Study of the decay and its intermediate states
We study the decay , reconstructing the baryon in the mode, using a data sample of pairs collected with the BABAR detector at the PEP-II storage rings at SLAC. We measure branching fractions for decays with intermediate baryons to be , , , and , where the uncertainties are statistical, systematic, and due to the uncertainty on the branching fraction, respectively. For decays without or resonances, we measure . The total branching fraction is determined to be . We examine multibody mass combinations in the resonant three-particle final states and in the four-particle final state, and observe different characteristics for the combination in neutral versus doubly-charged decays.
pacs:13.25.Hw, 13.60.Rj, 14.20.Lq
The BABAR Collaboration
Decays of mesons into final states with baryons account for (1) of all meson decays. Notwithstanding their significant production rate, the baryon production mechanism in meson decays is poorly understood.
Theoretical models of meson baryonic decays are currently limited to rough estimates of the branching fractions and basic interpretations of the decay mechanisms (2); (3); (4); (5); (6). Additional experimental information may help to clarify the underlying dynamics.
In this paper, we present a measurement of the -meson baryonic decay
Section II provides a brief description of the BABAR detector and data sample. The basic event selection procedure is described in Sec. III. Section IV presents the method used to extract results for channels that proceed via intermediate baryons. The corresponding results for channels that do not proceed via baryons are presented in Sec. V. Section VI presents the method used to determine signal reconstruction efficiencies, Sec. VII the branching fraction results, Sec. VIII the evaluation of systematic uncertainties, and Sec. IX the final results. A summary is given in Sec. X.
Ii BABAr Detector and Data Sample
The data sample used in this analysis was collected with the BABAR detector at the PEP-II asymmetric-energy storage ring at SLAC. PEP-II operates with a 9 and a 3.1 beam resulting in a center-of-mass energy equal to the mass of 10.58. The collected data sample contains pairs, which corresponds to an integrated luminosity of .
The BABAR detector (10) measures charged-particle tracks with a five-layer double-sided silicon vertex tracker (SVT) surrounded by a 40-layer drift chamber (DCH). Charged particles are identified using specific ionization energy measurements in the SVT and DCH, as well as Cherenkov radiation measurements in an internally reflecting ring imaging Cherenkov detector (DIRC). These detectors are located within the magnetic field of a superconducting solenoid.
Using information from the SVT, the DCH, and the DIRC for a particular track, the probability for a given particle hypothesis is calculated from likelihood ratios. The identification efficiency for a proton is larger than 90% with the probability of misidentifying a kaon or pion as a proton between 3% and 15% depending on the momentum. For a kaon, the identification efficiency is 90% with the probability of misidentifying a pion or proton as a kaon between 5% and 10%. The identification efficiency for a pion is larger than 95% with the probability of misidentifying a kaon or proton as a pion between 5% and 30%.
Monte Carlo (MC) simulated events are produced with an event simulation based on the EvtGen program (11) and an event simulation based on the JETSET program (12). Generated events are processed in a GEANT4 (13) simulation of the BABAR detector. MC-generated events are studied for generic background contributions as well as for specific signal and background modes. Baryonic meson decays are generated assuming that their daughters are distributed uniformly in phase space.
Iii Event Selection
The signal mode is reconstructed in the decay chain with . All final state particles are required to have well defined tracks in the SVT and DCH. Kaons and protons, as well as pions from the decay, are required to pass likelihood selectors based on information from the SVT, DCH, and DIRC. For pion candidates from the decay, a well reconstructed track is required.
To form a candidate, the , , and candidates are fitted to a common vertex and a probability greater than is required for the vertex fit. To form a candidate, the candidate is constrained to its nominal mass value and combined with an antiproton and two pions with opposite charge. The mass constraint value differs between events from data and MC. For the MC events a nominal mass of is chosen; this corresponds to the mass value used in the MC generation and to the value from fits to reconstructed MC events. For data, fits are performed on the invariant mass distribution to find the nominal mass. The fits are performed for each of the six distinct BABAR run periods. The results are found to vary between and , where the uncertainties are statistical. All invariant mass values are found to be consistent. The average result is used as the nominal value for the mass constraint in data.
Only candidates within a 25 mass window centered on the nominal mass (or for simulated events) are retained. The entire decay chain is refitted requiring that the direct daughters originate from a common vertex and that the probability for the vertex fit exceeds .
The decays with , which are described in more detail in section IV.1, can contribute a signal-like background through rearrangement of the final-state particles and are denoted “peaking background” in the following. To suppress these events, symmetric vetoes of around the nominal and mass values (1) are applied in the distributions of the invariant masses , , and , where subscripts denote the mother candidate of the particles.
To separate signal events from combinatorial background, two variables are used. The invariant mass is defined as with the four-momentum vector of the candidate measured in the laboratory frame. The energy-substituted mass is defined in the laboratory frame as with the center-of-mass energy and the four-momentum vector of the initial system measured in the laboratory frame. For both variables, genuine decays are centered at the meson mass. In MC, these variables exhibit a negligible correlation for genuine mesons.
To suppress combinatorial background, candidates are required to satisfy . Figure 1 shows the distribution after applying all of the above selection criteria. The dashed lines show sideband regions and , used to study background characteristics; both sideband regions are combined into a single sideband region.
The analysis is separated into two parts: I) the measurement of the four signal decays via intermediate resonances, i.e., , , , and , and II) the measurement of all other decays into the four-body final state , which are denoted as non- signal events in the following.
Decays via resonant intermediate states with resonances are studied in the two-dimensional planes spanned by and the invariant candidate invariant mass for decays with and for decays with . In the following the like-sign invariant mass is denoted as and the opposite-sign invariant mass as . If both invariant masses are referred to, we use the notation . For intermediate states, is assumed (1).
We perform fits in both planes and to extract the signal yields for the decays via the resonances. Background contributions are vetoed when feasible. We distinguish between different signal and remaining background contributions by using separate probability density functions (PDF) for each signal and background component. We use analytical PDFs as well as discrete histogram PDFs. The PDFs are validated using data from the sideband regions and from MC samples. The different, combined PDFs are fitted to the and planes and the resulting covariance matrices of the fits are used to calculate (7) distributions of signal events.
Figures 2(a) and 2(b) show the and distributions, respectively, after applying the selection criteria as described in Sec. III. Signal contributions from the , , and resonances are observed and a contribution from events with a resonance is visible. The doubly-charged resonances are seen to contribute larger numbers of events than the neutral resonances. The resonant structures sit on top of combinatorial background and peaking background events as well as non- signal events. The latter are distributed in like combinatorial background events.
iv.1 Background sources
The main source for combinatorial background events is other decays, while originate from events. Combinatorial events do not exhibit peaking structures in the distributions of the signal variables under study. In contrast, other sources of background do exhibit peaking structures, and are treated separately.
Decays of the type with , where , can have the same final state particles as signal decays. Rearrangement of the final state particles can yield a fake candidate, while the candidate is essentially a genuine suppressed only by the selection. Because these events represent fully reconstructed genuine -meson decays, they are distributed like signal events in the and variables. Table 1 shows the relevant decay modes and their misreconstruction rate as signal. Furthermore, these events can also be misreconstructed as higher resonances in the invariant masses. Figure 3 shows the
distributions of the MC-simulated background modes in the and planes. Additionally, events with have a minimum invariant mass in of and can introduce background in the study of events with intermediate resonances.
From the misreconstruction efficiency determined from signal MC events and scaled with the measured branching fractions (14), background events are expected to contribute as signal. To suppress these events, veto regions are set to 20 around the nominal and masses (1) in , , and , with the resulting suppression rates given in table 1. A systematic uncertainty is assigned to account for the remaining background events. No distortions are found in other variables due to the vetoes. Note that events with rearranged to do not contribute peaking background because the selection requirement on effectively vetoes these events.
Decays via charmonia, such as with and , or with , can also produce the same final state particles as signal events. We observe no indication of such contributions in data in the relevant combinations of daughters or in signal MC events when scaling the misreconstruction efficiencies with the measured branching fractions (1). We neglect these events, but assign a corresponding systematic uncertainty (see Sec. VIII).
|Decay mode||Fake signal|
Events from decays with or are found to have a signal-like shape in and . Because of the low-momentum daughters in the center-of-mass systems, fake can be generated by replacing the with a from the . Figure 4 shows the distributions of MC-generated events. These events cluster in the signal region as well as in in the and signal regions. A correlation between and is apparent. No significant structures are found in MC-generated events with nonresonant or with events due to the softer momentum constraints on the .
Combinatorial background with genuine events
In both MC and data-sideband events, combinatorial background events with genuine resonances are found to be distributed differently than purely combinatorial background events without resonances. These events produce a signal-like structure in or , but are distributed in similarly to purely combinatorial background. However, since combinatorial background events with genuine resonances scale differently in than purely combinatorial background events, no simple combined PDF can be constructed. Thus, both combinatorial background sources are treated as separate background classes.
events without a signal
Events also appear as background in the distribution when they contain decays into the four-body final state , not via the signal resonance. For example, decays such as are distributed as background to events in but as signal in . Therefore, decays to not cascading via the signal resonance are included as a background class.
iv.2 Fit Strategy
The signal yields of resonant decays are determined in binned maximum-likelihood fits to the two-dimensional distributions and . Since background events from decays are distributed similarly to signal events in all examined variables, one-dimensional measurements of the signal yield will not suffice. By extracting the signal yield in the plane, we exploit the fact that the distributions of events are more correlated in these variables than signal events.
Type of PDFs
Signal and background sources are divided into two classes of probability density functions. Background sources without significant correlations between and are described with analytical PDFs; independent analytical PDFs are used for each of the two variables and a combined two-dimensional PDF is formed by multiplication of the one-dimensional functions. Signal and background sources with correlations between and are described with binned histogram PDFs . For each source, a histogram is generated from MC events, which takes correlations into account by design. Each histogram is scaled with a parameter , which is allowed to float in the fit. Histogram PDFs are used for all resonant signal decays and peaking background decays .
In the fits to the two-dimensional distributions, the integrals of the analytical PDFs for each bin are calculated. Table 2 lists the PDFs and indicates whether they are included in the fit to for events or in the fit to for events.
Histogram PDF verification
When using a histogram PDF in fits, results prove to be sensitive to differences between data events and MC-generated events. As a cross-check, the projections onto are compared between data and MC simulation. The distributions are fitted using a Gaussian function to describe signal events. The means differ between data and MC by . The mass shift does not depend on the candidate selection or on . The most probable explanation for the difference is an underestimation of the SVT material in the simulation, as studied in detail in Ref. (15). Baryonic decays are especially affected by this issue, since heavier particles such as protons suffer more from such an underestimation compared to lighter particles. In each MC event, the baryon momenta and are therefore increased by and the particle energy is adjusted accordingly.
In the distributions, the means of the masses of the baryons differ between data and MC by . This effect originates from outdated mass inputs in the MC generation, and so this shift is not covered by the correction for detector density. events are especially sensitive to such mass differences due to their narrow width. The effect is taken into account by shifting each MC event in by . The fully corrected data sets are used to generate the histogram PDFs employed in the fits to data.
Combinatorial background PDF
The combinatorial background is described by the PDF term given in Table 2. It consists of two separable functions: for we use a first-order Chebyshev polynomial with a slope parameter and for a phenomenological function,
The upper and lower phase-space boundaries in are constants and . The phenomenological constant is obtained from MC and, for estimating an systematic uncertainty, varied within the values found in MC. The exponent terms and are allowed to float in the fits to MC and data. In Table 2, is the overall scaling parameter of the combinatorial background PDF.
Combinatorial background with genuine Pdf
Combinatorial background events with genuine resonances are described by uncorrelated functions in and . A first-order Chebyshev polynomial in is multiplied by a nonrelativistic Breit-Wigner function in ,
with mean , width , and an overall scaling factor , to form a two-dimensional PDF ( in Table 2) in .
The PDFs for combinatorial background with and without genuine resonances are validated using studies with MC events and from fits to data within the sidebands of the