Measurement of Ratios of Fragmentation Fractions for Bottom Hadrons in Collisions at TeV
This paper describes the first measurement of -quark fragmentation fractions into bottom hadrons in Run II of the Tevatron Collider at Fermilab. The result is based on a 360 pb sample of data collected with the CDF II detector in collisions at TeV. Semileptonic decays of , , and mesons, as well as baryons, are reconstructed. For an effective bottom hadron threshold of 7 GeV, the fragmentation fractions are measured to be , , and , where the uncertainty is due to uncertainties on measured branching ratios. The value of agrees within one standard deviation with previous CDF measurements and the world average of this quantity, which is dominated by LEP measurements. However, the ratio is approximately twice the value previously measured at LEP. The approximately 2 discrepancy is examined in terms of kinematic differences between the two production environments.
pacs:13.20.He, 13.30.Ce, 14.20.Mr, 14.40.Nd, 14.65.Fy
CDF Collaboration111With visitors from University of Athens, 15784 Athens, Greece, Chinese Academy of Sciences, Beijing 100864, China, University of Bristol, Bristol BS8 1TL, United Kingdom, University Libre de Bruxelles, B-1050 Brussels, Belgium, University of California Irvine, Irvine, CA 92697, University of California Santa Cruz, Santa Cruz, CA 95064, Cornell University, Ithaca, NY 14853, University of Cyprus, Nicosia CY-1678, Cyprus, University College Dublin, Dublin 4, Ireland, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom, University of Heidelberg, D-69120 Heidelberg, Germany, Universidad Iberoamericana, Mexico D.F., Mexico, University of Manchester, Manchester M13 9PL, England, Nagasaki Institute of Applied Science, Nagasaki, Japan, University de Oviedo, E-33007 Oviedo, Spain, Queen Mary, University of London, London, E1 4NS, England, Texas Tech University, Lubbock, TX 79409, IFIC(CSIC-Universitat de Valencia), 46071 Valencia, Spain,
Bottom quarks, , produced in collisions combine with anti-quarks or di-quarks to form bottom hadrons. In this process, called fragmentation, the color force field creates quark-antiquark pairs that combine with the bottom quark to create a meson or baryon . Since the fragmentation process, which is governed by the strong force, cannot be reliably calculated by perturbative QCD Politzer (1973); Gross and Wilczek (1973); Field and Feynman (1978), the fragmentation properties of quarks must be determined empirically. This paper describes a measurement of the species dependence of the -quark fragmentation rates into bottom hadrons produced in collisions at center of mass energy TeV during Run II of the Tevatron collider at Fermilab.
The probabilities that the fragmentation of a quark will result in a , , or meson or a baryon are denoted by , , , and , respectively. In this paper, indicates the fragmentation fraction integrated above the momentum threshold of sensitivity in the data: Ref (). In the case that the fragmentation fractions are momentum dependent, the measured fragmentation fractions are proportional to the relative yields of the bottom hadrons integrated above the effective . The contributions from the production of excited bottom hadrons that decay into final states containing a , , meson or baryon are implicitly included in this definition of the fragmentation fractions, . Throughout the paper, unless otherwise noted, references to a specific charge state are meant to imply the charge conjugate state as well.
In Run I of the Fermilab Tevatron, which collected data from 1992 - 1996, the fraction of mesons produced relative to the number of mesons was measured 2 higher at CDF Abe et al. (1996, 1999); Affolder et al. (2000a) than at the LEP experiments Abreu et al. (1992); Acton et al. (1992); Buskulic et al. (1995). Interestingly, the time-integrated flavor averaged mixing parameter, , where and are the time-integrated mixing parameters of and mesons respectively, was also measured 2 higher in Run I Abe et al. (1997); Acosta et al. (2004a) than the LEP averages of the same quantity Buskulic et al. (1992, 1994); Abreu et al. (1994); Acciarri et al. (2000); Abreu et al. (2001); Abbiendi et al. (2003). This second discrepancy led to speculations about possible sources of the enhanced average mixing rate at a hadron collider relative to electron-positron collisions, including suggestions that new physics may be the source of the disagreement Berger et al. (2001). Since the average momentum of quarks produced at LEP, 40 GeV, is significantly higher than at the Tevatron, 10 GeV, it is also possible that the fragmentation process depends on the -quark momentum. Another possible explanation is that is higher at the Tevatron than at LEP due to the different initial mechanism of -quark production. Of course, a more mundane possibility is that the Run I results relating to are simply statistical fluctuations. To shed light on the question of whether -quark fragmentation is different in a hadron environment than in collisions, the fragmentation fractions are measured in CDF Run II with high statistical precision and an updated treatment of the lepton-charm sample composition.
The analysis strategy is as follows. Semileptonic decays of bottom hadrons, , where stands for electron or muon, and represents a charm meson or baryon, in case of semileptonic bottom baryon decays, unless otherwise specified, provide large samples for studying the fragmentation properties of quarks. This measurement determines the -quark fragmentation fractions by reconstructing five semileptonic signatures, , , , , and . The selection requirements are kept similar among the five lepton-charm channels in order to cancel as many systematic uncertainties as possible. The final signal requirements, though similar, have been selected to maintain good acceptance for the individual decays, which have different kinematic features. The reconstructed signal yields, originating from the various semileptonic decays, are then related to the numbers of bottom hadrons (, , , or ) produced in the -quark fragmentation process. Since the neutrino from the semileptonic bottom hadron decay is not reconstructed, the missing energy in the decay allows semileptonic bottom hadron decays to excited charm states to contribute to the five final state decay signatures. This results in “cross-talk” between the bottom hadron species, particularly between the mesons. The observed semileptonic decay signatures are related to their corresponding parent bottom hadrons through a procedure used to extract the sample composition, as described later in the text. In order to reduce systematic uncertainties in trigger and tracking efficiencies, the -quark fragmentation fractions are measured relative to . This means that the relative fragmentation fractions , and are extracted from the five lepton-charm yields, taking the sample composition into account. Since the fragmentation of quarks into baryons other than the are ignored, a constraint requiring the fragmentation fractions , , , and to sum to unity is not applied.
This paper is organized as follows. The semileptonic signal reconstruction is discussed in Section II, while the sample composition procedure used to relate the lepton-charm signatures to the parent bottom hadron is described in Section III. The efficiencies needed to extract the sample composition are determined in Section IV. The fit to the fragmentation fractions is detailed in Section V. Finally, the systematic uncertainties assigned to the measurement are described in Section VI and the final results are discussed in Section VII.
Ii Data Reconstruction
ii.1 Experimental Apparatus
The data used in this measurement represent an integrated luminosity of approximately 360 pb collected with the CDF II detector between February 2002, and August 2004. The CDF detector employs a cylindrical geometry around the interaction region with the proton direction defining the positive -direction. Most of the quantities used for candidate selection are measured in the plane transverse to the -axis. In the CDF coordinate system, is the azimuthal angle, is the polar angle measured from the proton direction, and is the radius perpendicular to the beam axis. The pseudorapidity is defined as . The transverse momentum, , is the component of the track momentum, , transverse to the -axis (), while , with being the energy measured in the calorimeter.
The CDF II detector features excellent lepton identification and charged particle tracking and is described in detail elsewhere Acosta et al. (2005a); Blair et al. (1996). The parts of the detector relevant to the reconstruction of semileptonic bottom hadron decays used in this measurement are briefly summarized below. The detector nearest to the interaction region is a silicon vertex detector (SVX II) Sill (2000), which consists of five concentric layers of double-sided sensors located at radii between 2.5 and 10.6 cm. An additional single layer of silicon (L00) Hill (2004) is mounted on the beam pipe at radius 1.5 cm, but the information from this detector is not used in this measurement. In addition, two forward layers plus one central layer of double sided silicon located outside the SVX at radii of 20-29 cm make up the intermediate silicon layers (ISL) Affolder et al. (2000b). Together with the SVX II, the ISL detector extends the sensitive region of the CDF II tracking detector to . CDF’s silicon system provides three-dimensional track reconstruction and is used to identify displaced vertices associated with bottom hadron decays. The measurement of the momentum of charged particles in the silicon detector is significantly improved with the central outer tracker (COT) Affolder et al. (2004), an open-cell drift chamber with 30,200 sense wires arranged in 96 layers combined into four axial and four stereo super-layers (SL). It provides tracking from a radius of 40 cm out to a radius of 132 cm covering cm. The track reconstruction efficiency of the COT is found to be for charged particles with Acosta et al. (2004b) and Acosta et al. (2003) for charged particles with . For high-momentum charged particles, the resolution is found to be . The COT also provides specific energy loss, dd, information for charged particle identification with a separation between pions and kaons of approximately 1.4 Abulencia et al. (2006a). The central tracking system is immersed in a superconducting solenoid that provides a 1.4 T axial magnetic field.
Electromagnetic (CEM) Balka et al. (1988) and hadronic (CHA) Bertolucci et al. (1988) calorimeters are located outside the COT and the solenoid, where they are arranged in a projective-tower geometry. The electromagnetic and hadronic calorimeters are lead-scintillator and iron-scintillator sampling devices, respectively. The energy resolution for the CDF central calorimeter is for electromagnetic showers Balka et al. (1988); Abulencia et al. (2007) and for hadrons Blair et al. (1996); Bertolucci et al. (1988), where is measured in GeV. A layer of proportional chambers (CES), with wire and strip readout, is located six radiation lengths deep in the CEM calorimeters, near the electromagnetic shower maximum. The CES provides a measurement of electromagnetic shower profiles in both the - and -directions for use in electron identification. Muon candidates are identified with two sets of multi-layer drift chambers and scintillator counters Ascoli et al. (1988); Dorigo (2001), one located outside the calorimeters (CMU) and the other (CMP) behind an additional 60 cm of iron shielding, equivalent to approximately 3 pion interaction lengths. The CMU provides coverage for particles with and . The CMP covers the same pseudorapidity region, but identifies muons with with higher purity than muons reconstructed in the CMU only.
ii.2 Trigger Requirements
CDF uses a three-level trigger system Blair et al. (1996), where each level provides a rate reduction sufficient to allow for processing at the next level with minimal dead-time. At level 1, data from every beam crossing are stored in a pipeline memory capable of buffering data for . The level 1 trigger either rejects an event or copies the data into one of four level 2 buffers. At level 2, a substantial fraction of the event data is available for analysis by the dedicated trigger processors. Events that pass the level 1 and level 2 trigger selection criteria are then sent to the level 3 trigger Anikeev et al. (2000, 2001), a cluster of computers running a speed-optimized reconstruction code. Events selected by level 3 are written to permanent mass storage.
Tracking plays a significant role in the triggers utilized for this analysis. Semileptonic decays are recorded using a trigger that requires a lepton and a track displaced from the interaction point and identified with the silicon vertex trigger (SVT) Bardi et al. (2002). The decay topology of semileptonic decays is sketched in Fig. 1. Tracks are reconstructed at level 1 with the extremely fast tracker (XFT) Thomson et al. (2002) by examining COT hits from the four axial super-layers. The XFT provides - tracking information and can identify tracks with GeV with high efficiency () and good transverse momentum resolution, . XFT tracks can be matched with either calorimeter clusters to identify electron candidates or with track segments in the muon detectors to identify muon candidates. The XFT tracks are extrapolated into the silicon detector system, where the SVT uses the SVX II measurements of charge deposits from charged particles to form simplified tracks. In addition, the SVT determines the distance of closest approach in the transverse plane, , with respect to the beam line, which is determined from a time-dependent line fit to the locus of primary interaction vertices determined from all tracks available at trigger level (see Fig. 1). The impact parameter resolution of the SVT is approximately m Bardi et al. (2002); Ashmanskas et al. (2002), which includes a contribution of m from the width of the interaction region Acosta et al. (2005b).
The primary trigger used in this measurement requires that the lepton and the displaced track (SVT track) must have transverse momentum values greater than 4 GeV and 2 GeV, respectively. The displaced track’s impact parameter, , must exceed 120 m and be less than 1 mm to reject decay products of long-lived hadrons decays such as or . The opening angle, , between the lepton and SVT track is required to satisfy to increase the probability that the two tracks originate from the same hadron. Additionally, the invariant mass between the trigger lepton and SVT triggered track must be less than the nominal bottom hadron mass, , where the SVT track is assumed to have the pion mass. The trigger lepton requirements are described in conjunction with their analysis selections in Section II.3.1. Events that pass these trigger requirements are recorded to the lepton plus SVT trigger data stream for further analysis. In this measurement both the muon and electron plus SVT trigger data (+SVT and +SVT) are used. An additional trigger utilized for selecting events is the two-track trigger (TTT), which requires two displaced tracks. Large semileptonic samples are also available with this trigger Abulencia et al. (2006b, c), although the false lepton background is much larger as well. Semileptonic events from the TTT are used in this analysis for a study of the systematic uncertainty arising from false leptons.
ii.3 Data Selection and Reconstruction
Events from the lepton plus SVT trigger data stream are used to reconstruct semileptonic bottom hadron decays in this analysis. First, trigger leptons are identified by re-confirming the trigger decision with offline quantities after event reconstruction. Charm candidates are then reconstructed, with the SVT track required to match one of the daughter tracks from the charm decay. The selections on the lepton-charm signals obtained are optimized to reduce combinatoric background and improve signal significance. Non-combinatoric backgrounds in the charm signals are handled separately.
ii.3.1 Trigger Lepton Identification
The data analysis begins by identifying the trigger leptons from the +SVT and +SVT trigger streams. The electron candidates are identified by requiring the following selection criteria. The longitudinal shower profile must be consistent with that of an electron shower, with a leakage energy from the CEM into the CHA of less than 12.5%, in order to suppress hadron contamination. The lateral shower profile of the CEM cluster is required to be consistent with a profile obtained from test beam electrons after appropriate corrections. The association of a single track with the calorimeter shower is made based on the position matching at the CES plane, with both cm and cm conditions required. To achieve good agreement between data and Monte Carlo (MC) simulation (see Sec. IV.1), an isolation requirement is applied to the trigger electron candidates by requiring that exactly only one track is found that projects to the CEM towers used to define the electron energy. To reconfirm electron trigger cuts, the offline reconstructed and of the electron candidate are required to be greater than 4 GeV and 4 GeV, respectively. Additionally, electron candidates from photon conversions in the detector material are removed by rejecting those electron candidates that have a small opening angle with oppositely charged particles in the event.
Trigger muon candidates are reconstructed by extrapolating tracks measured in the COT to the muon system, where they are matched to track segments (stubs) reconstructed in the muon chambers. A CMU or CMP stub is required to have hits in at least three out of the four layers of planar drift chambers. Trigger muons are required to have hits in both the CMU and CMP muon chambers. The separation between a track segment reconstructed in the muon chamber and the extrapolated COT track is computed. The uncertainty in this quantity is dominated by multiple scattering in the traversed detector material. For good track to stub matching, this separation is required to be less than 15 cm and 20 cm in the -view for CMU and CMP, respectively. The transverse momentum of a muon candidate reconstructed offline is required to be greater than 4 GeV.
ii.3.2 Charm Candidate Selection
The SVT track is required to match one of the final state tracks in the five reconstructed charm signals: , , , , and . Only well-reconstructed tracks with and at least three silicon - hits are retained for offline analysis. To ensure good track quality, all charm daughter tracks, except for the soft pion from the decay, are required to have at least five hits in at least two axial and two stereo COT super-layers. There are no COT requirements on the soft pion. During data reconstruction the track parameters are corrected for the ionization energy loss appropriate to the mass hypothesis under consideration. In addition, tracks are required to be fiducial in the COT, so that only tracks which are well-described by the simulation (see Sec. IV.1) are used for further analysis. In particular, tracks that fall within 1.5 cm of the COT mid-plane, where no track information is recorded, and tracks that originate outside of the COT volume at 155 cm are excluded from the analysis. In addition, all tracks must at least pass through the axial SL 6 before exiting the COT. This means the exit radius of the track must be greater than the radius of the sixth super-layer = 106 cm. This requirement is tightened for the SVT trigger track and the trigger lepton. Both tracks must pass through SL 8 of the COT ( = 131 cm) as required in the trigger. The invariant mass of the and is reconstructed within GeVand GeV, respectively. The reconstructed mass is required to be within GeV, while the is reconstructed within GeV. Finally, the reconstructed charm signals are combined with the triggered lepton in a three-dimensional kinematic fit constraining all tracks to a common vertex (see Fig. 1) to establish signals that can be related to semileptonic , , , and decays. The vertex reconstruction does not use a constraint to the known mass Eidelman et al. (2004), although [GeV] is required in order to select a pure sample of candidates.
ii.3.3 Backgrounds to Lepton-Charm Signals
Several backgrounds affect the semileptonic signals. Some of these can be reduced by judicious signal selection, while some must be included in the modeling of the signal or treated as sources of systematic uncertainties. The simplest of these backgrounds to understand are those events arising from combinatoric sources, which are generally estimated from the sidebands of the charm signal. In these backgrounds, random tracks are combined to form a charm signal which passes all charm selection requirements. This combinatoric background can most easily be reduced by selection requirements and modeled by the sideband events, which are expected to exhibit the same shape underneath the signal. A related, but more subtle type of background is that arising from the mis-identification of tracks in one charm decay arising from incorrect assignment of particle identifications in a real charm decay, resulting in ”reflection” backgrounds. These backgrounds are often flat beneath the signal of interest, but occasionally they exhibit particular shapes that can affect the signal distribution non-uniformly. Some reflection backgrounds can be effectively reduced with particle identification selections, such as the specific ionization of particles, dd (see Section II.3.4.) Other reflection backgrounds, which have non-uniform distribution in mass beneath the charm signal are included in the fit to the signal (see Section II.3.5.) MC simulated data is used to determine the shape of these reflection backgrounds.
The third type of background to the semileptonic signals arises from physical processes that produce a real lepton and charm hadron, but not through a decay directly to . This includes processes which originate from the same , such as , where , and , where . These “physics backgrounds” are included in the fit to the sample composition (see Section III). Other backgrounds include processes in which the lepton and charm hadron originate from separate and quark pairs, i.e. , , or , . The background gives a wrong sign (WS) lepton-charm combination, in which the charm and lepton have the same charge, while the background gives right sign (RS) lepton-charm combinations, in which the charm and lepton have opposite charge. All of these processes are also possible with a real charm hadron and a false lepton. In the case of false leptons, both right sign and wrong sign lepton-charm are expected to be present. Backgrounds which do not originate from the same hadron are treated as a source of systematic uncertainty and described by the wrong sign lepton-charm events, which primarily describe false leptons (see Section VI.1.) The background is assumed to be small for a charm decaying to a lepton with Gibson (2006) and is ignored, while the background is implicitly included in the false lepton systematic uncertainty.
ii.3.4 Signal Optimization
Requirements to further enhance the lepton-charm signal include cuts on the , , and charm daughter tracks, and cuts on the invariant mass of the lepton-charm system, , to limit feed-down from excited charm and lepton-charm combinations which do not originate from direct semileptonic bottom hadron decays. Requirements are also made on the probability of the charm and lepton-charm vertex fits.
Since bottom hadrons are longer-lived, a powerful discriminant against these backgrounds is a cut on the proper time of candidate. The decay distance of the hadron is determined by defining a quantity, , which is the transverse decay distance of the lepton-charm combination from the primary interaction vertex (PV), projected on the momentum direction. The missing neutrino produced in the semileptonic decay prevents precise knowledge of and thus of the proper decay time of the candidate. Instead, a pseudo proper decay time is constructed as:
A cut is applied to guarantee a signal from long-lived bottom hadrons and to reduce signal contamination from false leptons and other processes that can contribute a lepton and a charm hadron from uncorrelated sources (see also Section II.3.3.) This requirement also drastically reduces the combinatoric background of charm candidates with real leptons. A cut on the significance of the transverse decay distance of the charm meson, , also reduces the light flavored hadron contamination in the signal. A cut on is applied to improve agreement between the data and Monte Carlo simulation used in determining the efficiencies (see Sec. IV). The selected candidates are a subset of the candidates. Instead of performing a vertex fit on the soft pion, , from the decay, A tight cut is used to select a very clean sample. This reduces the systematic uncertainty in the selection of the combination relative to a pair, since no additional vertex fit is performed. Consequently, the efficiency to detect the soft pion is better described by the simulation. Since the data agrees well with the simulation for tracks with greater than 400 MeV, as can be seen in Fig. 2, the soft pion efficiency is determined from the simulation. A tight cut is used to select a very clean sample.
In order to determine the final analysis selection, kinematic selection criteria are optimized with respect to the combinatoric background for each lepton-charm channel, with additional cuts designed to limit non-combinatoric background, such as the and cuts, applied during the optimization. The figure of merit (FOM) used for optimization is . The signal, , is taken from inclusive and Monte Carlo (see Sec. IV.1). The background, , is taken from the sidebands of the charm signal. In order for the FOM to accurately reflect the significance of the signals in data, is scaled to the expected data signal with a set of nominal cuts obtained by first optimizing each cut individually without applying any other cut. The cuts are then optimized a second time applying all optimal cuts from the prior optimization except the cut being optimized. After two or three successive iterations, a stable optimal cut point is reached for all cuts.
A particle identification cut using dd is found useful for reducing the combinatoric background in the signal. The combinatoric background can be significantly reduced by correctly identifying the proton from the decay utilizing the specific energy loss of the proton track measured in the COT. A dd likelihood ratio, , requirement is applied to the proton. The likelihood ratio is defined by the relation , where and . Figure 3 shows the resulting distributions for protons from the decay and kaons and pions from the decay with the proton hypothesis applied. Muons are indistinguishable from pions, while electrons are well-separated from all of the other distributions, since their mass is so much lower than the mass of the other particles. A cut on , as determined from the control samples, is applied to reduce background while keeping the proton efficiency high. This cut primarily removes pions, since the dd separation between protons and kaons is not as good.
To cancel as many differences in signal reconstruction as possible, the selection criteria are kept as similar as is feasible across charm channels. The optimized cuts designed to limit both the combinatoric and some non-combinatoric backgrounds are unified to minimize the differences in selections between channels. However, some cuts, in which different optimal values are expected due to differences in the decay kinematics, are not forced to be similar. For example, the proper decay time of the meson and baryon differ by a factor of about five. The selection criteria applied to the lepton-charm decay signatures are listed in Table 1. Additional selection requirements to reduce non-combinatoric backgrounds are discussed next.
ii.3.5 Reflection Backgrounds
The selection criteria discussed above (see Sec. II.3.4) optimize the signal sensitivity with respect to the combinatoric background. However, there are other non-combinatoric backgrounds that must be considered. This is partially achieved with the and cuts discussed previously. Another significant background arises from reflections, which occur when the particle identifications in charm decay are mis-assigned. For example, if the from a decay is assigned the pion mass, the combination can contribute to the signal. Figure 4 shows the shapes determined from MC for reflections from (a) , (b) , (c) , (d) , and (e) decays when these decay channels are reconstructed as a different charm mode. The shapes are normalized to their expected contributions, e.g. assuming , where these numerical values are for illustrative purposes only. The decay is the most significant reflection background below the signal, shown in Fig. 4(c). This reflection is particularly problematic because the reflection begins just underneath the real signal. Potential - mis-identification is a significant consideration in the signal, shown in Fig. 4(e). The decay significantly contributes to the background beneath the signal, although its contribution is flat underneath the signal.
The shape of the reflection background beneath the signal is determined from a Monte Carlo simulation (see Section IV.1) study, in which semileptonic decays are generated. In these MC events candidates are then reconstructed. The resulting invariant mass distribution is shown in Fig. 5. The normalization of the reflection shape in the fit to the signal is determined by reconstructing a signal from the wide signal window, , shown in Fig. 6. A mass cut of , designed to reduce background to the signal, is applied to the decay. Monte Carlo simulation is then used to measure the efficiency of the decay relative to the inclusive set of decays that contribute to the reflection. The converse reflection in the signal is negligible due to the mass cut applied to the invariant mass.
In a manner completely analogous to the way the signal yield, , is determined in data, the candidates decaying to the and states, and , respectively, are determined from the Monte Carlo simulation. The number of mesons expected to contribute to the signal can then be calculated by evaluating
The numbers of candidates that contribute to the lepton-charm samples in the wide mass window around the signal are and . The normalization of the reflection in the signal is later constrained to the predicted number of reflection events in the fit to the signal (see Sec. II.4).
Since the and reflections in the signal are relatively flat under the signal region, sideband subtraction is expected to remove the effect of the and reflections on the signal distributions within statistical uncertainty. Correspondingly, the event count obtained by fitting the signal is not expected to be significantly influenced by the presence of these backgrounds. Additionally, the dd cut applied to the proton (discussed in the previous section) reduces contamination from pions, which contribute to the and reflections.
ii.4 Signal Yields
The , , , and mass spectra are fit to determine the number of lepton-charm events for the , , , , and samples. The invariant mass distributions of the charm signals are shown in Fig. 7 for the +SVT data and in Fig. 8 for the +SVT data with all lepton, charm, and lepton-charm selection criteria applied. The distributions are fit with a double Gaussian and linear background shape. The reflection of decays into the final state is included in the fit to the signal. The normalization of the reflection is constrained to the predicted number of reflection events as described above. In order to keep the broad Gaussian and reflection shapes reasonably independent, the double Gaussian means and widths for the are determined before the reflection shape is added to the fit. When the combined fit is performed, the parameters of the double Gaussian are constrained within their uncertainties. The fits to the , , , , and charm signals for right sign lepton-charm pairs are shown in Fig. 7 for the +SVT data and in Fig. 8 for the +SVT data. The invariant mass distributions for wrong sign combinations of lepton-charm pairs, e.g. , are also included in Figs. 7 and 8, indicating no significant contributions of possible backgrounds, such as false leptons, to be present in the right sign signals (see also Sec. VI.1). The fitted lepton-charm yields are listed in Table 2. The reflection is not included in the yield, since the fit shape to the includes a separate shape for the reflection, as discussed in Section II.3.5. The dd cut flattens the background and reduces its overall level by a factor of five, while it reduces the signal by 35% in the +SVT data and 28% in the +SVT data as can be seen in Fig. 7(e)-(f) and Fig. 8(e)-(f).
|Decay||Yield||FOM||Fit Prob. [%]||Yield||FOM||Fit Prob. [%]|
Iii Sample Composition Determination Procedure
This measurement uses flavor SU(3) symmetry to describe the branching fractions of semileptonic meson decays; therefore, the partial widths of the semileptonic decays of mesons are chosen to be equal, namely
This assumption is referred to as the spectator model, which also implies that the partial widths of the semileptonic bottom hadron decays into the pseudoscalar, vector, or higher excited states are expected to be equal,