Search for the B 0 s D + K decay at LHCb

Transcription

1 Master Project Search for the s D + K decay at LHCb Author: Matthieu MARINANGELI Supervisors: Dr. Karim TRAELSI Dr. Mirco DORIGO March 14, 16 Laboratoire de Physique des Hautes Énergies.

2 Abstract We investigate the possibility to observe the decay s D + K in the Run I data set collected by the LHCb experiment, corresponding to an integrated luminosity of 3 fb 1 of proton-proton collisions at the center-of-mass energies of 7 and 8 TeV. The search of this decay is motivated by the measurement of the ratio of the doubly Cabibbo-suppressed decay amplitude and the Cabibbo-favored decay amplitude of the D π decay, with an alternative method to current available estimations. The ratio of these amplitudes is an important input for the time-dependent analysis of D π decays for measuring the CKM phase (β + γ). The search of the s D + K decay represents a test bed for a new strategy designed to search rare decays where a large background contamination from particle misidentification poses severe challenges. Contents 1 Introduction 4 Physics motivation 4..1 CP violation in the Standard Model CKM unitary triangle Measurement of the γ angle with D π + decays Measurement of the parameter R The LHCb experiment Tracking system Particle identification systems PID performances PID calibration Analysis strategy 13 5 Data selection for s D + K decays Trigger Offline selection Stripping Additionnal selection requirements Combinatorial background suppression Study of peaking backgrounds Λ b Λ + c π /K background suppression s D s π + /K + background suppression Description of the sample composition Model description of the Dπ sample Model description of the DK sample Simultaneous fit of the DK and Dπ sample

3 7 Study of the signal sensitivity Strategy A Strategy Conclusion 49 A Extraction of the pure D π + control sample 51 Agreement between MC and data of the DT input variables 53 C Distributions of the inputs variables of the final DT 54 D Probability density functions 55 D.1 Crystal all distribution D. Unbounded Johnson distribution D.3 Sum of Unbounded Johnson distribution and Gaussian distributions. 55 E Parameters of the fit model extracted from MC 56 E.1 Components of the Dπ model E. Components of the DK model F Pull distributions of the floating parameters in the fit model 58 3

4 1 Introduction The large data set collected by the LHCb experiment during Run I, corresponding to an integrated luminosity of 3 fb 1 of pp collision at 7 and 8 TeV center-ofmass energies, opens the way to search for rare decays of mesons that were not experimentally accessible before. The data planned to be collected in Run II (5 fb 1 ), and the huge sample (5 fb 1 ) to which the experiment aims after its upgrade in Run III, will push the limits of this exploration even further. Suppressing backgrounds coming from favored decay mis-reconstructed as the decays of interest represents a major challenge in these searches. An example of this case is represented by the search of the rare ρ ( π + π )γ decay, where the contamination of the K ( K π + )γ decay through kaon-pion misidentification makes the observation of the rare mode extremely challenging, despite the good capabilities of the particle identification system of the LHCb detector. Tightening the selection requirements to suppress the background to an affordable level could lower significantly the efficiency of the searched signal such that the large accumulated dataset becomes almost useless. In this project, we investigate a strategy to overcome the loss of signal candidates when trying to control the background contamination coming from particle misidentification. We will test the strategy motivated by the search of the rare decay s D + K, a very challenging case where the offending background is represented by a large amount of D + π decays, where the pion is misidentified as a kaon. This case is a relevant example to check the feasibility of the proposed strategy with respect to the ρ ( π + π )γ decay mentioned above, since it features only charged particles in the final states, allowing to focus only on the problem of the kaon-pion misidentification. In addition, the observation of the s D + K decay could allow to measure the parameter R, described in Section..3, with a method here proposed for the first time. The parameter R is an important input for one of the analysis currently ongoing in our laboratory. The physics motivation beyond the search of the s D + K decay is described in Section. The description of the LHCb experiment and the particle identification system is presented in Section 3. In Section 4 the new strategy is outlined. Data selection and the modeling of composition of the data sample are detailed in Sections 5 and 6, respectively. In Section 7, the new strategy is tested. Finally, Section 8 is devoted to show the conclusion of this project. Physics motivation The Standard Model (SM) description of the violation of the charge-parity (CP ) symmetry has been tested over the past years and proved to be very consistent. However there are some measurements where an improvement of the precision is needed, for instance the measurement of the interior angle γ of the unitarity triangle, which will be further described in the following sections. 4

5 ..1 CP violation in the Standard Model To date CP violation has only been observed in the quark sector and through the weak interaction. The weak interaction of quark is described by the Cabibbo- Kobayashi-Maskawa (CKM) matrix d V ud V us V ub d s = V cd V cs V cb s (1) b } V td V ts {{ V tb } b V CKM which links the quarks weak eigenstates to the mass eigenstates. The CKM matrix, V CKM, is an unitary 3 3 complex matrix, and can be described by three rotation angles and a complex phase: c 1 c 13 s 1 c 13 s 13 e iδ V CKM = s 1 c 3 c 1 s 3 s 13 e iδ c 1 c 3 s 1 s 3 s 13 e iδ s 3 c 13 () s 1 c 3 c 1 s 3 s 13 e iδ c 1 c 3 s 1 s 3 s 13 e iδ c 3 c 13 where s ij = sin θ ij, c ij = cos θ ij (θ 1 = θ C the Cabibbo angle) and δ is the CP violating phase. However the elements V ij of V CKM are not predicted by the SM and have to be determined from experiment [1]: V ud V us V ub.9747 ± ± ±.15 V cd V cs V cb =.5 ± ± ±.1 V td V ts V tb ±.5 (3) The off-diagonal elements of V CKM are relatively small which means that the weak interaction between quarks of different generation is suppressed relative to those of the same generation. This implies that the rotation angles between quark mass and weak eigenstates are also small, θ 1 = 13, θ 3 = 3 and θ 13 =., which leads to express the CKM matrix as an expansion in the relatively small parameter λ = s 1 =.5. In the Wolfenstein parametrization [] V CKM is defined as 1 λ λ Aλ 3 (ρ iη) V CKM = λ 1 λ Aλ + O(λ 4 ) (4) Aλ 3 (1 ρ iη) Aλ 1 where λ, A, ρ and η are four real parameters. In this parametrization, the complex components of V CKM are present only in V ub and V ud (if higher-order terms are included, V cd and V ts also contain small complex components). In order to have CP violation in the quark sector, V CKM must contain an irreducible complex phase which corresponds to η being non zero, so CP violation happens mainly in the quark transitions u b and t d. 5

6 Figure 1: Unitarity relation (Eq. 5) shown in the ρ η plane... CKM unitary triangle From the unitarity of the CKM matrix a set of 1 equations relating the matrix elements can be extracted. One of them is V ud Vub + V }{{} cdvcb + V }{{} tdvtb = (5) }{{} (ρ+iη)aλ 3 Aλ 3 (1 ρ iη)aλ 3 which can be represented as a triangle in the ρ η complex plane: where α = arg ( V ) tdvtb V ud Vub β = arg ( V ) cdvcb V td Vtb γ = arg ( V ) udvub V cd Vcb which satisfy α = π β γ. The plot in Fig. shows the current estimations of the interior angles of the CKM unitary triangle. The angle γ is the least known with an uncertainty around Measurement of the γ angle with D π + decays There are several possible decays that allow to measure the angle γ, e.g. + D K +, s Ds K +, and D π +. A current analysis is done in our laboratory on the time-dependent analysis of the D π + decays which allows to measure the β + γ phase [4]. In this channel the meson can either decay into D + π, the doubly Cabibbosuppressed decay mode (DSCD), or D π +, the Cabibbo-favored decay mode (CFD), and since is a neutral meson a - oscillation before the decay is then possible. The dominant Feynman diagrams for these processes are shown in Fig. 3. For one given initial state there are two possible ways to reach a given final state, for instance can decay directly into D π + (CFD) or oscillates into which then decays into D π + (DCSD). The interference between the CFD decay amplitude, which is proportional to the CKM matrix elements V ud Vcb, and the DSCD 6 (6) (7) (8)

7 Figure : Measurements of the interior angles of the CKM unitary triangle gathered by the CKMfitter group [3]. decay amplitude, proportional to V cd V ub, is sensitive to the angle γ. With - mixing the interference is also sensitive to β, hence the total weak phase difference between the interfering amplitudes is β + γ. From the time-dependent analysis of the D π + and D π + decays one can extract the CP asymmetry parameters S ± = R sin (δ ± (β + γ)) 1 + R, where R = A( D + π ) A( D π + ) (9) is the ratio of the magnitudes of the DCSD and CFD modes and δ is the strong phase difference between these two amplitudes. In order to extract the weak phase β + γ from the S ± parameters, an external input is needed, given that only observables are provided (S ± ) for 3 parameters (δ, β + γ, R). A method to measure R is presented in this project..1 Measurement of the parameter R Estimations of the parameter R are available through the measurement performed by the -factories, (the aar and elle experiments). An analysis similar to the ones of the -factories is ongoing in LHCb. The idea behind those estimations is to substitute the DCSD mode by a decay mode where a similar decay amplitude dominates. For instance, assuming SU(3) flavour symmetry, the DCSD mode can be substituted by D + s π decay (see Fig. 4). The parameter R can be then related to the branching ratio of this decay mode [5]: 7

8 (a) (b) (c) (d) Figure 3: Feynman diagrams for (a) CFD D π +, (b) DCSD D + π, (c)+(d). Figure 4: Feynman diagram for D s + π where the SU(3) flavor symmetry concerns the quark in the D (s) mesons from the W exchange. R ( D + s π ) ( D π + ) f D f Ds tan θ c (1) where θ c is the Cabibbo angle and f D (f Ds ) is the D(D s ) meson decay constant. The current measurements of R using this assumption are: aar [6]: R = [1.75 ±.14(stat) ±.9(syst) ±.1(th)]% elle [7]: R = [1.71 ±.11(stat) ±.9(syst) ±.(th)]% where the theory error only takes into account the uncertainty in the f D /f Ds estimation. Uncertainties due to other possible SU(3) breaking effects, of the order (1-15)%, are not included. 8

9 Figure 5: Feynman diagram for s D + π where the SU(3) flavour symmetry concerns the spectator quark in the meson. In this project another method to measure R is proposed, considering the SU(3) flavour symmetry on the spectator quark in the meson (see Fig. 5) to relate R to the branching ratio of the decay s D + K : R ( s D + K ) ( D π + ) f π f K (11) where f π and f K are the pion and the kaon decay constants, respectively. The ratio f π /f K is precisely estimated to be (1)( +6 18) from lattice QCD calculations [8]. This way of measuring R is the main motivation to search for the s decay. D + K 3 The LHCb experiment The LHCb is one of the experiments of the Large Hadron Collider (LHC) hosted by the European Organisation for Nuclear Research (CERN) situated near Geneva, in the Franco-Swiss border. The LHCb is dedicated to study CP violation and rare decays of beauty and charm hadrons produced in the proton-proton collisions provided by LHC. The LHCb detector [9] is designed as a one-arm spectrometer, due to the fact that the heavy bb pairs are mainly produced in the forward or backward direction at high energies. It covers an angle of 5 mrad in the horizontal plane (non-bending plane) and 3 mrad in the vertical plane (bending plane), equivalent to a pseudorapidity of 1.6 < η < 4.9. The detector is shown in Fig. 6: its components can be divided into two groups, the tracking system and the particule identification systems. 3.1 Tracking system This part of the detector is dedicated to reconstruct precisely vertices and tracks. Its components are: the VErtex LOcator (VELO), a 1 m large detector made of silicon strips dedicated to determine with a high precision the positions of primary vertices 9

10 Figure 6: View of the LHCb detector. (where pp collision occurs) and secondary vertices (decay points of b-hadrons on average 1 cm after the primary vertex); the Tracker Turicensis (TT), which is located before the magnet, and the Inner Tracker (IT) and the Outer Tracker (OT), covering the inner and outer acceptance of the detector stations T1, T and T3 which are located after the magnet. The IT together with the TT are made of silicon strips. The OT is a drift-tube detector filled with a gas composed of 7% Argon, 8.5% CO and 1.5% O. The trackers and magnet combined together allow to measure momentum and charge of charged particles. The average efficiency for the track reconstruction has been estimated to be above 96 % in 11, slightly lower in 1 due to the higher track multiplicity, in the momentum range 5 < p < GeV/c and in the pseudorapidity range < η < 5. The momentum resolution, δp/p, goes from 5 per mille for particles below GeV/c to about 8 per mille for particles around 1 GeV/c [1]. 3. Particle identification systems The particle identification (PID) in LHCb is provided by four different detectors: the Ring Imaging Čerenkov detectors (RICH1, RICH) are used to measure velocity of charged particles based on the Čerenkov effect. When a charged particle moves with a higher velocity than the speed of the light in the detector material, it emits a cone of electromagnetic radiation with an aperture angle given by cos θ = 1 βn 1

11 where β = v/c is the ratio between the velocity of the particles and the speed of light in the material, and n is the refractive index of the medium. The velocity information from the RICH detectors and the momentum information from the trackers allows to measure the mass of the charged particle. The Calorimeter system (SPD, PS, ECAL, HCAL) is used to identify electrons, photons and hadrons, and also to measure their energies and positions. The muon system (M1, M, M3, M4 and M5) is used for muon identification PID performances For the purpose of the project, we will only focus on the identification of charged hadron, which use informations from the RICH detectors. A mass hypothesis for a given track is obtained combining the Čerenkov angle measured by the RICH system with the momentum measured by the tracking system. A likelihood that the track is associated to a certain particle is formed [11]. The log-likelihood of the track is computed under the mass hypothesis of interest and the pion mass hypothesis. The difference between the two, given by DLL(X π) = ln L X ln L π, (1) is used to estimate if the track is more pion-like or X-like, where X can be a kaon or a proton. In order to determine the PID performances, large control samples of decay modes that can be reconstructed cleanly with kinematic selections, without using RICH informations, are required. These decay modes are K S π+ π, Λ pπ and D + D ( K π + )π +. For instance, using the sample of D + D ( K π + )π + decay, Fig. 7 shows the kaon efficiency (kaon identified as a kaon) and pion misidentification (pion identified as a kaon) rate for DLL(K π) > 5 applied on the kaon from the D, as a function of the momentum. Averaging the efficiency with the kaon momentum distribution, the total kaon efficiency is 73%, and the for a pion misidentification rate is.4%. Another method, known as ProbNN, is used to identify charged particle. This method combines PID informations of all the sub-detectors as input of a multivariate technique which gives as output a single probability value for each particle hypothesis. From simulations of the D K + decays, we found that the DLL(K π) variable is more efficient than the ProbNNk, i.e for the same kaon signal efficiency there is a lower pion misidentification rate, see Fig 8. However simulations do not represent well the data from what concerns the PID performances. A calibration is needed, as explained in the next section. For the stripping selection (see Section 5..1) used in this project, the calibration data for ProbNNk were not available. For this reason we decide to work with DLL(K π) in this project. 11

12 events Track p π as K K as K 1.8 efficiency P [GeV/c] Figure 7: Kaon identification efficiency (green) and pion misidentification rate (red) as a function of the track momentum for DLL(K π) > 5. The kaon momentum distribution is overlaid in the same plot (in blue). Signal Efficiency DLL(K-π) ProbNNk.5 1 ackground rejection Figure 8: Signal efficiency (computed in a MC sample of D K + decays versus background rejection (computed on a sample of MC D π + decays) for the requirements DLL(K π) > X (in red) and ProbNNk > X (in blue). 3.. PID calibration The PID variable distributions in the Monte Carlo (MC) samples do not match the ones in the data, thus PID efficiencies computed with MC cannot be trusted, see Fig. 9. PIDCalib [1] is the tool to resample the MC in order to compute properly efficiencies of PID selections. This is done by using the calibration samples described previously in Section As the PID efficiency can vary depending on the track momentum (p), its pseudorapidity (η), and the global number of tracks in the event (nt racks), a 3D binning of the distribution p, η and nt racks has been constructed, and PID distributions from the calibration samples for each bin are saved in histograms. Then, for each track in the MC sample that falls in a particular bin of (p, η, nt racks), the corresponding 1

13 histogram of the PID distribution is selected, and a random value extracted from that histogram is assigned as the PID value of the track. Once done for all the tracks, a new PID variable distribution is constructed. Fig. 1 shows that the kaon efficiency and pion misidentification rate in function of the track momentum of the resampled MC samples are consistent with the ones of the calibration sample, proving the validity of the correction method. In the following, each PID efficiency is computed in MC by using this correction method. 4 Analysis strategy The goal of the project is the determine the feasibility of the search of s D + K decay in the Run I LHCb dataset. Considering the current estimations of R the number of signal can be estimated from Eq. 11: N s D K + = N D π + f s f d R ( fk f π ) ɛ K(DLL(K π) > ) ɛ π (DLL(K π) < ) (13) where f s /f d =.56 [13] is the ratio of s and production fractions, i.e fraction of b quarks that hadronize with s or d quarks; N D π + is the number of D π + decays obtained in 3 fb 1 with DLL(K π) < (about 4 events, see Section 7); the last term is the ratio of the kaon efficiency of DLL(K π) > and pion efficiency of DLL(K π) <, computed in MC samples of D K + and D π + decays, respectively. About 3 signal candidates are expected. Figure 11 shows the DK invariant mass distribution of D K + decay candidates reconstructed in the 1 fb 1 dataset collected in 11, obtained in Ref. [13]. The D K + signal is peaking at the mass value, with a mass resolution events K_P Calib PIDK > 5 MC PIDK > efficiency events K_P Calib PIDK > 5 MC PIDK > mis-id rate P [GeV/c] 1 3 P [GeV/c] (a) identified kaon (b) misidentified pion Figure 9: (a) Kaon identification efficiency as a function of the track momentum, in the calibration sample (red) and in the D K + MC sample (green); (b) pion misidentification rate, in the calibration sample (red) and in the D π + MC sample (green), as a function of the track momentum for DLL(K π) > 5. The kaon and pion track momentum distributions are overlaid (in blue). 13

14 events K_P Calib PIDK > 5 MC PIDKcorr > efficiency events K_P Calib PIDK > 5 MC PIDKcorr > mis-id rate P [GeV/c] 1 3 P [GeV/c] (a) identified kaon (b) misidentified pion Figure 1: (a) Kaon identification efficiency as a function of the track momentum, in the calibration sample (red) and the D K + MC sample (green); (b) pion misidentification rate, in the calibration sample (red) and the D π + MC sample (green), as a function of the track momentum for DLL(K π) > 5 after resampling. The kaon and pion track momentum distributions are overlaid (in blue). Figure 11: Distribution of the D ± K invariant mass for D K + decay candidates reconstructed in 1 fb 1 of data collected in 11[13]. of about 15 MeV/c. The s D K + is expected to have a similar shape, peaking at the s mass value. Around the s D K + signal region, two main backgrounds are identified: the combinatorial background; the D π + decays surviving the PID cuts (pion misidentification), which contributes with a large yield. Projecting the mass distribution in Fig. 11 to 3 fb 1 of data, it s clear that an observation of the s D + K is nearly impossible due to the overwhelming D π + background. In the analysis of Ref. [13] the PID selection DLL(K π) > 5 reduces the misidentification rate down to 3% with around 75% signal ef- 14

15 ficiency. Applying further PID selection to reduce the pion-kaon misidentification wouldn t be a sufficient solution as it would also reduce the signal efficiency. A different strategy is proposed in this project which can be summarized into two main points: Use a large statistic sample of D π + data in order to control the amount of misidentified background using the measured misidentification rate. The D π + sample can be properly reconstructed (applying a PID selection on the pion from the meson) with over 4k signal candidates. The DK and Dπ invariant mass distributions will be fitted simultaneously. The DK sample will be split in bins of DLL(K π) and the sensitivity to the s D+ K signal of a simultaneous fit to all the bins will be studied. M(DK)-M(Dπ) [MeV/c] M(DK) [MeV/c] Exploit the kinematic separation between Dπ and DK. The misidentified background mass distribution depends on the bachelor momentum, whereas the signal mass distributions do not (Fig 1a). This separation can be encoded in the model of the D π + background using the variable δm = mdk mdπ where mdk and mdπ are the invariant mass of the Dh system calculated in the K and π mass hypothesis, respectively. Figure 1b shows that the DK invariant mass of a properly reconstructed decay like D K + does not depend on δm; on the contrary there is a dependence for a misidentified decay like D π +. This method has been used in Ref. [14] D K+ D π M(DK) [MeV/c] achelor P [GeV/c] (a) (b) Figure 1: (a) DK invariant mass as a function of the bachelor momentum in the MC samples of D π + (in red) and D K + in blue. (b) δm = mdk mdπ as a function of mdk in the MC sample of D π + (in red) and D K + (in blue). 15

16 5 Data selection for s D + K decays 5.1 Trigger The Trigger is divided into two levels. The first level (L) is implemented in hardware, and its output is sent to the software-based High Level Trigger (HLT) which is divided in HLT1, and HLT. Detailed information about the Trigger can be found in Ref. [15]. In the following we summarized the trigger decision requirements imposed in this analysis. L: since the meson is heavy, a large transverse momentum is expected on the decay products. At L level the trigger selects events containing particles with high transverse energy E T. The transverse energy of hadrons is measured in the calorimeters. Events passing LHadron TOS (Triggered On Signal) are selected, which correspond to a transverse energy deposition in the HCAL greater than 3.5 GeV for data collected in 11 and 3.6 GeV for data collected in 1. In addition, we retain also events are selected if triggered independently of the decay signal (LGlobal TIS). After this stage the event rate is reduced from 4 to 1 MHz. HLT1: the events are partially reconstructed using informations from the trackers and the VELO. Following the L lines, events passing Hlt1TrackAllL TOS line are selected by requiring a single, detached, high transverse-momentum (p T ) track in order to identify decays coming from. The event rate is then reduced from 1 MHz to 5 khz. HLT: the events are selected through the topological N-body lines (HltTopo- odydt TOS or HltTopo3odyDT TOS or HltTopo4odyDT TOS) which combine N-tracks to a common displaced vertex. The event rate is now reduced to 5 khz. 5. Offline selection 5..1 Stripping The raw data are then processed by the stripping S1 selection, using requirements to reconstruct the decay D h +, where no PID selection is applied on the bachelor track h, and the D candidate is reconstructed under the decay D h + h h. The requirements shown in Table 1 are applied at this stage. Figure 13 shows the D ± K invariant mass distribution of a part of the full dataset right after trigger and stripping selections. The sample is dominated by background candidates: the large peak is due to D + π background, partially reconstructed decays are in the low mass region, and there is a large component of combinatorial background. Few steps to suppress or control the different backgrounds are presented in the following sections. 16

17 Table 1: Selection cuts for Stripping S1. Variable achelor Track: χ fit Track < 4 p T > 5 MeV/c p > 5 MeV/c IP χ (PV) > 16 D daughter tracks: χ fit Track < 4 p T > 5 MeV/c p > MeV/c IP χ > 4 D candidate: Mass M M P DG (D ± ) < 1 MeV/c vertex fit χ < 9 flight distance χ > 36 p T > 15 MeV/c DIRA >.9 DOCA <.6 IP χ > candidate: p T > 5 MeV/c DIRA >.999 τ >. ps IP χ (PV) < 16 vertex fit χ < 9 Table : Preselection requirements. M(K ± π π ) window [184, 191] MeV π DLL(K π) < K DLL(K π) > 5 Max(GhostProb[All tracks]) < Additionnal selection requirements Figure 14 shows the distribution of the K ± π π invariant mass in data where a clean D + K π + π + signal is present centered at the D ± mass value. Another peak is present at higher mass peaking at the D ± mass value. In order to purify the signal and reject some backgrounds, requirements on the K ± π π invariant mass and on PID variables of the decay products of the D are applied. Table sums up the requirements applied in this preselection. A requirement on the maximum of the ghost probabilities of all the tracks is 17

18 Events M(DK) [MeV/c ] Figure 13: Distribution of the D ± K invariant mass in a partial dataset collected in 11 after trigger and stripping selections. Events M(Kππ) [MeV/c ] Figure 14: Distribution of the K π ± π ± invariant mass in 3 fb 1 of data collected between 11 and 1 after trigger and stripping selections. applied in order to avoid events reconstructed with fake tracks. The ghost probability is the probability that a reconstructed track has a trajectory that does not correspond to the one of a real charged particle. The requirement has 96% signal efficiency and 14% background rejection computed in data, in a D π + signal sample (see Appendix A) and in a sideband in the high-mass region which contains mostly combinatorial background. 18

19 5.3 Combinatorial background suppression A oosted Decision Tree (DT), from the scikit-learn package using the Adaoost classifier [16], has been used to distinguish between signal and combinatorial background candidates by training the DT on: a Monte Carlo sample of D K + to represent the signal ( 1 candidates); candidates taken from the region M(DK) > 6 MeV/c ( dubbed sideband) in 1/6 of the full dataset to represent the background ( 16 candidates). Each of the two samples is split in two parts: /3 of the samples is dedicated to train the DT and the other 1/3 to test the DT and check possible overtraining. A list of 17 input variables is shown in the Table 3, which contains kinematic variables and variables about the quality of the fit of vertices (like the χ of the fit of the D vertex). The variable DIRA OWNPV is the angle formed between the particle of interest (D or ) and the vector between the primary vertex (PV) and the secondary vertex (SV); cos(θ) of the bachelor kaon is the cosine of the angle between the bachelor kaon momentum (in the rest frame) and the direction of the Lorentz boost from the laboratory frame to the rest frame. The use of the MC for the D K + mode requires that all the variables are well described by simulations. Thanks to the large statistic of the D π +, a pure control sample has been extracted directly from data and the agreement of the distributions of the input variables between MC and the control sample has been checked, see Appendix. Except for the IP χ of the (Fig. 44j), all the MC distributions are in good agreement with distributions from data. The IP χ ( ) is still used in the DT since the discrepancies between data and MC is small compared to the difference between signal and background (Fig. 45b). A first DT training has been done with these input variables and the result is shown in Fig. 15. The Figure 15a shows the distribution of the DT output, which features a good discrimination between signal and background. This is confirmed by the ROC curve in Fig. 15b, which measures the performance, i.e. the discrimination power of the DT, represented by the area under the ROC curve, here.99. The initial set of input variables has been then reduced following two criteria: keeping a high DT efficiency by using the minimal set of input variables. The variables ranked by discriminating power are shown in the Table 4. We started by removing the ones with the lowest ranking. Keeping a good DT efficiency without reducing the kaon-pion discrimination of the DLL(K π) variable. From these criteria, three configurations have been constructed, as defined in Table 5: the Everything configuration contains the 1 most discriminating variables of Table 4; the Minimal configuration contains only variables that are not correlated with the DLL(K π); and the Intermediate configuration is a modification 19

20 Table 3: Input variables of the DT. Variable : DIRA OWNPV p T Impact Parameter (IP) χ Radial flight distance Vertex χ divided by ndof Lifetime Vertex χ divided by ndof achelor: IPχ p T cos(θ) D : DIRA OWNPV p T IPχ Decay time Vertex χ divided by ndof D children: minimum p T minimum IPχ achelor and D children: Maximum track ghost probability of the Minimal one, by adding the most discriminating variable, D IP χ, which has a small correlation with DLL(K π). As shown in Fig. 16, the reduction of input variables do not affect the overall performance of the DT. A comparison of the performances of each configuration has been done by fitting the control sample (Appendix ) for different DT selections and extracting the signal and combinatorial background yields. The result can be seen in Fig. 17 where the green dot represents the cut-based selection shown in Table 3 used in an analysis of D π + for flavour tagging calibration. The Minimal configuration suppresses less combinatorial background than the cutbased selection, and will no longer be taken into account. The correlation between the DT output and the PID variable DLL(K π) has been checked by plotting the profile plot of the PID variable in function of the DT output for the MC sample of D π + and D K +. The results for the Everything and Intermediate configurations of input variables are shown in Fig. 18. As the DT output increases, the pion-kaon discrimination power decreases in the Everything configuration, whereas in the Intermediate configuration it re-

21 (a) (b) Figure 15: Distribution of the DT output and plot of the Receiver Operating Curve (ROC) of the first DT training. Table 4: Ranking of the input variables of the DT. Higher ranks represent a larger discriminating power between signal and background. Variable Contribution 1. D IP χ 16. %. achelor K p T 1.5 % 3. p T 1. % 4. flight distance 7.5 % 5. Max(GhostProbability[K + D children]) 7.5 % 6. achelor K IP χ 6. % 7. D p T 6. % 8. IP χ 5.9 % 9. achelor K cos(θ) 5.6 % 1. D children Min(IP χ ) 5.1 % 11. D decay time 4.6 % 1. vertex χ /ndof 4.6 % 13. DIRA angle.9 % 14. D children Min(p T ).1 % 15. D DIRA angle 1.9 % 16. D vertex χ /ndof 1.8 % 17. decay time χ 1.7 % mains roughly constant. Since the Intermediate is only weakly correlated with DLL(K π), this is our final choice of DT input variables. The correlation between m DK and DT output has also been checked. The observed effect of the DT is to reduce the combinatorial background without sculpting the mass shape, see Fig.. 1

22 Table 5: Configurations of input variables used to train the DT. Everything Minimal Intermediate D IP χ DIRA angle DIRA angle achelor K p T IP χ IP χ p T vertex χ /ndof vertex χ /ndof flight distance flight distance flight distance achelor K IP χ achelor K IP χ achelor K IP χ D p T D decay time D decay time IP χ D children Min(IP χ ) D children Min(IP χ ) achelor K cos(θ) D IP χ D children Min(IP χ ) D decay time Figure 16: ROC of the DT obtained using all input variables in Table 4 and with the Everything configuration of Table 5. Signal events ackground events Figure 17: Signal events versus background events obtained with DTs trained with of the configurations of input variables Table 5, extracted from the fit of the control sample (Appendix). The cut-based selection is shown in Table 3.

23 Kfrom_PIDK 4 MC DK 3 1 MC Dπ Kfrom_PIDK 4 MC DK 3 1 MC Dπ DToutput DToutput (a) Everything (b) Intermediate Figure 18: Profile plot of DLL(K π) versus DT output from simulation. The blue points represents the distribution of D K + decays and the red points D π + decays. (a) (b) Figure 19: Distribution of the DT output and plot of the ROC curve for the final choice of DT input variables, the Intermediate configuration. 5.4 Study of peaking backgrounds In Ref [13], several peaking backgrounds in the D π + signal region of the D ± π invariant mass distribution have been reported, see Fig. 1. From Table 6, these backgrounds seem negligible compared to the amount of D π + signal, but could pollute the s D K + region in the DK sample. 3

24 .3.5. DToutput > -. DToutput > -.1 DToutput >. DToutput >.1 DToutput > M(DK) [MeV/c ] Figure : Normalized distributions of the DK invariant mass for different DT selections. Parameter Value N D π ± 344 N D K + 88 ± 5 N Ds π ± ± 863 N D ρ N D π ± 6 N Λ Λ c π + 63 ± 83 N Combinatorial 9539 ± 591 Figure 1: Distribution of the D π + invariant mass of D π + decay candidates reconstructed in 1 fb 1 of data collected in 11, from Ref. [13]. Table 6: Yields of each components of the D π + invariant mass distribution in 1 fb 1 of data with DLL(K π) <, obtained from the fit of the distribution (except for D K + and Ds π + yields which are constrained) in Ref. [13]. Indeed, if we consider a selection similar to the one in Ref. [13] (reported in Table 7), from the yields in Table 6, the numbers of background events expected in 3 fb 1 of data in the DK sample with DLL(K π) > 5 are: 17 Λ b Λ + c π events and 8 s D s π + events, obtained by scaling the yields in Table 6 using PID efficiencies (Table 7) such that N (in DK) = N (in Dπ) (14) where the factor 3 accounts for 3 fb 1 of data w.r.t. to the dataset of 1fb 1 of Ref. [13]. 4

25 Table 7: DT and PID requirements equivalent to the ones used in Ref. [13] and their efficiencies. D π + D K + DToutput > ±.1 % 8. ±. % DLL(K π) < 83.7 ±.1 % 9.5 ±.1 % DLL(K π) > 5.3 ±.3 % 69.7 ±. % 37 Λ b Λ + c K events and 16 s D s K + events, obtained by scaling the yields using branching ratios and PID efficiencies such that N (in DK) = (X Y K+ ) (X Y π + ) N (in Dπ) (15) where (X, Y ) can be ( s,d s ) or (Λ b,λ c ). which are larger than the expected s D K + yield, in the same m DK mass region. These background contaminations will be studied in detail in the following section in the Dπ control sample defined by the requirement DLL(K π) <. Vetoes to suppress these contaminations will be defined and we will study their applications in the DK sample, defined by the requirement DLL(K π) > Λ b Λ + c π /K background suppression We consider the Λ b Λ + c π decay with Λ ± c pk π ± as it is the most probable decay ((Λ ± c pk π ± [1]) = %), and the decay features four charged particles as the candidate reconstructed in our sample. In order to estimate the Λ c background in data, a mass reassignment to the proton mass is performed for one of the reconstructed pion; the reassignment of the mass is done independently for each pion, since both pions have the same charge in the D decay. The resulting pk π ± invariant mass distributions are shown in Fig., for candidates within the Dπ mass range where the Λ b Λ c π decay is expected ( MeV/c ]) and for candidates with Dπ invariant mass in the range MeV/c. A very clean peak is observed at the Λ c mass value (86.46 MeV/c [1]). A fit of this distribution is performed in order to check the consistency between the amount of this background obtained here and in Ref. [13]. 5

26 Events < M(Dπ) < 55 MeV/c 56 < M(Dπ) < 59 MeV/c 3 4 M(pKπ) [MeV/c ] Figure : Distribution of the pk π ± invariant mass for candidates in two regions of M(Dπ) in 1 fb 1 of data. ) Events / ( 1.5 MeV/c Parameter Value Units Yield 157 ± 8 σ 6.17 ±.5 MeV/c µ 87.7 ±. MeV/c M(pKπ) (MeV/c ) Figure 3: Distribution of the pk π ± invariant mass in 1 fb 1 of data with fit projection overlaid. Table 8: Parameters of the fit of the pk π ± invariant mass distribution in 1 fb 1 of data, for candidates in the D π ± invariant mass window MeV/c. The model used for the fit in Fig 3 is a gaussian function for the signal and a linear function for the background. The resolution of the gaussian function (Table 8) is consistent with the one obtained in the MC sample of Λ b Λ + c π, which is 6.11 ±.5 MeV/c. The yield of Λ b Λ + c π obtained from the fit, 157 ± 8, is compatible to the one obtained in Ref. [13], 63 ± 83 (Table 8). In order to suppress this background while preserving a good signal efficiency, the following requirements ( Λ c veto ) are applied: mass veto applied on the pk π ± invariant mass in the window 4-34 MeV/c for candidates where one of the two reconstructed pions satisfies DLL(p π) > 8; DLL(p π) < 5 on the pion candidates when the pk π ± invariant mass lies 6

27 within the window 6-3 MeV/c. The effect of these requirements can be seen in Fig. 4, where 98% of the Λ b contribution is removed in the Dπ invariant mass distribution. The efficiencies of the Λ c veto are also computed in Table 9. Events no veto Λ c mass Λ c anti-veto veto on Λ c mass MC Signal efficiency [%] D K ±.1 D π ± M(Dπ) [MeV/c ] Figure 4: Distributions of the D π ± invariant mass in 3 fb 1 of data with and without the Λ c veto, and with the antiveto. ackground rejection [%] Λ b Λ + c π 98.1 ±.1 Table 9: Efficiencies and background rejections of the Λ c veto computed on the MC samples after corrections with PID- Calib (Section 3..). The effect of the Λ c veto is checked in the DK sample. In Fig. 5 we show the candidates with DK invariant mass in [5,55] MeV/c where the proton mass is reassigned to the pions from the D. A peak is found at the Λ c mass and removed via the the veto. Fitting this distribution the yield of this background in the DK sample is calculated to be 546 ± 3, in agreement with what was estimated in Section 5.4. About 1 Λ b Λ + c π /K events are expected in the DK sample in 3 fb 1 after the Λ c veto is applied, of which 4 are expected to be in the s region s D s π + /K + background suppression The s Ds π + decays are looked for with D s ± K K ± π ±, where the kaon mass is reassigned to one of the two reconstructed pions, considering each pion independently, since the D candidates are reconstructed from one kaon and two pions of the same charge. The K K ± π ± invariant mass distribution is shown in Fig. 6a in two Dπ mass ranges, the s Ds π + signal region [533,54] MeV/c, and a sideband [55,57] MeV/c. A peak is observed at the D s mass value ( MeV/c [1]) and the background below the peak is found to be mostly from D π + decay (see Fig. 6b). The two following D s decays are considered: D ± s φπ ±, φ K ± K with branching ratio (.7 ±.8)% [1]; D ± s K (89) K ±, K (89) K ± π with branching ratio (.61 ±.9)% 7

28 Events 4 no veto Λ c mass 35 3 anti-veto Λ c mass veto on Λ c M(pKπ) [MeV/c ] Figure 5: Distribution of the pk ± π invariant mass in 3 fb 1 of data for candidates in 5 < M(DK) < 55 MeV/c with DLL(K π) > 5, with and without the Λ c veto, and with the anti-veto. Events < M(Dπ) < 54 MeV/c < M(Dπ) < 57 MeV/c Events < M(Dπ) < 54 MeV/c MC D π M(KKπ) [MeV/c ] (a) M(KKπ) [MeV/c ] (b) Figure 6: Distribution of the K K ± π ± invariant mass in 3 fb 1 of data (a) with candidates in two Dπ mass ranges, (b) with candidates in the s mass region of M(Dπ), compared to MC candidates of D π +. To study the D s ± φπ ± decay, the K K ± invariant mass distribution is shown in Fig. 7a, for candidates with Dπ invariant mass in [533, 54] MeV/c and in [55, 57] MeV/c. A clean peak is seen at the φ mass value ( MeV/c [1]). Candidates around this peak are selected to plot again the K K ± π ± invariant mass distribution (Fig 7b): the D s peak is seen. An estimation of the amount of D s ± φπ ± background in 1 fb 1 of data is performed by fitting the K ± K invariant mass distribution, using a gaussian function for the signal and a linear function for the background. Fit projection and results are shown in Fig. 8 and Table 1. 8

29 Events < M(Dπ) < 54 MeV/c 55 < M(Dπ) < 57 MeV/c Events < M(Dπ) < 54 MeV/c 55 < M(Dπ) < 57 MeV/c M(KK) [MeV/c ] (a) M(KKπ) [MeV/c ] (b) Figure 7: (a) distribution of the K K ± invariant mass; (b) distribution of K K ± π ± invariant mass for candidates in 11 < M(KK) < 13 MeV/c, and in two D ± π mass ranges, using 3 fb 1 of data ) Events / ( MeV/c M(KK) (MeV/c ) Figure 8: Distribution of the K K ± invariant mass distribution in 1 fb 1 of data with fit projection overlaid. Parameter Value Units Yield 8 ± 6 σ 3.6 ±.84 MeV/c µ ±.76 MeV/c Table 1: Parameters of the fit of the K K ± invariant mass distribution in 1 fb 1 of data, for candidates in the Dπ invariant mass window 5-54 MeV/c. The resolution of the gaussian function (Table 1) is consistent with the one found in the MC sample of s D s π + decays (.7 ±.5 MeV/c ). The contribution from D s ± K (89) K ± is investigated by selecting candidates with K ± π invariant mass in [84-95] MeV/c. In Fig. 9 the K ± K π invariant mass distribution is plotted for candidates with the Dπ mass in [533, 54] MeV/c and in [55, 57] MeV/c. The D s peak is seen for candidates in the s Ds π + signal region. 9

30 Events < M(Dπ) < 54 MeV/c 55 < M(Dπ) < 57 MeV/c M(KKπ) [MeV/c ] Figure 9: K ± K π invariant mass distribution for candidates in two D ± π mass regions and K ± π mass window [84-95] MeV/c, using 3 fb 1 of data. ) Events / ( MeV/c M(KKπ) (MeV/c ) Figure 3: Distribution of the K K ± π ± invariant mass distribution in 1 fb 1 of data, with fit projection overlaid. Parameter Value Units Yield 589 ± 34 σ 9.7 ±.6 MeV/c µ ±.53 MeV/c Table 11: Parameters of the fit of the K K ± π ± invariant mass distribution in 1 fb 1 of data, for candidates in the Dπ invariant mass window [53-54] MeV/c. The amount of this background contamination is obtained by fitting the K K ± π ± invariant mass distribution (Fig 3 and Table 11) for candidates with 53 < M(Dπ) < 54 MeV/c with a gaussian function to model the signal and a nonparametric function for the D π + background, extracted from the MC simulation. The total amount of s Ds π + background from the D s ± φπ ± and D s ± K (89) K ± contributions found in 1 fb 1 of data is 797 ± 43 which is lower than the yield estimated in Ref. [13] of 977 ± events, but other D s ± K (89) K ± events are expected for M(Dπ) < 53 MeV/c. Due to the difficulty to disentangle s Ds π + from D π + in this region, these events are not estimated. In addition non resonant D s ± K K ± π ± decays can also contribute. In order to suppress the s Ds π + background, the following requirements are applied ( D s veto ) : 3

31 veto on the K ± K invariant mass in the window MeV/c when the K ± K π invariant mass lies within the window 194- MeV/c ; veto on the K ± π invariant mass in the window 8-97 MeV/c when the K ± K π invariant mass lies within the window 195- MeV/c, and when one of the reconstructed pions fulfills DLL(K π) > 4; DLL(K π) < 3 on the pions candidates when the K ± K π invariant mass lies within the window 194- MeV/c. The effect of the D s veto applied on data is shown in Fig. 31, where 96% of the s D s π + is removed. Signal efficiencies on D π + and D K + decays and background rejection are listed in Table 1. Events no veto D s mass D s anti-veto veto on D s mass M(KKπ) [MeV/c ] Figure 31: Distributions of the K K ± π ± invariant mass in 3 fb 1 of data in the s D s π + signal region ([533, 54] MeV/c ) with and without the D s veto, and with the anti-veto. MC Signal efficiency D + K ±.5 % D + π ±.9 % ackground rejection s D + s π 95.6 ±.1 % Table 1: Efficiencies and background rejections of the D s veto computed on the MC samples after corrections with PIDCalib (Section 3..). In the DK sample, the effect of the D s veto to suppress the s D s π + /K + has been also studied. From Fig. 3 a very small peak is seen around the D s mass value and is removed via the D s veto. Once the veto is applied, about 1 s D s π + /K + events ( 4% of events estimated in Section 5.4) can survive in the DK sample in 3 fb 1. 6 Description of the sample composition A model to fit the unbinned invariant mass distribution of reconstructed candidates of the DK and Dπ sample is derived in this section. The Dπ and DK samples are defined by the DLL(K π) requirements shown in Table 13; the DT requirement applied on the two samples is also shown in this table. Each probability density function (pdf) to describe the two samples is presented. A maximum likelihood is constructed to fit simultaneously the two samples using the PID efficiencies of the DLL(K π) requirements as constraints to control the D π + 31

32 Events 8 no veto D s mass D s anti-veto 7 veto on D s mass M(KKπ) [MeV/c ] Figure 3: Distribution of the K K ± π ± invariant mass for candidates in 534 < M(DK) < 54 MeV/c with DLL(K π) > 5, with and without the D s veto, and with the anti-veto, using 3 fb 1 of data. Table 13: DT and PID requirements used to study the fit model, efficiencies are computed from the MC samples (corrected with PIDCalib). D π + D K + DT output > ±.1 % 8. ±. % DLL(K π) < ±.1 % 3.3 ±.3 % DLL(K π) > 5.3 ±.1 % 69.7 ±. % background in the DK sample, and the D K + background in the Dπ sample. 6.1 Model description of the Dπ sample The pdf of each component of the Dπ sample is parametrized from the fit to MC simulations, following the model in Ref. [13] (shown in Fig. 33), except for the s D s π + and Λ b Λ + c π components that won t be included since these backgrounds are suppressed by the vetoes described in Section 5.4. The components of the sample are: the D π + signal peak, described by a sum of a JohnsonSU pdf (see Appendix D.) and two Gaussian pdfs, where the two Gaussians share the same mean value, i.e. Eq. 33 of Appendix D.3 with N = and µ 1 = µ = µ (Fig.34a); the D K + background, described with a sum of JohnsonSU and two Gaussian pdfs is used, i.e. Eq. 33 with N = (Fig. 34b); 3

33 Figure 33: Distribution of the D ± π invariant mass for D π + decay candidates reconstructed in 1 fb 1 of data collected in 11 [13] the D ρ + partially reconstructed background, where a π from the decay of the ρ ± is not reconstructed, modeled with a JohnsonSU pdf (Fig. 34c); the D π + partially reconstructed background, where a π or a γ from the decay of the D ± is not reconstructed, modeled with the Crystall all pdf of Appendix D.1 (Fig. 34d); The combinatorial background is modeled using an exponential pdf ( x ) f(x; τ) exp τ (16) with the parameter τ left free in the fit to data. The other parameters floating in the fit to data are the yields of each component, and the parameters µ, σ, τ J and σ J of the signal component. The σ i s, µ i s (i=1,) and µ J s of the other components are constrained to the µ and σ parameters of the signal pdf, respectively, such that: ( σ σ i )MC = ( σ σ i )data and (µ µ i ) MC = (µ µ i ) data (17) The σ J s and other shape parameters are fixed from MC and are reported in the Appendix E Model description of the DK sample Following the model from Ref. [13] shown in Fig. 11, the pdf of each component of the DK is extracted from MC simulation as follows: the D K + signal peak is described with a sum of a JohnsonSU pdf and two Gaussian pdfs, where the two Gaussians share the same mean value, i.e. Eq. 33 with N = and µ 1 = µ = µ (Fig. 35a); 33