Measurement of branching ratio and lifetime in the decay at CDF
We present a study of decays to the CP-odd final state with and . Using collision data with an integrated luminosity of collected by the CDF II detector at the Tevatron we measure a lifetime of . This is the first measurement of the lifetime in a decay to a CP eigenstate and corresponds in the standard model to the lifetime of the heavy eigenstate. We also measure the product of branching fractions of and relative to the product of branching fractions of and to be , which is the most precise determination of this quantity to date.
pacs:13.25.Hw, 14.40.Nd, 12.15.Nf
CDF Collaboration222With visitors from University of MA Amherst, Amherst, MA 01003, USA, Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari, 09042 Monserrato (Cagliari), Italy, University of CA Irvine, Irvine, CA 92697, USA, University of CA Santa Barbara, Santa Barbara, CA 93106, USA, University of CA Santa Cruz, Santa Cruz, CA 95064, USA, CERN,CH-1211 Geneva, Switzerland, Cornell University, Ithaca, NY 14853, USA, University of Cyprus, Nicosia CY-1678, Cyprus, University College Dublin, Dublin 4, Ireland, University of Fukui, Fukui City, Fukui Prefecture, Japan 910-0017, Universidad Iberoamericana, Mexico D.F., Mexico, Iowa State University, Ames, IA 50011, USA, University of Iowa, Iowa City, IA 52242, USA, Kinki University, Higashi-Osaka City, Japan 577-8502, Kansas State University, Manhattan, KS 66506, USA, University of Manchester, Manchester M13 9PL, United Kingdom, Queen Mary, University of London, London, E1 4NS, United Kingdom, University of Melbourne, Victoria 3010, Australia, Muons, Inc., Batavia, IL 60510, USA, Nagasaki Institute of Applied Science, Nagasaki, Japan, National Research Nuclear University, Moscow, Russia, University of Notre Dame, Notre Dame, IN 46556, USA, Universidad de Oviedo, E-33007 Oviedo, Spain, Texas Tech University, Lubbock, TX 79609, USA, Universidad Tecnica Federico Santa Maria, 110v Valparaiso, Chile, Yarmouk University, Irbid 211-63, Jordan, On leave from J. Stefan Institute, Ljubljana, Slovenia, University of Warwick, Coventry CV4 7AL, United Kingdom,
In the standard model, the mass and flavor eigenstates of the meson are not identical. This gives rise to particle – anti-particle oscillations Gay:2001ra (), which proceed in the standard model through second order weak interaction processes, and whose phenomenology depends on the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix. The time evolution of mesons is approximately governed by the Schrödinger equation
where and are mass and decay rate symmetric matrices. Diagonalization of leads to mass eigenstates
with distinct masses () and distinct decay rates (), where and are complex numbers satisfying . An important feature of the system is the non-zero matrix element representing the partial width of and decays to common final states which translates into a non-zero decay width difference of the two mass eigenstates through the relation
where . The phase describes CP violation in mixing. In the standard model is predicted to be Lenz:2006hd (); Nierste:2011ti (). The small value of the phase causes the mass and CP eigenstates to coincide to a good approximation. Thus the measurement of the lifetime in a CP eigenstate provides directly the lifetime of the corresponding mass eigenstate. If new physics is present, it could enhance to large values, a scenario which is not excluded by current experimental constraints. In such a case the correspondence between mass and CP eigenstates does not hold anymore and the measured lifetime will correspond to the weighted average of the lifetimes of the two mass eigenstates with weights dependent on the size of the CP violating phase Dunietz:2000cr (). Thus a measurement of the lifetime in a final state which is a CP eigenstate provides, in combination with other measurements, valuable information on the decay width difference and the CP violation in mixing.
One of the most powerful measurements to constrain a new physics contribution to the phase is the measurement of CP violation in the decay with . The decay has a mixture of the CP-even and -odd components in the final state and an angular analysis is needed to separate them Dighe:1995pd (). In the standard model, CP violation in the decay is given by . New physics effects in mixing would shift and from the standard model value by the same amount. A sufficiently copious signal with , where stands for , and flavor identified at production can be used to measure without the need of an angular analysis Stone:2009hd () as is a pure CP-odd final state. Since the is a spin 0 particle and the decay products and have quantum numbers and , respectively, the final state has an orbital angular momentum of leading to a CP eigenvalue of . Further interest in the decay arises from its possible contribution to an -wave component in the decay if the decays to . This contribution could help to resolve an ambiguity in the and values determined in the analyses. Because it was neglected in the first tagged results Aaltonen:2007he (); Abazov:2008fj (), each of which showed an approximately 1.5 deviation from the standard model, it was argued that the omission may significantly bias the results Stone:2008ak (); Stone:2010dp (). However, using the formalism in Ref. Azfar:2010nz (), the latest preliminary CDF measurement beta_s () has shown that the -wave interference effect is negligible at the current level of precision.
In Refs. Lenz:2006hd (); Nierste:2011ti () the decay width difference in the standard model is predicted to be ps and the ratio of the average lifetime, , to the lifetime, , to be . Using these predictions in the relations
where , together with the world average lifetime, ps Nakamura:2010zzi (), we find the theoretically-derived values ps and ps.
While no direct measurements of lifetimes in decays to pure CP eigenstates are available, various experimental results allow for the determination of the lifetimes of the two mass eigenstates. Measurements sensitive to these lifetimes are the angular analysis of decays and the branching fraction of , which can be complemented by measurements of the lifetime in flavor specific final states. The combination of available measurements yields ps and ps Asner:2010qj (). From CDF measurements we can infer the two lifetimes from the result of the angular analysis of decays. The latest preliminary result beta_s (), that is not yet included in the above average, yields ps and ps assuming standard model CP violation.
Compared to measurements using decays, lifetime and future CP violation measurements in the decay suffer from a lower branching fraction. Based on a comparison to meson decays Ref. Stone:2008ak () makes a prediction for the branching fraction of decay relative to the decay,
to be approximately 0.2. The CLEO experiment estimates from a measurement of semileptonic decays Ecklund:2009fia (). A theoretical prediction based on QCD factorization yields a range of between and Leitner:2010fq (). With the world average branching fraction for the decay of and the branching fraction of in the region between 0.5–0.8, predictions of Colangelo:2010bg (); Colangelo:2010wg () translate into a wide range of values of approximately 0.1–0.5.
The first experimental search was performed by the Belle experiment Louvot:2010es (). Their preliminary result did not yield a signal and they extract an upper limit on the branching fraction of . Recently the LHCb experiment reported the first observation of the decay Aaij:2011fx () with a relative branching fraction of . Shortly after the LHCb result was presented, the Belle collaboration announced their result of an updated analysis using 121.4 of data Li:2011pg (). They observe a significant signal and measure , where the first uncertainty is statistical, the second systematic, and the third one is an uncertainty on the number of produced pairs. Using their preliminary measurement of the branching fraction Louvot:2009xg (), and assuming that the uncertainty on the number of produced pairs is fully correlated for the two measurements, this translates into . A preliminary measurement of the D0 experiment yields D0:6152 ().
In this paper we present a measurement of the ratio of the branching fraction of the decay relative to the decay and the first measurement of the lifetime in a decay to a pure CP eigenstate. We use data collected by the CDF II detector from February 2002 until October 2008. The data correspond to an integrated luminosity of .
This paper is organized as follows: In Sec. II we describe the CDF II detector together with the online data selection, followed by the candidate selection in Sec. III. Section IV describes details of the measurement of the ratio of branching fractions of the decay relative to the decay while Sec. V discusses the lifetime measurement. We finish with a short discussion of the results and conclusions in Sec. VI.
Ii CDF II detector and trigger
Among the components of the CDF II detector Acosta:2004yw () the tracking and muon detection systems are most relevant for this analysis. The tracking system lies within a uniform, axial magnetic field of T strength. The inner tracking volume hosts 7 layers of double-sided silicon micro-strip detectors up to a radius of cm Hill:2004qb (). An additional layer of single-sided silicon is mounted directly on the beam-pipe at a radius of cm, providing an excellent resolution of the impact parameter , defined as the distance of closest approach of the track to the interaction point in the transverse plane. The silicon tracker provides a pseudorapidity coverage up to . The remainder of the tracking volume up to a radius of cm is occupied by an open-cell drift chamber Affolder:2003ep (). The drift chamber provides up to 96 measurements along the track with half of them being axial and other half stereo. Tracks with pass the full radial extent of the drift chamber. The integrated tracking system achieves a transverse momentum resolution of (GeV) and an impact parameter resolution of for tracks with a transverse momentum greater than 2 . The tracking system is surrounded by electromagnetic and hadronic calorimeters, which cover the full pseudorapidity range of the tracking system Balka:1987ty (); Bertolucci:1987zn (); Albrow:2001jw (); Apollinari:1998bg (). We detect muons in three sets of multi-wire drift chambers. The central muon detector has a pseudorapidity coverage of Ascoli:1987av () and the calorimeters in front of it provide about 5.5 interaction lengths of material. The minimum transverse momentum to reach this set of muon chambers is about 1.4 . The second set of chambers covers the same range in , but is located behind an additional 60 cm of steel absorber, which corresponds to about 3 interaction lengths. It has a higher transverse momentum threshold of 2 , but provides a cleaner muon identification. The third set of muon detectors extends the coverage to a region of and is shielded by about 6 interaction lengths of material.
A three-level trigger system is used for the online event selection. The trigger component most important for this analysis is the extremely fast tracker (XFT) Thomson:2002xp (), which at the first level groups hits from the drift chamber into tracks in the plane transverse to the beamline. Candidate events containing decays are selected by a dimuon trigger Acosta:2004yw () which requires two tracks of opposite charge found by the XFT that match to track segments in the muon chambers and have a dimuon invariant mass in the range 2.7 to 4.0 GeV/.
Iii Reconstruction and candidate selection
In the offline reconstruction we first combine two muon candidates of opposite charge to form a candidate. We consider all tracks that can be matched to a track segment in the muon detectors as muon candidates. The candidate is subject to a kinematic fit with a vertex constraint. We then combine the candidate with two other oppositely charged tracks that are assumed to be pions and have an invariant mass between 0.85 and 1.2 to form a candidate. In the final step a kinematic fit of the candidate is performed. In this fit we constrain all four tracks to originate from a common vertex, and the two muons forming the are constrained to have an invariant mass equal to the world average mass Nakamura:2010zzi (). In a similar way we also reconstruct candidates using pairs of tracks of opposite charge assumed to be kaons and having an invariant mass between 1.009 and 1.029 . During the reconstruction we place minimal requirements on the track quality, the quality of the kinematic fit, and the transverse momentum of the candidate to ensure high quality measurements of properties for each candidate. For the branching fraction measurement we add a requirement which aims at removing a large fraction of short-lived background. We require the decay time of the candidate in its own rest frame, the proper decay time, to be larger than three times its uncertainty. This criterion is not imposed in the lifetime analysis since it would bias the lifetime distribution. The proper decay time is determined by the expression
where is the flight distance projected onto the momentum in the plane transverse to the beamline, is the transverse momentum of the given candidate, and is the reconstructed mass of the candidate. The uncertainty on the proper decay time is estimated for each candidate by propagating track parameter and primary vertex uncertainties into an uncertainty on . The proper decay time resolution is typically of the order of 0.1 ps.
The selection is performed using a neural network based on the neurobayes package Feindt:2006pm (); Feindt:2004aa (). The neural network combines several input variables to form a single output variable on which the selection is performed. The transformation from the multidimensional space of input variables to the single output variable is chosen during a training phase such that it maximizes the separation between signal and background distributions. For each of the two measurements presented in this paper we use a specialized neural network. For the training we need two sets of events with a known classification of signal or background. For the signal sample we use simulated events. We generate the kinematic distributions of mesons according to the measured -hadron momentum distribution. The decay of the generated particles into the final state is simulated using the evtgen package Lange:2001uf (). Each event is passed through the standard CDF II detector simulation, based on the geant3 package Brun:1978fy (); Gerchtein:2003ba (). The simulated events are reconstructed with the same reconstruction software as real data events. The background sample is taken from data using candidates with the invariant mass above the signal peak, where only combinatorial background events contribute. Because the requirement on the proper decay time significance efficiently suppresses background events in the branching ratio measurement, we use an enlarged sideband region of 5.45 to 5.55 in this analysis, compared to an invariant mass range from 5.45 to 5.475 for the lifetime measurement.
For the branching fraction measurement, the inputs to the neural network, ordered by the importance of their contribution to the discrimination power, are the transverse momentum of the , the of the kinematic fit of the candidate using information in the plane transverse to the beamline, the proper decay time of the candidate, the quality of the kinematic fit of the candidate, the helicity angle of the positive pion, the transverse momentum of the candidate, the quality of the kinematic fit of the two pions with a common vertex constraint, the helicity angle of the positive muon, and the quality of the kinematic fit of the two muons with common vertex constraint. The helicity angle of the muon (pion) is defined as the angle between the three momenta of the muon (pion) and candidate measured in the rest frame of the (). For the selection of decays we use the same neural network without retraining and simply replace variables by variables and pions by kaons.
For the lifetime measurement we modify the list of inputs by removing the proper decay time. We also do not use the helicity angles as they provide almost no additional separation power on the selected sample. Since we are not concerned about a precise efficiency determination for the lifetime measurement, we add the following inputs: the invariant mass of the two pions, the likelihood based identification information for muons Thesis:Giurgiu (), and the invariant mass of the muon pair. The muon identification is based on the matching of tracks from the tracking system to track segments in the muon system, energy deposition in the electromagnetic and hadronic calorimeters, and isolation of the track. The isolation is defined as the transverse momentum carried by the muon candidate over the scalar sum of transverse momenta of all tracks in a cone of , where () is the difference in azimuthal angle (pseudorapidity) of the muon candidate and the track. There is no significant change in the importance ordering of the inputs. The invariant mass of the pion pair becomes the second most important input, the likelihood based identification of the two muon candidates is ranked fourth and sixth in the importance list, and the muon pair invariant mass is the least important input.
For the branching fraction measurement we select the threshold on the neural network output by maximizing Punzi:2003bu (), where is the reconstruction efficiency for decays and is the number of background events estimated from the mass sideband. The invariant mass distributions of selected and candidates are shown in Figs. 1 and 2. A clear signal at around 5.36 is visible in both mass distributions.
For the lifetime measurement we use simulated experiments to determine the optimal neural network output requirement. We select a value that minimizes the statistical uncertainty of the measured lifetime. We scan a wide range of neural network output values and for each requirement we simulate an ensemble of experiments with a lifetime of 1.63 ps, where the number of signal and background events as well as the background distributions are simulated according to data. For a broad range of selection requirements we observe the same uncertainty within a few percent. Our final requirement on the network output is chosen from the central region of this broad range of equivalent options.
iii.3 Physics backgrounds
We study possible physics backgrounds using simulated events with all -hadrons produced and decayed inclusively to final states containing a . For this study we use the selection from the branching fraction measurement. While several physics backgrounds appear in the mass spectrum, none contributes significantly under the peak. The most prominent physics backgrounds are with , where stands for , and . In the first case the kaon is mis-reconstructed as a pion and gives rise to a large fraction of the structure seen below 5.22 , while the second one is correctly reconstructed and produces the narrow peak at approximately 5.28 . Another possible physics type of background would consist of properly reconstructed combined with a random track. This type of background would contribute only to higher masses with a threshold above the signal. As we do not find evidence of such background in Ref. Aaltonen:2011sy () which is more sensitive we conclude that this kind of background is also negligible here. The stacked histogram of physics backgrounds derived from simulation is shown in Fig. 3. From this study we conclude that the main physics background that has to be included as a separate component in a fit to the mass spectrum above 5.26 stems from decays of . It is properly reconstructed and therefore simple to parametrize. All other physics backgrounds are negligible.
Iv Branching fraction measurement
In this Section we describe details of the branching fraction measurement. These involve the maximum likelihood fit to extract the number of signal events, the efficiency estimation, and the systematic uncertainties. We conclude this Section with the result for the ratio of branching fractions between and decays.
iv.1 Fit description
We use an unbinned extended maximum likelihood fit of the invariant mass to extract the number of decays in our samples. In order to avoid the need for modeling most of the physics background, we restrict the fit to the mass range from 5.26 to 5.5 . The likelihood is
where is the invariant mass of the -th candidate and is the total number of candidates in the sample. The fit components are denoted by the subscripts for signal, for combinatorial background, for physics background, and for background. The yields of the components are given by , , , and , and their probability density functions (PDFs) by , respectively. The physics background yield is parametrized relative to the signal yield via the ratio to allow constraining it by other measurements in the fit.
The signal PDF is parametrized by a sum of two Gaussian functions with a common mean. The relative size of the two Gaussians and their widths are determined from simulated events. Approximately 82% of the decays are contained in a narrower Gaussian with width of 9.4 . The broader Gaussian has width of 18.4 . In the case of , the narrow Gaussian with a width of 7.2 accounts for 79% of the signal, with the rest of the events having a width of 13.3 . To take into account possible differences between simulation and data, we multiply all widths by a scaling parameter . Because of kinematic differences between and we use independent scale factors for both modes. In the fits all parameters of the PDF are fixed except for the scaling parameter . In addition the mean of the Gaussians is allowed to float in the fit. Doing so we obtain a value that is consistent with the world average mass Nakamura:2010zzi (). For the fit we fix the position of the signal to the value determined in the fit to the candidates.
The combinatorial background PDF is parametrized using a linear function. In both fits we leave its slope floating. In each of the two fits there is one physics background. In the case of the spectrum, the physics background describes properly reconstructed decays using a shape identical to the signal and position fixed to the world average mass Nakamura:2010zzi (). The number of events is left free in the fit. For the fit, we have a contribution from decays where the pion from the decay is mis-reconstructed as a kaon. This contribution peaks at a mass of approximately 5.36 with an asymmetric tail towards larger masses. The shape itself is parametrized by a sum of a Gaussian function and an exponential function convolved with a Gaussian. The parameters are derived from simulated events. The normalization of this component relative to the signal is fixed to , which is derived from the CDF Run I measurement of the ratio of cross section times branching fraction for and decays Abe:1996kc (), the world average branching fractions for and Nakamura:2010zzi (), and the ratio of reconstruction efficiencies obtained from simulation.
The fit determines a yield of events and events, where the uncertainties are statistical only. The number of background events in the fit is .
To extract the ratio of branching fractions we need to estimate the relative efficiency for reconstruction of with and with decays, . We estimate the efficiency using simulated events in which we generate a single meson per event. The meson then decays with equal probabilities to or final states with exclusive , , and . Generated events are then processed through a detailed detector simulation and the offline reconstruction software used to reconstruct data. In both cases angular and decay time distributions are generated assuming no CP violation and parameters taken from the preliminary result of the angular distributions analysis beta_s (): , , , and As a strong phase between and is not measured we use the world average value from decays of Nakamura:2010zzi () as a reasonable approximation Gronau:2008hb (). An additional peculiarity of the decay is the unusual mass shape of the meson. It is modeled using a Flatté distribution Flatte:1976xu () with input parameters measured by the BES experiment Ablikim:2004wn () to be , , and , where the errors are statistical and systematic, respectively. The meson mass distribution is modeled using a relativistic Breit-Wigner distribution with world average values for its parameters Nakamura:2010zzi (). With these inputs to the simulation we find , which accounts for the and mass window selection requirements.
iv.3 Systematic uncertainties
We investigate several sources of systematic uncertainties. They can be broadly separated into two classes: one dealing with assumptions made in the fits that may affect yields, and the other related to assumptions in the efficiency estimation. In the first class we estimate uncertainties by refitting data with a modified assumption and taking the difference with respect to the original value as an uncertainty. For the second class we recalculate the efficiency with a modified assumption and take the difference with respect to the default efficiency as an uncertainty unless specified otherwise. The summary of assigned uncertainties is given in Table 1.
For the yield of we investigate the effect of the assumption on the combinatorial background shape, the limited knowledge of mis-reconstructed decays and the shape of the signal PDF. The uncertainty due to the shape of combinatorial background is estimated by changing from the first order polynomial to a constant or a second order polynomial. For the physics background we vary the normalization of the component in the fit and use an alternative shape determined by varying the momentum distribution and the decay amplitudes of in simulation. Finally, to estimate the effect of the signal PDF parametrization we use an alternative model with a single Gaussian rather than two Gaussian functions and an alternative shape from simulation, where we vary the momentum distribution of the produced mesons and the decay amplitudes of the decay.
To estimate the uncertainty on the yield we follow a procedure similar to that for and conservatively treat the systematic effects as independent between the two modes in the calculation of . For the sensitivity to the parametrization of the combinatorial background we switch to a second order polynomial or a constant as alternative parametrization. For the shape of the signal PDF we use two alternatives, one with a single Gaussian function instead of two and another one with two Gaussians, but varying the momentum distribution in simulation. We also vary the position of the signal within the uncertainty determined in the fit.
The systematic uncertainty on the relative efficiency stems from the statistics of simulation, an imperfect knowledge of the momentum distribution, physics parameters of decays like lifetimes or decay amplitudes, and differences in the efficiencies of the online selection of events. To estimate the effect of the imperfect knowledge of the momentum distribution we vary the momentum distribution of mesons in the simulation. The physics parameters entering the simulation are grouped into three categories, those defining the mass shape, the ones determining decay amplitudes in decays, and those affecting the lifetimes of the two mass eigenstates. In the first two cases we vary each parameter independently and add all changes in the efficiency in quadrature. For the last case we vary the mean lifetime and the decay width difference simultaneously and take the largest variation as the uncertainty. We add the uncertainty from the third class in quadrature with all others to obtain the uncertainty due to the parameters describing the particle decays. The last effect deals with how events are selected during data taking. The CDF trigger has several different sets of requirements for the selection of events. The ones used in this analysis can be broadly sorted into three classes depending on momentum thresholds and which subdetectors detected muons. The fraction of events for each different class varies depending on the instantaneous luminosity, which is not simulated. To estimate the size of a possible effect we calculate the efficiency for each class separately and take half of the largest difference as the uncertainty.
To obtain the total uncertainty we add all partial uncertainties in quadrature. In total we assigned events (2.1%) as the systematic uncertainty on the yield, events (3.6%) on the yield, and 0.040 (3.4%) on the relative efficiency . A summary of the systematic uncertainties in the branching ratio is provided in Table 1.