in the long K S category. The purity in the signal regionis found to be 98 . . B ± → DK ± channels, a total signal yield of approximately 3900 (530) is found in the10ignal region of the D → K S π + π − ( D → K S K + K − ) channel, again finding 31 % (32 %) ofthe candidates in the long K S category. The purity in the signal region is found to be 81 %.The dominant background is from misidentified B ± → Dπ ± decays, which accounts for66 % of the background in the signal region. Equal amounts of combinatorial backgroundand partially reconstructed decays, predominantly including a misidentified companionpion, make up the remaining background. ( ) B → D ∗± µ ∓ ( ) ν µ decays A sample of ( ) B → D ∗± µ ∓ ( ) ν µ X , D ∗± → ( ) D π ± , ( ) D → K S h + h − decays is used to determinethe quantities F i , defined in Eq. (5), as the expected fractions of D decays falling intothe i th Dalitz plot bin, taking into account the efficiency profile of the signal decay. Thesemileptonic decay of the B meson and the strong-interaction decay of the D ∗± mesonallow the flavour of the D meson to be determined from the charges of the muon and thesoft pion from the D ∗± decay. This particular decay chain, involving a flavour-tagged D decay, is chosen due to its high yield, low background level, and low mistag probability.The selection requirements are chosen to minimise changes to the efficiency profile withrespect to those associated with the B ± → DK ± channels.The selection is identical to that applied in Ref. [9], except for a tighter requirementon the significance of the D flight distance that helps to suppress backgrounds fromcharmless B decays. To improve the resolution of the distribution of candidates across theDaltiz plot, the B -decay chain is refitted [41] with the D and K S candidates constrainedto their known masses. An additional fit, in which only the K S mass is constrained, isperformed to improve the D and D ∗± mass resolution in the invariant-mass fit used todetermine signal yields.The invariant mass of the D candidate, m ( K S h + h − ), and the invariant-mass difference,∆ m ≡ m ( K S h + h − π ± ) − m ( K S h + h − ), are fitted simultaneously to determine the signalyields. This two-dimensional parameterisation allows the yield of selected candidates tobe measured in three categories: true D ∗± candidates (signal), candidates containinga true D meson but random soft pion (RSP) and candidates formed from randomtrack combinations that fall within the fit range (combinatorial background). Backgroundcontributions from real D ∗± decays paired with a random µ are determined to be negligibleby selecting pairs of D ∗± mesons and µ ± with the same charge.An example projection of m ( K S π + π − ) and ∆ m is shown in Fig. 5. The result of atwo-dimensional extended, unbinned, maximum likelihood fit is superimposed. The fit isperformed simultaneously for the two D final states and the two K S categories with someparameters allowed to be independent between categories. Candidates selected from datarecorded in 2015 and 2016 are fitted separately, in order to accommodate different triggerthreshold settings that result in slightly different Dalitz plot efficiency profiles. The fitregion is defined by 1830 < m ( K S h + h − ) < /c and 139 . < ∆ m < . /c .Within this m ( K S h + h − ) range, the ∆ m resolution does not vary significantly.The signal is parameterised in ∆ m with a sum of two Crystal Ball functions, as forthe B ± → Dh ± signal. The mean, µ , is shared between all categories, while the otherparameters are different for long and downstream candidates. The tail parameters are11
840 1860 1880 1900 ] c [MeV/ ) - p + p m(K ) c C a nd i d a t e s / ( M e V / SignalCombinatorialpionRandom soft
LHCb
140 145 150 ] c [MeV/ m D ) c C a nd i d a t e s / ( . M e V / SignalCombinatorialpionRandom soft
LHCb
Figure 5: Result of the simultaneous fit to ( ) B → D ∗± µ ∓ ( ) ν µ , D ∗± → ( ) D ( → K S π + π − ) π ± decays with downstream K S candidates, in 2016 data. The projections of the fit result are shownfor (left) m ( K S π + π − ) and (right) ∆ m . The (blue) total fit PDF is the sum of componentsdescribing (solid red) signal, (dashed black) combinatorial background and (dotted green) randomsoft pion background. fixed from simulation. The combinatorial and RSP backgrounds are both parameterisedwith an empirical model given by f (∆ m ; ∆ m , x, p , p ) = (cid:20) − exp (cid:18) − ∆ m − ∆ m x (cid:19)(cid:21) (cid:18) ∆ m ∆ m (cid:19) p + p (cid:18) ∆ m ∆ m − (cid:19) (11)for ∆ m − ∆ m > f (∆ m ) = 0 otherwise, where ∆ m , x , p , and p are free parameters.The parameter ∆ m , which describes the kinematic threshold for a D ∗± → ( ) D π ± decay,is shared in all data categories and for both the combinatorial and RSP shapes. Theremaining parameters are determined separately for D → K S π + π − and D → K S K + K − candidates.In the m ( K S h + h − ) fit, all of the parameters in the signal and RSP PDFs are constrainedto be the same as both describe a true D candidate. These are also fitted with a sum oftwo Crystal Ball functions, with the tail parameters fixed from simulation. The parametersare fitted separately for the D → K S π + π − and D → K S K + K − shapes, due to the differentphase space available in the D decay. The combinatorial background is parameterised byan exponential function in m ( K S h + h − ).A total signal yield of approximately 113 000 (15 000) D → K S π + π − ( D → K S K + K − )decays is obtained. This is approximately 25 times larger than the B ± → DK ± yield.In the range surrounding the signal peaks, defined as 1840–1890 (1850–1880) MeV /c in m ( K S π + π − ) ( m ( K S K + K − )) and 143.9–146.9 MeV /c in ∆ m , the background componentsaccount for 2–5 % of the yield depending on the category.The two-dimensional fit in m ( K S h + h − ) and ∆ m of the ( ) B → D ∗± µ ∓ ( ) ν µ X decay isrepeated in each Dalitz plot bin with all of the PDF parameters fixed, resulting in a rawcontrol-mode yield, R i , for each bin i . The measured R i are not equivalent to the F i fractions required to determine the CP parameters due to unavoidable differences fromselection criteria in the efficiency profiles of the signal and control modes. Examples of theefficiency profiles from simulation of the downstream candidates in 2016 data are shownin Fig. 6. For each Dalitz plot bin i a correction factor ξ i is determined to account for12 ] c / ) [GeV - p K ( m ] c / ) [ G e V + p S K ( m E ff i c i e n c y r e l a ti v e t o a v e r a g e LHCbSimulation ] c / ) [GeV - p K ( m ] c / ) [ G e V + p S K ( m E ff i c i e n c y r e l a ti v e t o a v e r a g e LHCbSimulation ] c / ) [GeV - K K ( m ] c / ) [ G e V + K S K ( m E ff i c i e n c y r e l a ti v e t o a v e r a g e LHCbSimulation ] c / ) [GeV - K K ( m ] c / ) [ G e V + K S K ( m E ff i c i e n c y r e l a ti v e t o a v e r a g e LHCbSimulation
Figure 6: Example efficiency profiles of (left) B ± → Dπ ± and (right) ( ) B → D ∗± µ ∓ ( ) ν µ X decaysin the simulation. The top (bottom) plots are for D → K S π + π − ( D → K S K + K − ) decays. Theseplots refer to downstream K S candidates under 2016 data taking conditions. The normalisationis chosen so that the average over the Dalitz plot is unity. these efficiency differences, defined as ξ i ≡ (cid:82) i dm − dm | A D ( m − , m ) | η ( m − , m ) Dπ (cid:82) i dm − dm | A D ( m − , m ) | η ( m − , m ) D ∗ µ , (12)where η ( m − , m ) Dπ and η ( m − , m ) D ∗ µ are the efficiency profiles of the B ± → Dπ ± and ( ) B → D ∗± µ ∓ ( ) ν µ X decays, respectively, and are determined from simulation. The B ± → Dπ ± decay mode is used rather than B ± → DK ± as the simulation is more easilycompared to the data, due to the larger decay rate and the smaller interference between B ± → D π ± and B ± → D π ± decays, compared to in the B ± → DK ± decay mode. It isverified using simulation that the efficiency profiles of the B ± → Dπ ± and B ± → DK ± decays are the same. The simulated events are generated with a flat distribution acrossthe D → K S h + h − phase space; hence the distribution of simulated events after triggering,13econstruction and selection is directly proportional to the efficiency profile. The amplitudemodels used to determine the Dalitz plot intensity for the correction factor are those fromRef. [23] and Ref. [24] for the D → K S π + π − and D → K S K + K − decays, respectively.The amplitude models provide a description of the intensity distribution over the Dalitzplot and introduce no significant model dependence into the analysis. The F i values canbe determined via the relation F i = h (cid:48) ξ i R i , where h (cid:48) is a normalisation factor such that thesum of all F i is unity. The F i values are determined separately for each year of data takingand K S category and are then combined in the fractions observed in the B ± → Dπ ± signal region in data. This method of determining the F i parameters is preferable tousing solely the amplitude models and B ± → Dπ ± simulated events, since the method isdata-driven. The amplitude models and simulation data enter the correction factor as aratio, and thus imperfections in the simulation and the model cancel at first order. Theaverage correction factor over all bins is approximately 2 % from unity and the largestcorrection factor is within 7 %. Uncertainties on these correction factors are driven by thesize of the simulation samples and are of a similar size as the corrections themselves. CP -violating pa-rameters x ± and y ± The Dalitz plot fit is used to measure the CP -violating parameters x ± and y ± , as introducedin Sect. 2. Following Eq. (4), these parameters are determined from the populations of the B + and B − Dalitz plot bins, given the external information of the c i and s i parametersfrom CLEO-c data and the values of F i from the semileptonic control decay modes.Although the absolute numbers of B + and B − decays integrated over the D Dalitz plothave some dependence on x ± and y ± , the sensitivity gained compared to using just therelations in Eq. (4) is negligible [49] given the available sample size. Consequently, asstated previously, the integrated yields are not used to provide information on x ± and y ± and the analysis is insensitive to B meson production and detection asymmetries.A simultaneous fit is performed on the B ± → Dh ± data, split into the two B charges,the two K S categories, the B ± → DK ± and B ± → Dπ ± candidates, and the two D → K S h + h − final states. The invariant mass of each B ± candidate is calculated usingthe results of a kinematic fit in which the D and K S masses are constrained to their knownvalues. Each category is then divided into the Dalitz plot bins shown in Fig. 1, wherethere are 16 bins for D → K S π + π − and 4 bins for D → K S K + K − . The B ± → DK ± and B ± → Dπ ± samples are fitted simultaneously because the yield of B ± → Dπ ± signalin each Dalitz plot bin is used to determine the yield of misidentified candidates in thecorresponding B ± → DK ± Dalitz plot bin. The PDF parameters for both the signaland background invariant-mass distributions are fixed to the values determined in theinvariant-mass fit described in Sect. 4. The B ± mass range is reduced to 5150–5800 GeV /c to avoid the need of a detailed description of the shape of the partially reconstructedbackground. The yields of signal candidates for each bin in the B ± → Dπ ± sample arefree parameters. In each of the B ± → DK ± channels, the total yield integrated over theDalitz plot is a free parameter. The fractional yields in each bin are defined using theexpressions for the Dalitz plot distribution in terms of x ± , y ± , F i , c i , and s i in Eq. (4),where the x ± and y ± parameters are free and the values of F i are Gaussian-constrainedwithin their uncertainties. The values of c i and s i are fixed to their central values, which14s taken into account as a source of systematic uncertainty. The yields of the componentdue to B ± → Dπ ± decays, where the companion has been misidentified as a kaon, arefixed in each B ± → DK ± bin, relative to the yield in the corresponding B ± → Dπ ± bin,using the known PID efficiencies. A component for misidentified B ± → DK ± decaysin the B ± → Dπ ± channels is not included, as it is found to contribute less than 0 . B ± and B backgrounds is fitted in each bin, using thesame shape in all bins, with the fractions of each component taken from the global fit.The total yield of the B s → D π + K − ( B s → D π − K + ) background is fixed in eachchannel, using the results of the global fit. The yield in each bin is then fixed from the F i parameters, using the known Dalitz distribution of D ( D ) → K S h + h − decays. Theseparate treatment of the partially reconstructed background from B s decays is necessarydue to the significantly different Dalitz distribution, arising because only a D meson isproduced along with a K − meson, while for the remaining modes, the D meson is eithera D meson or an admixture where the D component is r B -suppressed. The yield of thecombinatorial background in each bin is a free parameter. In bins in which an auxiliaryfit determines the yield of the partially reconstructed or combinatorial background tobe negligible, the corresponding yields are set to zero to facilitate the calculation of thecovariance matrix [50, 51].A large ensemble of pseudoexperiments is performed to validate the fit procedure. Ineach pseudoexperiment the numbers and distributions of signal and background candidatesare generated according to the expected distribution in data, and the full fit procedureis then executed. The input values for x ± and y ± correspond to γ = 70 ◦ , r B = 0 .
1, and δ B = 130 ◦ . The uncertainties determined by the fit to data are consistent with the sizeof the uncertainties determined by the pseudoexperiments. Small biases are observed inthe central values and are due to the low event yields in some of the bins. These biasesare observed to decrease in simulated experiments of larger size. The central values arecorrected for the biases and a systematic uncertainty is assigned, as described in Sect. 7.The CP parameters obtained from the fit are x − = ( 9 . ± . × − ,y − = ( 2 . ± . × − ,x + = ( − . ± . × − ,y + = ( − . ± . × − , where the uncertainties are statistical only. The correlation matrix is shown in Table 1.The total B ± → DK ± yields in the signal region, where the invariant mass of the B candidate is in the interval 5249–5319 MeV /c , are shown in Table 2.The measured values of ( x ± , y ± ) from the fit to data are displayed in Fig. 7, along withtheir likelihood contours, corresponding to statistical uncertainties only. The systematicuncertainties are discussed in the next section. The two vectors defined by the coordinates( x − , y − ) and ( x + , y + ) are not consistent with zero magnitude and they have a non-zeroopening angle. Therefore the data sample exhibits the expected features of CP violation.The opening angle is equal to 2 γ , as illustrated in Fig. 7.In order to assess the goodness of fit, and to demonstrate that the equations in ( x ± , y ± )provide a good description of data, an alternative fit is performed where the B ± → DK ± yields are measured independently in each bin. In Fig. 8 (left) the obtained yields are15 able 1: Statistical correlation matrix for the fit to data. x − y − x + y + x − − .
21 0 .
05 0 . y − − .
01 0 . x + . y + Table 2: Fit results for the total B ± → DK ± yields in the signal region, where the invariantmass of the B candidate is in the interval 5249–5319 MeV /c , integrated over the Dalitz plots. B − → DK − B + → DK + Long Downstream Long Downstream D → K S π + π − ±
26 1 315 ±
39 606 ±
26 1 334 ± D → K S K + K − ±
10 189 ±
15 82 ±
10 193 ± x ± , y ± ) obtained in the default fit.The yields from the direct fit agree with the prediction with a p -value of 0.33. In Fig. 8(right) the difference N iB + − N − iB − in each bin is calculated using the results of the direct fitof the B ± → DK ± yields. This distribution is compared to that predicted by the central( x ± , y ± ) values. The measured yield differences are compatible with the prediction witha p -value of 0.58. In addition, data are fitted with the assumption of no CP violationby enforcing x + = x − ≡ x and y + = y − ≡ y . The obtained x and y values are usedto determine the predicted values of N iB + − N − iB − , which are also shown in Fig. 8 (right). x ± y ± γ γ LHCb B − B + Figure 7: Confidence levels at 68.2%, 95.5% and 99.7% probability for ( x + , y + ) and ( x − , y − ) asmeasured in B ± → DK ± decays (statistical uncertainties only). The parameters ( x + , y + ) relateto B + decays and ( x − , y − ) refer to B − decays. The black dots show the central values obtainedin the fit. ffective bin number -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 -2 -1 1 2 - B i - N + + B i N LHCb - p + p S K - K + K S K Effective bin number -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 -2 -1 1 2 - B i - N - + B i N - - - - LHCb - p + p S K - K + K S K Figure 8: (Left) Comparison of total signal yields from the direct fit (points) to those calculatedfrom the central values of x ± and y ± (solid line). The yields are given for the effective bin: + i for B + and − i for B − , and summed over B charge and K S decay category. (Right) Comparisonof the difference between the B + and B − yield obtained in the direct fit for each effective bin(points), the prediction from the central values of x ± and y ± (solid line), and the predictionassuming no CP violation (dotted line). This prediction is not zero because the B meson production and various detection effectscan induce a global asymmetry in the measured yields. The comparison of the data tothis hypothesis yields a p -value of 1 × − , which strongly disfavours the CP -conservinghypothesis. Systematic uncertainties on the measurements of the x ± and y ± parameters are evaluatedand are presented in Table 3. The source of each systematic uncertainty is describedbelow. The systematic uncertainties are generally determined from an ensemble ofpseudoexperiments where the simulated data are generated in an alternative configurationand fitted with the default method. The mean shifts in the fitted values of x ± and y ± incomparison to their input values are taken as the systematic uncertainty.The limited precision on ( c i , s i ) coming from the CLEO measurement induces un-certainties on x ± and y ± [18]. These uncertainties are evaluated by fitting the datamultiple times, each with different ( c i , s i ) values sampled according to their experimentaluncertainties and correlations. The resulting widths in the distributions of x ± and y ± values are assigned as the systematic uncertainties. Values of (0 . . × − are foundfor the fit to the full sample. The uncertainties are similar to, but different from, thosereported in Ref. [9]. This is as expected since it is found from simulation studies that the( c i , s i )-related uncertainty depends on the particular sample under study. It is found thatthe uncertainties do become constant when simulated samples with very high signal yieldsare studied. The uncertainties arising from the CLEO measurements are kept separatefrom the other experimental uncertainties.A systematic uncertainty arises from imperfect modelling in the simulation usedto derive the efficiency correction for the determination of the F i parameters. As thesimulation enters the correction in a ratio, it is expected that imperfections cancel to firstorder. To determine the residual systematic uncertainty associated with this correction,17 able 3: Summary of uncertainties for the parameters x ± and y ± . The various sources ofsystematic uncertainties are described in the main text. All entries are given in multiples of10 − . Source x − y − x + y + Statistical 1.7 2.2 1.9 1.9Strong phase measurements 0.4 1.1 0.4 0.9Efficiency corrections 0.6 0.2 0.6 0.1Mass fit PDFs 0.2 0.3 0.2 0.3Different mis-ID shape over Dalitz plot 0.2 0.1 0.1 0.1Different low mass shape over Dalitz plot 0.1 0.2 0.1 0.1Uncertainty on B s → D π + K − yield 0.1 0.1 0.1 0.1Bias correction 0.1 0.1 0.1 0.1Bin migration 0.1 0.1 0.1 0.1 K CP violation and material interaction 0.1 0.2 0.1 0.1Total experimental systematic uncertainty 0.7 0.5 0.7 0.4an additional set of correction factors is calculated and used to evaluate an alternative setof F i parameters. To determine this additional factor, a new rectangular binning schemeis used, which is shown in Fig. 9. The bin-to-bin efficiency variation in this rectangularscheme is significantly larger than for the default partitioning and is more sensitive toimperfections in the simulated data efficiency profile. The yields of the B ± → Dπ ± and ( ) B → D ∗± µ ∓ ( ) ν µ X decays in each bin of the rectangular scheme are compared to thepredictions from the amplitude model and the simulated data efficiency profile. Theusage of the rectangular binning also helps to dilute the small level of CP violation in B ± → Dπ ± such that differences from this comparison will come primarily from efficiencyeffects. The alternative correction factors ξ alt i are calculated as ξ alt i = (cid:82) i dm − dm η ( m − , m ) Dπ | A D ( m − , m ) | C Dπ ( m − , m ) (cid:82) i dm − dm η ( m − , m ) D ∗ µ | A D ( m − , m ) | C D ∗ µ ( m − , m ) , (13)where the C ( m − , m ) terms are the ratios between the predicted and observed data yieldsin the rectangular bins. Many pseudoexperiments are performed, in which the data aregenerated according to the alternative F i parameters and then fitted with the default F i parameters. The overall shift in the fitted values of the CP parameters in comparison totheir input values is taken as the systematic uncertainty, yielding 0 . × − for x ± and0 . . × − for y + ( y − ).Various effects are considered to assign an uncertainty for the imperfections in thedescription of the invariant-mass spectrum. For the PDF used to fit the signal, theparameters of the PDF used in the binned fit are varied according to the uncertaintiesobtained in the global fit. An alternative shape is also tested. The global fit is repeatedwith the mean and width of the shape used to describe the background due to misidentifiedcompanions allowed to vary freely. The results are used to generate data sets with analternative PDF, and fit them using the default setup. The description of the partiallyreconstructed background is changed to a shape obtained from a fit of the PDF to simulateddecays. The slope of the exponential used to fit the combinatorial background is also18 c / [GeV +2 m ] c / [ G e V - m | B i n nu m b e r | c / [GeV +2 m ] c / [ G e V - m | B i n nu m b e r | Figure 9: Rectangular binning schemes for (left) D → K S π + π − decays and (right) D → K S K + K − decays. The diagonal line separates the positive and negative bins, where the positivebins are in the region in which m − > m is satisfied. fluctuated according to the uncertainty obtained in the global fit. The contributions fromeach change are summed in quadrature and are 0 . × − for each of the x ± parametersand 0 . × − for each of the y ± parameters.Two systematic uncertainties associated with the misidentified B ± → Dπ ± backgroundin the B ± → DK ± sample are considered. First, the uncertainties on the particlemisidentification probabilities are found to have a negligible effect on the measured valuesof x ± and y ± . Second, it is possible that the invariant-mass distribution of the misidentifiedbackground (the mis-ID shape) is not uniform over the Dalitz plot, as assumed in thefit. This can occur through kinematic correlations between the reconstruction efficiencyacross the Dalitz plot of the D decay and the momentum of the companion pion from the B ± decay. Alternative mass shapes are constructed by repeating the procedure used toobtain the default shape for each Dalitz bin individually. The alternative shapes are usedwhen generating data sets for pseudoexperiments, and the fits then performed assuming asingle shape, as in the fit to data. The resulting uncertainty is at most 0 . × − for all CP parameters.In the fit to the data, the relative contributions of the partially reconstructed B ± and B backgrounds are kept the same in each Dalitz bin. This is a simplification assome partially reconstructed backgrounds will be distributed as D ( D ) → K S h + h − forreconstructed B − ( B + ) candidates, while partially reconstructed B ± → D ( ∗ ) K ( ∗ ) ± decayswill be distributed as a D − D admixture depending on the relevant CP violationparameters. Pseudoexperiments are generated, where the D -decay Dalitz plot distributionfor B ± → D ∗ K + is based on the CP parameters reported in Ref. [52] and those for B ± → DK ∗ + are taken from Ref. [53]. The generated samples are fitted with the standardmethod. The resulting uncertainty is at most 0 . × − for all CP parameters.The total yield of the B s → D π + K − background in the B ± → DK ± channels is fixedrelative to the corresponding B ± → Dπ ± yield. The systematic uncertainty due to theuncertainty on the relative rate is estimated via pseudoexperiments, where data sets aregenerated with the rate varied by ± σ and fitted using the default value. The maximalmean bias for each parameter is taken as the uncertainty. The resulting uncertainty is19 . × − for all CP parameters.An uncertainty is assigned to each CP parameter to accompany the correction that isapplied for the small bias observed in the fit procedure. These uncertainties are determinedby performing sets of pseudoexperiments, each generated with different values of x ± and y ± throughout a range around the values predicted by the world averages. The spreadin observed bias is combined in quadrature with the uncertainty in the precision of thepseudoexperiments. This is taken as the systematic uncertainty and is 0 . × − for all CP parameters.The systematic uncertainty from the effect of candidates being assigned the wrongDalitz bin number is considered. The resolution in m and m − is approximately0.006 GeV /c for candidates with long K S decays and 0.007 GeV /c for candidates withdownstream K S decays. While this is small compared to the typical width of a bin, netmigration can occur in regions where the presence of resonances cause the density tochange rapidly. To first order this effect is accounted for by use of the control channel.However, differences in the distributions of the Dalitz plots due to efficiency differences orthe nonzero value of r B in the signal decay may cause residual effects. The uncertaintyfrom this is determined via pseudoexperiments, in which different input F i values are usedto reflect the residual migration. The size of any possible bias is found to be 0 . × − for all CP parameters.There is a systematic uncertainty related to CP violation in the neutral kaon systemdue to the fact that the K S state is not an exact CP eigenstate and, separately, due todifferent nuclear interaction cross-sections of the K and K mesons. The measurementis insensitive to global asymmetries, but is affected by the different Dalitz distributionsof D → K S h − h + and D → K L h − h + decays, as well as any correlations between Dalitzcoordinates and the net material interaction. The potential bias on x ± and y ± is assessedusing a series of pseudoexperiments, where data are generated taking the effects intoaccount and fitted using the default fit. The D → K L h − h + Dalitz distribution is estimatedby transforming an amplitude model of D → K S h − h + [22], following arguments andassumptions laid out in Ref. [18]. The effect of material interaction is treated using theformalism described in Ref. [54]. The size of the potential bias is found to be ≤ . × − for all CP parameters, corresponding to a bias on γ of approximately 0 . ◦ , which is withinexpected limits [55].The nonuniform efficiency profile over the Dalitz plot means that the values of ( c i , s i )appropriate for this analysis can differ from those measured by the CLEO collaboration,which correspond to the constant-efficiency case. Amplitude models are used to calculatethe values of c i and s i both with and without the efficiency profiles determined fromsimulation. The models are taken from Ref. [23] for D → K S π + π − decays and fromRef. [24] for D → K S K + K − decays. The difference is taken as an estimate of the size ofthis effect. Pseudoexperiments are generated in which the values have been shifted bythis difference, and then fitted with the default ( c i , s i ) values. The resulting bias on x ± and y ± is found to be negligible.The effect that a detection asymmetry between hadrons of opposite charge can haveon the symmetry of the efficiency across the Dalitz plot is found to be negligible. Changesin the mass model used to describe the semileptonic control sample are also found to havea negligible effect on the F i values.Finally, several checks are conducted to assess the stability of the results. Theseinclude repeating the fits separately for both K S categories, for each data-taking year,20 able 4: Correlation matrix of the experimental and strong-phase related systematic uncertainties. x − y − x + y + x − − .
25 0 . − . y − − . − . x + . y + pp collision. No anomalies are found and no additional systematic uncertainties are assigned.In total the systematic uncertainties are less than half of the corresponding statisticaluncertainties. The correlation matrix obtained for the combined effect of the sources ofexperimental and strong-phase related systematic uncertainties is given in Table 4. The CP observables are measured to be x − = ( 9 . ± . ± . ± . × − ,y − = ( 2 . ± . ± . ± . × − ,x + = ( − . ± . ± . ± . × − ,y + = ( − . ± . ± . ± . × − , where the first uncertainty is statistical, the second is the total experimental systematicuncertainty and the third is that arising from the precision of the CLEO measurements.The signature for CP violation is that ( x + , y + ) (cid:54) = ( x − , y − ). The distance between( x + , y + ) and ( x − , y − ) is calculated, taking all uncertainties and correlations into account,and found to be | ( x + , y + ) − ( x − , y − ) | = (17 . ± . × − , which is different from zeroby 6.4 standard deviations. This constitutes the first observation of CP violation in B ± → DK ± decays for the D → K S h + h − final states.These results are compared to the expected central values of x ± and y ± that can becomputed from r B , δ B , and γ as determined in the LHCb combination in Ref. [52], andthe results are shown in Fig. 10 (the later LHCb combination in Ref. [56] includes theresults of this measurement and is therefore unsuitable for comparison). The two setsof ( x + , y + ) are in agreement within 1.6 standard deviations when the uncertainties andcorrelations of both the LHCb combination and this measurement are taken into account.There is a 2.7 standard deviation tension between the measured values of ( x − , y − ) and thevalues calculated from the LHCb combination. This tension will be investigated furtherwhen this measurement and the LHCb combination are updated using data taken in 2017and 2018.The results for x ± and y ± are interpreted in terms of the underlying physics parameters γ , r B and δ B . The interpretation is done via a maximum likelihood fit using a frequentisttreatment as described in Ref. [57]. The solution for the physics parameters has a two-fold21 x – y - - - - LHCb - B + B Figure 10: Two-dimensional 68.3 %, 95.5 % and 99.7 % confidence regions for ( x ± , y ± ) obtainedin this measurement, as well as for the LHCb combination in Ref. [52], taking statistical andsystematic uncertainties, as well as their correlations, into account. ambiguity as the equations are invariant under the simultaneous substitutions γ → γ +180 ◦ and δ B → δ B + 180 ◦ . The solution that satisfies 0 < γ < ◦ is chosen. The centralvalues and 68% (95%) confidence intervals, calculated with the PLUGIN [58] method, are γ = 87 ◦ +11 ◦ − ◦ (cid:0) +22 ◦ − ◦ (cid:1) ,r B = 0 . +0 . − . (cid:0) +0 . − . (cid:1) ,δ B = 101 ◦ +11 ◦ − ◦ (cid:0) +22 ◦ − ◦ (cid:1) . The values for γ and r B are consistent with those presented in Ref. [52]. This is the mostprecise measurement of γ from a single analysis. The value of δ B shows some disagreementwith Ref. [52], where the angle is determined to be (cid:0) . +4 . − . (cid:1) ◦ .The values of x ± , y ± measured in this analysis can be combined with those from thecorresponding analysis of Run 1 data [9]. This procedure is done via a maximum likelihoodfit, as implemented in the gammacombo package [57]. The previous measurements areidentified by the index I, and the results within this paper are identified by the index II.When combining the two results, the fit determines the (ˆ x ± , ˆ y ± ) parameters that maximizethe multivariate Gaussian likelihood function L ( z | ˆ z ) = ((2 π ) | Σ | ) − / exp (cid:20) −
12 ( z − ˆ z ) T Σ − ( z − ˆ z ) (cid:21) , (14)where z = ( x I ± , y I ± , x II ± , y II ± ) T and ˆ z = (ˆ x ± , ˆ y ± , ˆ x ± , ˆ y ± ) T are 8 × × (cid:18) Σ I Σ I–II Σ II–I Σ II (cid:19) . (15)The covariance matrix is expressed in terms of the covariance matrices obtained for theindividual measurements, Σ I and Σ II , and the cross-covariance matrix Σ I–II describing22 able 5: Correlation matrix between Run 1 results (I) and the results presented in this paper (II),when fitting data while varying the inputs from the CLEO collaboration in a correlated way.
CLEO cross-run correlation matrix x II − y II − x II+ y II+ x I − .
02 0 . − . − . y I − . − .
23 0 . − . x I+ − .
19 0 .
01 0 . − . y I+ − . − .
28 0 .
13 0 . Table 6: Total correlation matrix for the systematic uncertainties of the Run 1 results (I) and theresults presented in this paper (II), including experimental and strong phase related systematicuncertainties.
Total systematic cross-run correlation matrix x II − y II − x II+ y II+ x I − .
76 0 .
04 0 .
55 0 . y I − . − . − . − . x I+ . − .
19 0 .
91 0 . y I+ − . − .
24 0 .
17 0 . II ,is calculated using the total statistical and systematic uncertainties, and the correlationmatrices in Tables 1 and 4. The covariance matrix for the Run 1 measurement, Σ I , istaken from Ref. [9], where it was calculated taking strong-phase-related correlations intoaccount, but treating the experimental systematic uncertainties as uncorrelated. Theimpact of using the correlation matrix in Table 4 for these instead is found to be negligible.The dominant uncertainty in both measurements is the statistical uncertainty. As themeasurements use independent data sets, the statistical uncertainties are uncorrelated.The cross-correlations of the systematic errors between measurements due to the strongphase inputs are obtained from the results of a series of fits to the two data sets in whichthe strong phases are varied identically. This mirrors the procedure used to evaluate theuncertainties within a single data set. The obtained cross-correlations between the fitresults are given in Table 5. The elements on the diagonal do not have unit value becausethe obtained correlations depend on the specific data sets for the two measurements.The combination is performed assuming full correlation between the non-strong-phaserelated experimental systematic uncertainties in Run 1 and this measurement. Thecorrelation matrix for the experimental uncertainties of this analysis is used as the cross-run correlation of the experimental systematic uncertainties. The complete correlationmatrix for the experimental and strong-phase-related systematic uncertainties is givenin Table 6. The impact on the combination due to different assumptions on the cross-correlations of the systematic uncertainties is found to be negligible. This is unsurprisingas both measurements remain limited in precision by their statistical uncertainties. Thecentral values, along with the combined statistical and systematic uncertainties for this23 (cid:176) [ g B r Run 12015 & 2016 dataCombined result
LHCb ] (cid:176) [ g ] (cid:176) [ B d Run 12015 & 2016 dataCombined result
LHCb
Figure 11: Two-dimensional 68.3 % and 95.5 % confidence regions for ( γ, r B , δ B ) for the x ± , y ± parameters obtained in the fit to 2015 and 2016 data, the fit to Run 1 data, and theircombinations. combination are < x − > = ( 7 . ± . × − ,< y − > = ( 4 . ± . × − ,< x + > = ( − . ± . × − ,< y + > = ( − . ± . × − . The interpretation in terms of the underlying physics parameters is performed on thecombined values of x ± and y ± and the central values and their 68% (95%) confidenceintervals are γ = 80 ◦ +10 ◦ − ◦ (cid:0) +19 ◦ − ◦ (cid:1) ,r B = 0 . +0 . − . (cid:0) +0 . − . (cid:1) ,δ B = 110 ◦ +10 ◦ − ◦ (cid:0) +19 ◦ − ◦ (cid:1) . The results of the interpretation for both the combined and individual data sets are shownin Fig. 11, where the projections of the three-dimensional surfaces bounding the oneand two standard deviation volumes on the ( γ , r B ) and ( γ , δ B ) planes are shown. Theuncertainty on γ is inversely proportional to r B . Therefore the lower central value of r B in the combined results lead to a larger than naively expected uncertainty on γ whenboth data sets are used. The contribution of each source of uncertainty are estimated byperforming the combination while taking only subsets of the uncertainties into account. Itis found that the statistical uncertainty on γ is 8 . ◦ , the uncertainty due to strong-phaseinputs is 4 ◦ , and the uncertainty due to experimental systematic effects is 2 ◦ . Approximately 4100 (560) B ± → DK ± decays with the D meson decaying to K S π + π − ( K S K + K − ) are selected from data corresponding to an integrated luminosity of 2.0 fb − collected with the LHCb detector in 2015 and 2016. These samples are analysed todetermine the CP -violating parameters x ± ≡ r B cos( δ B ± γ ) and y ± ≡ r B sin( δ B ± γ ),24here r B is the ratio of the absolute values of the B + → D K − and B + → D K − amplitudes, δ B is their strong-phase differences, and γ is an angle of the Unitarity Triangle.The analysis is performed in bins of the D -decay Dalitz plot and existing measurementsperformed by the CLEO collaboration [18] are used to provide input on the D -decaystrong-phase parameters ( c i , s i ). Such an approach allows the analysis to be free frommodel-dependent assumptions on the strong-phase variation across the Dalitz plot. Thispaper also gives the combination with the results obtained with an earlier data set,thereby allowing further improvements in the precision on γ . Considering only the datacollected in 2015 and 2016 and choosing the solution that satisfies 0 < γ < ◦ yields r B = 0 . +0 . − . , δ B = (101 ± ◦ , and γ = (87 +11 − ) ◦ . The values of r B and γ are consistentwith world averages, while there is some tension in the determined value of δ B . This couldbe resolved by future analyses of the B → DK mode in a variety of D decays, includingthose analysed here, utilising the data set that is being collected with LHCb in 2017 and2018. The measurement reported in this paper represents the most precise determinationof γ from a single analysis. 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); MinES and FASO (Russia); MinECo (Spain);SNSF and SER (Switzerland); NASU (Ukraine); STFC (United Kingdom); 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 indebted tothe communities behind the multiple open-source software packages on which we depend.Individual groups or members have received support from AvH Foundation (Germany),EPLANET, Marie Sk(cid:32)lodowska-Curie Actions and ERC (European Union), ANR, LabexP2IO and OCEVU, and R´egion Auvergne-Rhˆone-Alpes (France), Key Research Programof Frontier Sciences of CAS, CAS PIFI, and the Thousand Talents Program (China),RFBR, RSF and Yandex LLC (Russia), GVA, XuntaGal and GENCAT (Spain), HerchelSmith Fund, the Royal Society, the English-Speaking Union and the Leverhulme Trust(United Kingdom).
References [1] N. Cabibbo,
Unitary symmetry and leptonic decays , Phys. Rev. Lett. (1963) 531.[2] M. Kobayashi and T. Maskawa, CP-violation in the renormalizable theory of weakinteraction , Prog. Theor. Phys. (1973) 652.[3] J. Brod and J. Zupan, The ultimate theoretical error on γ from B → DK decays ,JHEP (2014) 051, arXiv:1308.5663 .254] Heavy Flavor Averaging Group, Y. Amhis et al. , Averages of b -hadron, c -hadron, and τ -lepton properties as of summer 2016 , Eur. Phys. J. C77 (2017) 895, arXiv:1612.07233 , updated results and plots available at https://hflav.web.cern.ch .[5] D. Atwood, I. Dunietz, and A. Soni,
Improved methods for observing CP violation in B ± → KD and measuring the CKM phase γ , Phys. Rev. D63 (2001) 036005.[6] A. Giri, Y. Grossman, A. Soffer, and J. Zupan,
Determining γ using B ± → DK ± with multibody D decays , Phys. Rev. D68 (2003) 054018, arXiv:hep-ph/0303187 .[7] A. Bondar,
Proceedings of BINP special analysis meeting on Dalitz analysis, 24-26Sep. 2002, unpublished .[8] LHCb collaboration, R. Aaij et al. , A study of CP violation in B ± → DK ± and B ± → Dπ ± decays with D → K S K ± π ∓ final states , Phys. Lett. B733 (2014) 36, arXiv:1402.2982 .[9] LHCb collaboration, R. Aaij et al. , Measurement of the CKM angle γ using B ± → DK ± with D → K S π + π − , K S K + K − decays , JHEP (2014) 097, arXiv:1408.2748 .[10] LHCb collaboration, R. Aaij et al. , A study of CP violation in B ∓ → Dh ∓ ( h = K, π ) with the modes D → K ∓ π ± π , D → π + π − π and D → K + K − π , Phys. Rev. D91 (2015) 112014, arXiv:1504.05442 .[11] LHCb collaboration, R. Aaij et al. , Measurement of CP observables in B ± → DK ± and B ± → Dπ ± with two- and four-body D decays , Phys. Lett. B760 (2016) 117, arXiv:1603.08993 .[12] LHCb collaboration, R. Aaij et al. , Measurement of CP violation parameters in B → DK ∗ decays , Phys. Rev. D90 (2014) 112002, arXiv:1407.8136 .[13] LHCb collaboration, R. Aaij et al. , Measurement of CP asymmetry in B s → D ∓ s K ± decays , JHEP (2014) 060, arXiv:1407.6127 .[14] LHCb collaboration, R. Aaij et al. , Study of B − → DK − π + π − and B − → Dπ − π + π − decays and determination of the CKM angle γ , Phys. Rev. D92 (2015) 112005, arXiv:1505.07044 .[15] LHCb collaboration, R. Aaij et al. , Constraints on the unitarity triangle angle γ from Dalitz plot analysis of B → DK + π − decays , Phys. Rev. D93 (2016) 112018, arXiv:1602.03455 .[16] A. Bondar and A. Poluektov,
Feasibility study of model-independent approachto φ measurement using Dalitz plot analysis , Eur. Phys. J. C47 (2006) 347, arXiv:hep-ph/0510246 .[17] A. Bondar and A. Poluektov,
The use of quantum-correlated D decays for φ measurement , Eur. Phys. J. C55 (2008) 51, arXiv:0801.0840 .2618] CLEO collaboration, J. Libby et al. , Model-independent determination of the strong-phase difference between D and D → K , L h + h − ( h = π, K ) and its impacton the measurement of the CKM angle γ/φ , Phys. Rev. D82 (2010) 112006, arXiv:1010.2817 .[19] Belle collaboration, H. Aihara et al. , First measurement of φ with a model-independent Dalitz plot analysis of B ± → DK ± , D → K π + π − decay , Phys. Rev. D85 (2012) 112014, arXiv:1204.6561 .[20] Belle collaboration, K. Negishi et al. , First model-independent Dalitz analysisof B → DK ∗ , D → K π + π − decay , Prog. Theor. Exp. Phys. arXiv:1509.01098 .[21] LHCb collaboration, R. Aaij et al. , Model-independent measurement of the CKMangle γ using B → DK ∗ decays with D → K S π + π − and K S K + K − , JHEP (2016) 131, arXiv:1604.01525 .[22] BaBar collaboration, B. Aubert et al. , Measurement of the Cabibbo-Kobayashi-Maskawa angle γ in B ∓ → D ( ∗ ) K ∓ decays with a Dalitz analysis of D → K π − π + ,Phys. Rev. Lett. (2005) 121802, arXiv:hep-ex/0504039 .[23] BaBar collaboration, B. Aubert et al. , Improved measurement of the CKM angle γ in B ∓ → D ( ∗ ) K ( ∗ ) ∓ decays with a Dalitz plot analysis of D decays to K π + π − and K K + K − , Phys. Rev. D78 (2008) 034023, arXiv:0804.2089 .[24] BaBar collaboration, P. del Amo Sanchez et al. , Evidence for direct CP violation inthe measurement of the Cabibbo-Kobayashi-Maskawa angle γ with B ∓ → D ( ∗ ) K ( ∗ ) ∓ decays , Phys. Rev. Lett. (2010) 121801, arXiv:1005.1096 .[25] Belle collaboration, A. Poluektov et al. , Measurement of φ with Dalitz plot analysisof B ± → D ( ∗ ) K ± decay , Phys. Rev. D70 (2004) 072003, arXiv:hep-ex/0406067 .[26] Belle collaboration, A. Poluektov et al. , Measurement of φ with Dalitz plot analysisof B + → D ( ∗ ) K ( ∗ )+ decay , Phys. Rev. D73 (2006) 112009, arXiv:hep-ex/0604054 .[27] Belle collaboration, A. Poluektov et al. , Evidence for direct CP violation in the decay B ± → D ( ∗ ) K ± , D → K π + π − and measurement of the CKM phase φ , Phys. Rev. D81 (2010) 112002, arXiv:1003.3360 .[28] LHCb collaboration, R. Aaij et al. , Measurement of CP violation and constraintson the CKM angle γ in B ± → DK ± with D → K S π + π − decays , Nucl. Phys. B888 (2014) 169, arXiv:1407.6211 .[29] M. Battaglieri et al. , Analysis Tools for Next-Generation Hadron Spectroscopy Exper-iments , Acta Phys. Polon.
B46 (2015) 257, arXiv:1412.6393 .[30] LHCb collaboration, R. Aaij et al. , A model-independent Dalitz plot analysis of B ± → DK ± with D → K S h + h − ( h = π, K ) decays and constraints on the CKMangle γ , Phys. Lett. B718 (2012) 43, arXiv:1209.5869 .2731] A. Bondar, A. Poluektov, and V. Vorobiev,
Charm mixing in a model-independent analysis of correlated D D decays , Phys. Rev. D82 (2010) 034033, arXiv:1004.2350 .[32] LHCb collaboration, A. A. Alves Jr. et al. , The LHCb detector at the LHC , JINST (2008) S08005.[33] LHCb collaboration, R. Aaij et al. , LHCb detector performance , Int. J. Mod. Phys.
A30 (2015) 1530022, arXiv:1412.6352 .[34] V. V. Gligorov and M. Williams,
Efficient, reliable and fast high-level triggering usinga bonsai boosted decision tree , JINST (2013) P02013, arXiv:1210.6861 .[35] T. Sj¨ostrand, S. Mrenna, and P. Skands, A brief introduction to PYTHIA8.1 , Comput. Phys. Commun. (2008) 852, arXiv:0710.3820 ; T. Sj¨ostrand,S. Mrenna, and P. Skands,
PYTHIA 6.4 physics and manual , JHEP (2006) 026, arXiv:hep-ph/0603175 .[36] I. Belyaev et al. , Handling of the generation of primary events in Gauss, the LHCbsimulation framework , J. Phys. Conf. Ser. (2011) 032047.[37] D. J. Lange,
The EvtGen particle decay simulation package , Nucl. Instrum. Meth.
A462 (2001) 152.[38] P. Golonka and Z. Was,
PHOTOS Monte Carlo: A precision tool for QED correctionsin Z and W decays , Eur. Phys. J. C45 (2006) 97, arXiv:hep-ph/0506026 .[39] Geant4 collaboration, J. Allison et al. , Geant4 developments and applications , IEEETrans. Nucl. Sci. (2006) 270; Geant4 collaboration, S. Agostinelli et al. , Geant4:A simulation toolkit , Nucl. Instrum. Meth.
A506 (2003) 250.[40] M. Clemencic et al. , The LHCb simulation application, Gauss: Design, evolution andexperience , J. Phys. Conf. Ser. (2011) 032023.[41] W. D. Hulsbergen,
Decay chain fitting with a Kalman filter , Nucl. Instrum. Meth.
A552 (2005) 566, arXiv:physics/0503191 .[42] Particle Data Group, C. Patrignani et al. , Review of particle physics , Chin. Phys.
C40 (2016) 100001, and 2017 update.[43] L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stone,
Classification andregression trees , Wadsworth international group, Belmont, California, USA, 1984.[44] Y. Freund and R. E. Schapire,
A decision-theoretic generalization of on-line learningand an application to boosting , J. Comput. Syst. Sci. (1997) 119.[45] T. Skwarnicki, A study of the radiative cascade transitions between the Upsilon-primeand Upsilon resonances , PhD thesis, Institute of Nuclear Physics, Krakow, 1986,DESY-F31-86-02.[46] M. Pivk and F. R. Le Diberder, sPlot: A statistical tool to unfold data distributions ,Nucl. Instrum. Meth.
A555 (2005) 356, arXiv:physics/0402083 .2847] LHCb collaboration, R. Aaij et al. , Measurement of CP observables in B ± → D ( ∗ ) K ± and B ± → D ( ∗ ) π ± decays , Phys. Lett. B777 (2017) 16, arXiv:1708.06370 .[48] LHCb collaboration, R. Aaij et al. , Dalitz plot analysis of B s → D K − π + decays ,Phys. Rev. D90 (2014) 072003, arXiv:1407.7712 .[49] T. Gershon, J. Libby, and G. Wilkinson,
Contributions to the width differencein the neutral D system from hadronic decays , Phys. Lett. B750 (2015) 338, arXiv:1506.08594 .[50] F. James and M. Winkler,
MINUIT user’s guide , 2004.[51] F. James and M. Roos,
Minuit: A System for Function Minimization and Analysisof the Parameter Errors and Correlations , Comput. Phys. Commun. (1975) 343.[52] LHCb collaboration, Update of the LHCb combination of the CKM angle γ using B → DK decays , LHCb-CONF-2017-004.[53] LHCb collaboration, R. Aaij et al. , Measurement of CP observables in B ± → DK ∗± decays using two- and four-body D final states , JHEP (2017) 156, arXiv:1709.05855 .[54] LHCb collaboration, R. Aaij et al. , Measurement of CP asymmetry in D → K − K + and D → π − π + decays , JHEP (2014) 041, arXiv:1405.2797 .[55] Y. Grossman and M. Savastio, Effects of K – K mixing on determining γ from B ± → DK ± , JHEP (2014) 008, arXiv:1311.3575 .[56] LHCb collaboration, Update of the LHCb combination of the CKM angle γ , LHCb-CONF-2018-002.[57] LHCb collaboration, R. Aaij et al. , Measurement of the CKM angle γ from a combi-nation of LHCb results , JHEP (2016) 087, arXiv:1611.03076 .[58] B. Sen, M. Walker, and M. Woodroofe, On the unified method with nuisance parame-ters , Statistica Sinica (2009) 301. 29 HCb collaboration
R. Aaij , B. Adeva , M. Adinolfi , C.A. Aidala , Z. Ajaltouni , S. Akar , P. Albicocco ,J. Albrecht , F. Alessio , M. Alexander , A. Alfonso Albero , S. Ali , G. Alkhazov ,P. Alvarez Cartelle , A.A. Alves Jr , S. Amato , S. Amerio , Y. Amhis , L. An ,L. Anderlini , G. Andreassi , M. Andreotti ,g , J.E. Andrews , R.B. Appleby , F. Archilli ,P. d’Argent , J. Arnau Romeu , A. Artamonov , M. Artuso , K. Arzymatov , E. Aslanides ,M. Atzeni , S. Bachmann , J.J. Back , S. Baker , V. Balagura ,b , W. Baldini ,A. Baranov , R.J. Barlow , S. Barsuk , W. Barter , F. Baryshnikov , V. Batozskaya ,B. Batsukh , V. Battista , A. Bay , J. Beddow , F. Bedeschi , I. Bediaga , A. Beiter ,L.J. Bel , N. Beliy , V. Bellee , N. Belloli ,i , K. Belous , I. Belyaev , , E. Ben-Haim ,G. Bencivenni , S. Benson , S. Beranek , A. Berezhnoy , R. Bernet , D. Berninghoff ,E. Bertholet , A. Bertolin , C. Betancourt , F. Betti , , M.O. Bettler , M. van Beuzekom ,Ia. Bezshyiko , S. Bhasin , J. Bhom , S. Bifani , P. Billoir , A. Birnkraut , A. Bizzeti ,u ,M. Bjørn , M.P. Blago , T. Blake , F. Blanc , S. Blusk , D. Bobulska , V. Bocci ,O. Boente Garcia , T. Boettcher , A. Bondar ,w , N. Bondar , S. Borghi , , M. Borisyak ,M. Borsato , , F. Bossu , M. Boubdir , T.J.V. Bowcock , C. Bozzi , , S. Braun ,M. Brodski , J. Brodzicka , D. Brundu , E. Buchanan , A. Buonaura , C. Burr ,A. Bursche , J. Buytaert , W. Byczynski , S. Cadeddu , H. Cai , R. Calabrese ,g ,R. Calladine , M. Calvi ,i , M. Calvo Gomez ,m , A. Camboni ,m , P. Campana ,D.H. Campora Perez , L. Capriotti , A. Carbone ,e , G. Carboni , R. Cardinale ,h ,A. Cardini , P. Carniti ,i , L. Carson , K. Carvalho Akiba , G. Casse , L. Cassina ,M. Cattaneo , G. Cavallero ,h , R. Cenci ,p , D. Chamont , M.G. Chapman , M. Charles ,Ph. Charpentier , G. Chatzikonstantinidis , M. Chefdeville , V. Chekalina , C. Chen ,S. Chen , S.-G. Chitic , V. Chobanova , M. Chrzaszcz , A. Chubykin , P. Ciambrone ,X. Cid Vidal , G. Ciezarek , P.E.L. Clarke , M. Clemencic , H.V. Cliff , J. Closier ,V. Coco , J. Cogan , E. Cogneras , L. Cojocariu , P. Collins , T. Colombo ,A. Comerma-Montells , A. Contu , G. Coombs , S. Coquereau , G. Corti , M. Corvo ,g ,C.M. Costa Sobral , B. Couturier , G.A. Cowan , D.C. Craik , A. Crocombe ,M. Cruz Torres , R. Currie , C. D’Ambrosio , F. Da Cunha Marinho , C.L. Da Silva ,E. Dall’Occo , J. Dalseno , A. Danilina , A. Davis , O. De Aguiar Francisco ,K. De Bruyn , S. De Capua , M. De Cian , J.M. De Miranda , L. De Paula ,M. De Serio ,d , P. De Simone , C.T. Dean , D. Decamp , L. Del Buono , B. Delaney ,H.-P. Dembinski , M. Demmer , A. Dendek , D. Derkach , O. Deschamps , F. Desse ,F. Dettori , B. Dey , A. Di Canto , P. Di Nezza , S. Didenko , H. Dijkstra , F. Dordei ,M. Dorigo ,y , A. Dosil Su´arez , L. Douglas , A. Dovbnya , K. Dreimanis , L. Dufour ,G. Dujany , P. Durante , J.M. Durham , D. Dutta , R. Dzhelyadin , M. Dziewiecki ,A. Dziurda , A. Dzyuba , S. Easo , U. Egede , V. Egorychev , S. Eidelman ,w ,S. Eisenhardt , U. Eitschberger , R. Ekelhof , L. Eklund , S. Ely , A. Ene , S. Escher ,S. Esen , T. Evans , A. Falabella , N. Farley , S. Farry , D. Fazzini , ,i , L. Federici ,G. Fernandez , P. Fernandez Declara , A. Fernandez Prieto , F. Ferrari ,L. Ferreira Lopes , F. Ferreira Rodrigues , M. Ferro-Luzzi , S. Filippov , R.A. Fini ,M. Fiorini ,g , M. Firlej , C. Fitzpatrick , T. Fiutowski , F. Fleuret ,b , M. Fontana , ,F. Fontanelli ,h , R. Forty , V. Franco Lima , M. Frank , C. Frei , J. Fu ,q , W. Funk ,C. F¨arber , M. F´eo Pereira Rivello Carvalho , E. Gabriel , A. Gallas Torreira , D. Galli ,e ,S. Gallorini , S. Gambetta , M. Gandelman , P. Gandini , Y. Gao , L.M. Garcia Martin ,B. Garcia Plana , J. Garc´ıa Pardi˜nas , J. Garra Tico , L. Garrido , D. Gascon ,C. Gaspar , L. Gavardi , G. Gazzoni , D. Gerick , E. Gersabeck , M. Gersabeck ,T. Gershon , D. Gerstel , Ph. Ghez , S. Gian`ı , V. Gibson , O.G. Girard , L. Giubega ,K. Gizdov , V.V. Gligorov , D. Golubkov , A. Golutvin , , A. Gomes ,a , I.V. Gorelov , . Gotti ,i , E. Govorkova , J.P. Grabowski , R. Graciani Diaz , L.A. Granado Cardoso ,E. Graug´es , E. Graverini , G. Graziani , A. Grecu , R. Greim , P. Griffith , L. Grillo ,L. Gruber , B.R. Gruberg Cazon , O. Gr¨unberg , C. Gu , E. Gushchin , Yu. Guz , ,T. Gys , C. G¨obel , T. Hadavizadeh , C. Hadjivasiliou , G. Haefeli , C. Haen ,S.C. Haines , B. Hamilton , X. Han , T.H. Hancock , S. Hansmann-Menzemer ,N. Harnew , S.T. Harnew , T. Harrison , C. Hasse , M. Hatch , J. He , M. Hecker ,K. Heinicke , A. Heister , K. Hennessy , L. Henry , E. van Herwijnen , M. Heß ,A. Hicheur , D. Hill , M. Hilton , P.H. Hopchev , W. Hu , W. Huang , Z.C. Huard ,W. Hulsbergen , T. Humair , M. Hushchyn , D. Hutchcroft , D. Hynds , P. Ibis ,M. Idzik , P. Ilten , K. Ivshin , R. Jacobsson , J. Jalocha , E. Jans , A. Jawahery ,F. Jiang , M. John , D. Johnson , C.R. Jones , C. Joram , B. Jost , N. Jurik ,S. Kandybei , M. Karacson , J.M. Kariuki , S. Karodia , N. Kazeev , M. Kecke ,F. Keizer , M. Kelsey , M. Kenzie , T. Ketel , E. Khairullin , B. Khanji ,C. Khurewathanakul , K.E. Kim , T. Kirn , S. Klaver , K. Klimaszewski , T. Klimkovich ,S. Koliiev , M. Kolpin , R. Kopecna , P. Koppenburg , I. Kostiuk , S. Kotriakhova ,M. Kozeiha , L. Kravchuk , M. Kreps , F. Kress , P. Krokovny ,w , W. Krupa ,W. Krzemien , W. Kucewicz ,l , M. Kucharczyk , V. Kudryavtsev ,w , A.K. Kuonen ,T. Kvaratskheliya , , D. Lacarrere , G. Lafferty , A. Lai , D. Lancierini , G. Lanfranchi ,C. Langenbruch , T. Latham , C. Lazzeroni , R. Le Gac , A. Leflat , J. Lefran¸cois ,R. Lef`evre , F. Lemaitre , O. Leroy , T. Lesiak , B. Leverington , P.-R. Li , T. Li , Z. Li ,X. Liang , T. Likhomanenko , R. Lindner , F. Lionetto , V. Lisovskyi , X. Liu , D. Loh ,A. Loi , I. Longstaff , J.H. Lopes , G.H. Lovell , D. Lucchesi ,o , M. Lucio Martinez ,A. Lupato , E. Luppi ,g , O. Lupton , A. Lusiani , X. Lyu , F. Machefert , F. Maciuc ,V. Macko , P. Mackowiak , S. Maddrell-Mander , O. Maev , , K. Maguire ,D. Maisuzenko , M.W. Majewski , S. Malde , B. Malecki , A. Malinin , T. Maltsev ,w ,G. Manca ,f , G. Mancinelli , D. Marangotto ,q , J. Maratas ,v , J.F. Marchand , U. Marconi ,C. Marin Benito , M. Marinangeli , P. Marino , J. Marks , G. Martellotti , M. Martin ,M. Martinelli , D. Martinez Santos , F. Martinez Vidal , A. Massafferri , R. Matev ,A. Mathad , Z. Mathe , C. Matteuzzi , A. Mauri , E. Maurice ,b , B. Maurin ,A. Mazurov , M. McCann , , A. McNab , R. McNulty , J.V. Mead , B. Meadows ,C. Meaux , F. Meier , N. Meinert , D. Melnychuk , M. Merk , A. Merli ,q , E. Michielin ,D.A. Milanes , E. Millard , M.-N. Minard , L. Minzoni ,g , D.S. Mitzel , A. Mogini ,J. Molina Rodriguez ,z , T. Momb¨acher , I.A. Monroy , S. Monteil , M. Morandin ,G. Morello , M.J. Morello ,t , O. Morgunova , J. Moron , A.B. Morris , R. Mountain ,F. Muheim , M. Mulder , C.H. Murphy , D. Murray , D. M¨uller , J. M¨uller , K. M¨uller ,V. M¨uller , P. Naik , T. Nakada , R. Nandakumar , A. Nandi , T. Nanut , I. Nasteva ,M. Needham , N. Neri , S. Neubert , N. Neufeld , M. Neuner , T.D. Nguyen ,C. Nguyen-Mau ,n , S. Nieswand , R. Niet , N. Nikitin , A. Nogay , D.P. O’Hanlon ,A. Oblakowska-Mucha , V. Obraztsov , S. Ogilvy , R. Oldeman ,f , C.J.G. Onderwater ,A. Ossowska , J.M. Otalora Goicochea , P. Owen , A. Oyanguren , P.R. Pais , A. Palano ,M. Palutan , , G. Panshin , A. Papanestis , M. Pappagallo , L.L. Pappalardo ,g ,W. Parker , C. Parkes , G. Passaleva , , A. Pastore , M. Patel , C. Patrignani ,e ,A. Pearce , A. Pellegrino , G. Penso , M. Pepe Altarelli , S. Perazzini , D. Pereima ,P. Perret , L. Pescatore , K. Petridis , A. Petrolini ,h , A. Petrov , S. Petrucci ,M. Petruzzo ,q , B. Pietrzyk , G. Pietrzyk , M. Pikies , M. Pili , D. Pinci , J. Pinzino ,F. Pisani , A. Piucci , V. Placinta , S. Playfer , J. Plews , M. Plo Casasus , F. Polci ,M. Poli Lener , A. Poluektov , N. Polukhina ,c , I. Polyakov , E. Polycarpo , G.J. Pomery ,S. Ponce , A. Popov , D. Popov , , S. Poslavskii , C. Potterat , E. Price ,J. Prisciandaro , C. Prouve , V. Pugatch , A. Puig Navarro , H. Pullen , G. Punzi ,p ,W. Qian , J. Qin , R. Quagliani , B. Quintana , B. Rachwal , J.H. Rademacker , . Rama , M. Ramos Pernas , M.S. Rangel , F. Ratnikov ,x , G. Raven ,M. Ravonel Salzgeber , M. Reboud , F. Redi , S. Reichert , A.C. dos Reis , F. Reiss ,C. Remon Alepuz , Z. Ren , V. Renaudin , S. Ricciardi , S. Richards , K. Rinnert ,P. Robbe , A. Robert , A.B. Rodrigues , E. Rodrigues , J.A. Rodriguez Lopez ,M. Roehrken , A. Rogozhnikov , S. Roiser , A. Rollings , V. Romanovskiy ,A. Romero Vidal , M. Rotondo , M.S. Rudolph , T. Ruf , J. Ruiz Vidal ,J.J. Saborido Silva , N. Sagidova , B. Saitta ,f , V. Salustino Guimaraes , C. Sanchez Gras ,C. Sanchez Mayordomo , B. Sanmartin Sedes , R. Santacesaria , C. Santamarina Rios ,M. Santimaria , E. Santovetti ,j , G. Sarpis , A. Sarti ,k , C. Satriano ,s , A. Satta ,M. Saur , D. Savrina , , S. Schael , M. Schellenberg , M. Schiller , H. Schindler ,M. Schmelling , T. Schmelzer , B. Schmidt , O. Schneider , A. Schopper , H.F. Schreiner ,M. Schubiger , M.H. Schune , R. Schwemmer , B. Sciascia , A. Sciubba ,k ,A. Semennikov , E.S. Sepulveda , A. Sergi , , N. Serra , J. Serrano , L. Sestini ,P. Seyfert , M. Shapkin , Y. Shcheglov , † , T. Shears , L. Shekhtman ,w , V. Shevchenko ,E. Shmanin , B.G. Siddi , R. Silva Coutinho , L. Silva de Oliveira , G. Simi ,o ,S. Simone ,d , N. Skidmore , T. Skwarnicki , J.G. Smeaton , E. Smith , I.T. Smith ,M. Smith , M. Soares , l. Soares Lavra , M.D. Sokoloff , F.J.P. Soler , B. Souza De Paula ,B. Spaan , P. Spradlin , F. Stagni , M. Stahl , S. Stahl , P. Stefko , S. Stefkova ,O. Steinkamp , S. Stemmle , O. Stenyakin , M. Stepanova , H. Stevens , S. Stone ,B. Storaci , S. Stracka ,p , M.E. Stramaglia , M. Straticiuc , U. Straumann , S. Strokov ,J. Sun , L. Sun , K. Swientek , V. Syropoulos , T. Szumlak , M. Szymanski ,S. T’Jampens , Z. Tang , A. Tayduganov , T. Tekampe , G. Tellarini , F. Teubert ,E. Thomas , J. van Tilburg , M.J. Tilley , V. Tisserand , S. Tolk , L. Tomassetti ,g ,D. Tonelli , D.Y. Tou , R. Tourinho Jadallah Aoude , E. Tournefier , M. Traill , M.T. Tran ,A. Trisovic , A. Tsaregorodtsev , A. Tully , N. Tuning , , A. Ukleja , A. Usachov ,A. Ustyuzhanin , U. Uwer , C. Vacca ,f , A. Vagner , V. Vagnoni , A. Valassi , S. Valat ,G. Valenti , R. Vazquez Gomez , P. Vazquez Regueiro , S. Vecchi , M. van Veghel ,J.J. Velthuis , M. Veltri ,r , G. Veneziano , A. Venkateswaran , T.A. Verlage , M. Vernet ,M. Vesterinen , J.V. Viana Barbosa , D. Vieira , M. Vieites Diaz , H. Viemann ,X. Vilasis-Cardona ,m , A. Vitkovskiy , M. Vitti , V. Volkov , A. Vollhardt , B. Voneki ,A. Vorobyev , V. Vorobyev ,w , J.A. de Vries , C. V´azquez Sierra , R. Waldi , J. Walsh ,J. Wang , M. Wang , Y. Wang , Z. Wang , D.R. Ward , H.M. Wark , N.K. Watson ,D. Websdale , A. Weiden , C. Weisser , M. Whitehead , J. Wicht , G. Wilkinson ,M. Wilkinson , I. Williams , M.R.J. Williams , M. Williams , T. Williams ,F.F. Wilson , , J. Wimberley , M. Winn , J. Wishahi , W. Wislicki , M. Witek ,G. Wormser , S.A. Wotton , K. Wyllie , D. Xiao , Y. Xie , A. Xu , M. Xu , Q. Xu ,Z. Xu , Z. Xu , Z. Yang , Z. Yang , Y. Yao , L.E. Yeomans , H. Yin , J. Yu ,ab , X. Yuan ,O. Yushchenko , K.A. Zarebski , M. Zavertyaev ,c , D. Zhang , L. Zhang , W.C. Zhang ,aa ,Y. Zhang , A. Zhelezov , Y. Zheng , X. Zhu , V. Zhukov , , J.B. Zonneveld , S. Zucchelli . 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 Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy, France Clermont Universit´e, Universit´e Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France LAL, Univ. Paris-Sud, CNRS/IN2P3, Universit´e Paris-Saclay, 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 INFN Sezione di 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 (PNPI), Gatchina, Russia Institute of Theoretical and Experimental Physics (ITEP), 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 (IHEP), 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 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 School 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 Syracuse University, Syracuse, NY, United States Pontif´ıcia Universidade Cat´olica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to
University of Chinese Academy of Sciences, Beijing, China, associated to
School of Physics and Technology, Wuhan University, Wuhan, China, associated to
Institute of Particle Physics, Central China Normal University, Wuhan, Hubei, China, associated to Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia, associated to
Institut f¨ur Physik, Universit¨at Rostock, Rostock, Germany, associated to
Van Swinderen Institute, University of Groningen, Groningen, 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 Tomsk Polytechnic University, Tomsk, Russia, associated to
Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia - CSIC, Valencia, Spain,associated to
University of Michigan, Ann Arbor, United States, associated to