Relative branching ratio measurements of charmless B ± decays to three hadrons

LHCb-CONF-011-059 November 10, 011 Relative branching ratio measurements of charmless B ± decays to three hadrons The LHCb Collaboration 1 LHCb-CONF-011-059 10/11/011 Abstract With an integrated luminosity of 34 pb 1 collected by LHCb during the 010 run, we analyse the charmless three-body B ± decays B ± K ± π + π, B ± K ± K + K and B ± p pk ±. The branching ratios relative to B ± K ± π + π are found to be B(B± K ± K + K ) B(B ± K ± π + π ) 0.0(stat) ± 0.0(syst). = 0.5 ± 0.03(stat) ± 0.01(syst) and B(B ± p pk ± ) B(B ± K ± π + π ) = 0.19 ± 1 Contact authors: Jussara Miranda, Irina Nasteva.

1 Introduction In recent years the B factory experiments BaBar and Belle were able not only to confirm the CP violation in B decays but also to provide hints for rich physics to pursue in the near future. In this context, a matter of great interest is the study of B ± decays to three charmless hadrons. Most of these channels have branching ratios of the order of 10 5 to 10 6, and thereby large data samples are needed to provide precision measurements. The B ± K ± π + π decay, for instance, has been observed by Belle and BaBar [1, ] which claimed evidence for CP violation in the channel B ± ρ 0 K ± (asymmetry A CP away from zero by 3.9σ). The LHCb experiment [3] will go a step further, providing larger data sets and allowing a detailed study. From the data collected by LHCb in 010, no CP violation studies can be addressed yet. Nonetheless, it is useful to measure the relative branching ratios in order to gain confidence in our detector understanding and analysis strategy. The most recent branching ratio results from the PDG [4] are averages of the BaBar and Belle measurements: B(B ± K ± π + π ) =(5.10 ± 0.9) 10 5, B(B ± K ± K + K )=(3.37 ± 0.) 10 5 and B(B ± p pk ± )=(0.59 ± 0.05) 10 5. For the B ± p pk decay mode, however, these values are quoted by excluding charmonium contributions such as J/ψ p p and η C p p, which are included in this note. The branching ratio of B ± p pk including these contributions was measured by the Belle collaboration to be (1.076 ± 0.04) 10 5 [5]. From these values, the current relative branching ratios to B ± K ± π + π are 0.661 ± 0.057 for B ± K ± K + K and 0.11 ± 0.014 for B ± p pk ±. In this analysis we perform a measurement of the branching ratios of B ± K ± K + K and B ± p pk ± relative to B ± K ± π + π with the data collected by LHCb during 010 at a centre of mass energy of 7 TeV, corresponding to an integrated luminosity of 34 pb 1. Event selection The B ± decay modes in three charmless hadrons have topological similarities, which have led to defining an inclusive selection. The B ± candidates are reconstructed first by using the pion hypothesis for all tracks and selecting candidates within a three-pion invariant mass range of 4 to 6 GeV/c, which includes the channels of interest. At a later stage the B ± invariant masses are recalculated by assigning the correct mass hypothesis separately for each decay channel, and particle identification (PID) requirements are applied. The three final state tracks come from a common secondary vertex (SV), which is displaced from the primary (PV) due to the large flight distance (FD) of the B ± meson before decaying. The candidates are filtered by requiring good quality decay vertices. The reconstructed B ± momentum vector points to the primary vertex, resulting typically in a small impact parameter (IP) and angle θ between the momentum and the flight direction. In contrast, the daughter tracks tend to have larger impact parameters as they do not originate from the primary vertex. Selecting high transverse momenta (P T ) 1

Variables Selection cuts B ± candidate IP < 0.04 mm B ± candidate P T > 1.7 GeV/c Distance from SV to any PV > 3 mm Secondary Vertex χ < 1 B ± candidate cos(θ) > 0.99998 B ± Pointing = P sin θ/(p sin θ + i P T i ) < 0.1 B ± Flight Distance χ > 700 B ± corrected mass M COR M + p miss T + p miss T < 5.8 GeV/c Sum of P T of tracks > 4.5 GeV/c Sum of IPχ of tracks > 00 P T of the highest-p T track > 1.5 GeV/c P T of the second highest-p T track > 0.9 GeV/c IP of the highest-p T track > 0.05 mm Tracks IPχ > 14 Tracks χ /n.d.f. < 5 Maximum DOCA < 0.3 mm Number of tracks in the event < 40 Table 1: Selection criteria for B ± decays to three charmless hadrons. of the tracks and of the B ± candidate is very efficient for the signals and improves the signal-to-background ratio. A summary of the selection criteria is given in Table 1. Particle identification requirements are applied to each B ± decay daughter, based on the RICH sub-detectors information. The distinguishing variables between different particle hypotheses (π, K, p) are the differences between log likelihoods logl ij. We apply PID filters to the tracks that pass the kinematic selection of log L Kπ > 0 for kaons, log L Kπ < 0 for pions, and log L pk > 0 and log L pπ > 0 for protons. The surviving events after PID undergo further selection to remove the reflection and peaking background contributions that populate the signal region. The B ± K ± π + π Dalitz plot distribution shows a concentration of events in bands, which are explained by the presence of backgrounds from B ± D 0 (D 0 )π ±, D 0 (D 0 ) K ± π on the K + π axis, and B ± J/ψK ±, J/ψ µ + µ and B ± ψ(s)k ±, ψ(s) µ + µ on the π + π axis. The B ± D 0 (D 0 )π ± contaminations are eliminated by requiring m Kπ < 1.844 or m Kπ > 1.884 GeV/c, and muons are rejected with the PID requirement log L µπ < 0. In the B ± K ± K + K mode, no evident sources of peaking backgrounds were identified in the Dalitz plot. For the B ± p pk ± mode there is a population which matches a possible contribution from J/ψ p p and η C p p, and we do not explicitly veto these events. Although there was no reflection removal in the B ± K ± K + K and B ± p pk ± spectra, the muon veto requirement was also applied to those modes to guarantee the uniformity of the relative efficiency.

The B ± candidates are filtered according to hadronic trigger decisions at the hardware level (L0 trigger) and at the high level triggers (HLT). The candidates are required to have been selected by the hadronic L0 trigger, the HLT1 track trigger [6] and the HLT topological trigger [7] for two-, three- or four-body hadronic decays. 3 B ± mass fit The signal event yield is extracted from the B ± mass fit of the signal and backgrounds. The relative branching ratio is given by the equation: B(B ± h ± h + h ) B(B ± K ± π + π ) = N ɛacc Kππ N Kππ ɛ acc ɛreco&sel Kππ ɛ reco&sel ɛp ID Kππ ɛ P ID ɛtrigger Kππ ɛ trigger, (1) where the label stands for B ± K ± K + K or B ± p pk ±, N is the number of signal events from the mass fit, ɛ acc is the efficiency of the acceptance, ɛ reco&sel the efficiency of the reconstruction and offline selection, ɛ P ID accounts for the particle identification efficiency and ɛ trigger for the trigger efficiency. The efficiencies are described in Section 4. We perform an unbinned extended maximum likelihood fit to the selected events. The signals were parameterised with a Gaussian probability density function (PDF) with the mean, width and number of events as free parameters. The combinatorial background is parameterised as an exponential PDF with two free parameters for the number of combinatorial events and its slope. The shapes of the partially reconstructed background contributions from other B decays are estimated by MC and fixed in the fit. They are generically parameterised by a modified Gaussian with the functional form of: [ ] (m µi ) βi (m) F i (m) = N i exp, () where N i is the normalisation parameter giving the number of events, µ i the maximum of the function, σ i is the width and β i (m) = exp( λ i (m µ i )) is an exponential function, responsible for the typical asymmetry of the mis-identified distribution. In order to fix the shape of the distribution, the parameters µ i, σ i and λ i are determined by MC studies. The number of events which belong to a given background is estimated as N i = f i,s N S, where the label S is for the signal, i for the relevant background component, and f i,s is the fraction expected. This fraction is calculated by: σ i B i B S ɛ i ɛ S = N i N S = f i,s, (3) where B i and B S are the branching ratios taken from the PDG, and ɛ i and ɛ S are the efficiencies from the MC selection. The number of events in the final sample is fixed by these parameters. The systematic uncertainty related to fixing f i,s is taken into account by performing the mass fits with floating fractions of backgrounds. 3

Number of Entries / 10 MeV/c 0 00 180 160 140 10 100 80 60 40 0 LHCb Preliminary = 101 +- 40 evts N B signal combinatorics 0 0 B D (kππ ) π 0 B η' (ρ γ) K *+ 0 B K (K π ) ππ B πππ 0 5100 500 5300 5400 [MeV/c ] M Kππ Figure 1: Fit to the invariant mass of B ± K ± π + π, with contributions from the B ± K ± π + π signal (red), B ± D 0 (D 0 )π ± with D 0 (D 0 ) K ± π π 0 (blue), B ± η K ± with η ρ 0 γ and ρ 0 π + π (green), B ± K ± π + π with K ± K ± π 0 (grey), mis-identification of B ± π ± π + π (magenta), and combinatorial background (yellow). Decay channel B ± mass [MeV] B ± width [MeV] Fit χ /n.d.f. B ± K ± π + π 574.6 ± 1.0 4.1 ± 0.9 0.885 B ± K ± K + K 577.8 ± 1.0 19.0 ± 0.9 0.980 B ± p pk ± 574.9 ±. 1.4 ±.1 0.495 Table : Parameters of the B ± mass fits. The total B ± mass fit function is the sum of the three components: [ ] (m m0 ) F total (m) = N S exp + N comb exp [a(m 5079)] + σ 0 n B i=1 F i (m), (4) where the first term is the signal PDF, the second is the combinatorial background, and the third is a sum of the PDFs of the partially reconstructed backgrounds from Equation (). The fit has five free parameters: the signal mean m 0 and its width σ 0, its integral giving the number of signal events N S, the slope a and the integral N comb of the combinatorial background PDF. Figure 1 shows the mass fit of the B ± K ± π + π mode, for which 101 ± 40 signal events were found. The dominant background contributions were identified and included in the fit to the B ± K ± π + π invariant mass. Other sources of contamination from B ± J/ψK ± (J/ψ µ + µ ), B ± ψ(s)k ± (ψ(s) µ + µ ), B ± J/ψK ± (J/ψ ρ 0 π 0 and ρ 0 π + π ), and B ± ρ 0 ρ + (ρ 0 π + π and ρ + π + π 0 ) were studied and were found to not contribute to the fit. Figure shows the mass fit to B ± K ± K + K, where the signal yield is 610 ± 9 events and one type of peaking background was found to contribute. The potential 4

Number of Entries / 10 MeV/c 160 140 10 100 80 60 40 0 LHCb Preliminary = 610 +- 9 evts N B signal combinatorics *+ 0 B K (K π ) KK 0 5100 500 5300 5400 [MeV/c ] M KKK Figure : Fit to the invariant mass of B ± K ± K + K, with contributions from the B ± K ± K + K signal (red), B ± K ± K + K with K ± K + π 0 (blue), and combinatorial background (yellow). Number of Entries / 10 MeV/c 45 40 35 30 5 0 15 10 5 LHCb Preliminary = 171 +- 17 evts N B signal combinatorics 0 5100 500 5300 5400 [MeV/c ] M ppk Figure 3: Fit to the invariant mass of B ± p pk ±. The red line shows the B ± p pk ± signal, and the yellow line shows the combinatorial background. contamination from B ± D 0 (D 0 )π ± ( D 0 (D 0 ) K + K ) with a misidentified pion was found to be negligible. The B ± p pk ± mass spectrum in Figure 3 has a signal yield of 171 ± 17 events. The considered backgrounds with a missed neutral particle, B ± K ± J/ψ (J/ψ p pπ 0 ) and B ± K ± J/ψ (J/ψ p p and K ± K ± π 0 ) were found to have negligible contributions. The results for the B ± masses and widths, extracted from the fits, and the fit χ /n.d.f. values for the three channels are given in Table. 5

Variable B ± K ± K + K B ± p pk ± N /N Kππ 0.603 ± 0.037 0.169 ± 0.018 Kππ 1.067 ± 0.004 1.165 ± 0.003 ɛ acc /ɛacc ɛ reco&sel ɛ trigger ɛ P ID ɛ T ot /ɛ reco&sel Kππ 0.950 ± 0.005 0.745 ± 0.005 /ɛ trigger Kππ 1.003 ± 0.018 0.9 ± 0.03 ID /ɛpkππ 1.139 ± 0.00 1.137 ± 0.008 ot /ɛtkππ 1.158 ± 0.0 0.910 ± 0.04 Table 3: Summary of the measurements used to estimate the relative branching ratios. The uncertainties are statistical. 4 Signal efficiencies and systematic uncertainties The relative efficiencies of the acceptance (ɛ acc ), reconstruction and selection (ɛ reco&sel ), PID (ɛ P ID ) and trigger selection (ɛ trigger ) enter directly into the relative branching ratio of Equation (1). The acceptance, reconstruction and selection, and trigger efficiencies are determined from MC simulations, while the particle identification efficiency is extracted from PID calibration data. Each efficiency term is estimated separately, and the resulting values are given in Table 3. The acceptance at the generator level, ɛ acc, includes the effects of the geometrical acceptance of the LHCb detector and the polarity of the LHCb magnetic field. For B ± K ± π + π and B ± K ± K + K the efficiencies are comparable, while the B ± p pk ± efficiency is higher since it is produced in a more forward region of the detector. The ɛ reco&sel is a convolution of the reconstruction and selection efficiencies. The efficiencies are extracted by calculating the fraction of selected events among the total number of generated events. In addition to the topology, B ± K ± π + π and B ± K ± K + K modes have comparable phase spaces, giving a relative efficiency close to one. The B ± p pk ± phase space is considerably smaller due to the larger masses of the two protons, so its relative efficiency is reduced. In order to validate the approach of estimating the selection efficiencies from Monte Carlo, we checked the MC-data agreement using the decay B ± J/ψK ±, J/ψ µ + µ as a control channel, since its topology is similar to the B ± h ± h + h signal. We compared the distributions of kinematic variables of the surviving B ± J/ψK ± candidates from MC and data after the selection, and found good agreement. The MC samples for this study were generated including only the kinematics of the process, and not the dynamics, resulting in a flat Dalitz plot phase space distribution. To evaluate the discrepancy between MC and data due to the flat MC phase space, we weight the acceptance evaluated from MC by the fraction of data found in each bin. Weighting the MC acceptance bin-by-bin by the average data remaining after the selection gives relative branching ratios that differ from the nominal values by 0.06% for B ± K ± K + K and by 0.5% for B ± p pk ±, and these are treated as systematic uncertainties. A reliable measurement of the trigger efficiency is crucial to the analysis. The MC 6

Uncertainty K ± K + K /K ± π + π p pk ± /K ± π + π MC acceptance < 0.001 0.001 Trigger efficiency 0.010 0.015 PID efficiency 0.004 0.008 Fit function 0.004 0.006 Total 0.011 0.018 Table 4: Absolute systematic uncertainties of the branching ratio measurements. simulations were found to agree with trigger calibration data up to a discrepancy factor of 5 10% for L0 in some detector regions. This discrepancy was shown to factorise out in the relative efficiencies, within the statistical uncertainties of the trigger calibration samples. The L0 decision efficiency is calculated from Monte Carlo by the fraction of selected events that pass L0. To test the validity of estimating the trigger efficiency from MC simulation, we compared the P T of tracks that pass the hadronic L0 trigger between data and MC, and found good agreement within the statistical uncertainties. The systematic uncertainty of the efficiency estimation method is taken from the deviations of the efficiency ratios from unity. For the B ± K ± K + K mode, the efficiency ratio is consistent with one, and therefore its uncertainty due to the limited sample size is used, giving a relative branching ratio difference from the nominal value of 1.9%. For B ± p pk ± the difference in the relative efficiency leads to a relative branching ratio difference of 7.9%. This conservative estimate represents the dominant systematic contribution for B ± p pk ±. The PID selection efficiency ɛ P ID was determined from PID efficiency tables of Cherenkov detector calibration data. Calibration data are collected in parallel with physics data and contain large samples of kaons from D and φ decays, pions from KS 0, D and Λ 0 decays, and protons from Λ 0 decays. The PID performances are determined from calibration data samples, reweighted according to the kinematical properties of our signals obtained from data. The uncertainty of the reweighting procedure is evaluated as a systematic effect by computing the difference in efficiency between the calibration tracks MC sample, reweighted with the kinematics of the relevant B ± decay, and the B ± decay MC sample. The resulting discrepancy from the nominal relative branching ratio measurement is 0.8% for B ± K ± K + K and 4.% for B ± p pk ±. Finally, a systematic uncertainty is evaluated for the signal yields of the B ± mass fits by implementing different fit parameterisations. For the signal shape a double Gaussian is used instead of a single one. This results in a systematic uncertainty of 0.8% for B ± K ± K + K and 3.% for B ± p pk ±. We also allow the individual fractions of the reflections to float in the fit procedure. This leads to a branching ratio discrepancy smaller than 0.01%, and is therefore neglected. The systematic uncertainties are summarised in Table 4, where the total is the sum in quadature. 7

5 Results The final result for the relative branching ratios of Equation (1) from LHCb 010 data is the following: B(B ± K ± K + K ) = 0.5 ± 0.03(stat) ± 0.01(syst), B(B ± K ± π + π ) (5) B(B ± p pk ± ) = 0.19 ± 0.0(stat) ± 0.0(syst), B(B ± K ± π + π ) (6) where the first uncertainty is statistical and the second is systematic. The efficiencies and event yields used in obtaining these results are given in Table 3. 6 Conclusion From a sample of 34 pb 1 of data taken in 010, we have studied the charmless hadronic decay modes B ± K ± π + π, B ± K ± K + K and B ± p pk ± with the purpose of measuring the relative branching ratios of the two latter channels with respect to the former. The final yields for the three channels were found to be: 101 ± 40 events of B ± K ± π + π, 610±9 events of B ± K ± K + K, and 171±17 events of B ± p pk ±. Taking into account the relative efficiencies of the latter two with respect to the former, the relative branching ratios are measured to be B(B± K ± K + K ) = 0.5 ± 0.03(stat) ± B(B ± K ± π + π ) 0.01(syst) and B(B± p pk ± ) = 0.19 ± 0.0(stat) ± 0.0(syst). B(B ± K ± π + π ) Our result for B ± K ± K + K has smaller uncertainties than the previously published results, and is.1 σ away from the PDG value. The result for B ± p pk ± is compatible with the previously published results, and also with the LHCb measurement from 010 data of the B ± p pk ± branching ratio relative to its charmonium contribution, B ± J/ψK ± with J/ψ p p [8]. The increased amount of data collected by LHCb in 011 will not only greatly improve the precision of the branching ratio measurements, but will also allow detailed studies of CP violation in these decay modes. References [1] B. Aubert et al. [BaBar Collaboration], Phys.Rev. D78 01004 (008), hepex/0803.4451. [] A. Garmash et al. [Belle Collaboration], Phys.Rev.Lett. 96 51803 (006), hepex/051.066. [3] A. A. Alves et al. [LHCb Collaboration], JINST 3 (008) S08005. [4] K. Nakamura et al. [Particle Data Group], J.Phys. G37, 07501 (010) and 011 partial update for the 01 edition, page 10. 8

[5] J.T. Wei et al. [Belle Collaboration], Phys.Lett. B659:80-86,008. [6] V. Gligorov, A Single Track HLT1 Trigger, LHCb-PUB-011-003. [7] M. Williams, V. Gligorov, C. Thomas, H. Dijkstra, J. Nardulli and P. Spradlin, The HLT Topological Lines, LHCb-PUB-011-00. [8] R. Cardinale and C. Patrignani [LHCb Collaboration], Measurements of the relative branching fractions of the B ± p pk ± decay channel including charmonium contributions, LHCb-CONF-011-058. 9