Search for T, CP, and CPT violation in B0-B0 mixing with inclusive dilepton events.

We report the results of a search for T , CP , and CPT violation in B 0 - (cid:1) B 0 mixing using an inclusive dilepton sample collected by the BABAR experiment at the PEP-II B factory. Using a sample of 232 (cid:1) 10 6

Since the first observation of CP violation in 1964 [1], the neutral kaon system has provided many results probing the discrete symmetries CPT and T in K 0 -K 0 mixing [2].Similarly, the BABAR experiment can investigate T, CP, and CPT violation in B 0 -B 0 mixing.The physical states (solutions of the complex effective Hamiltonian for the B 0 -B 0 system) [3] can be written as where H and L stand for heavy and light.Under CPT symmetry, the complex parameter z vanishes.Similarly, T invariance implies jq=pj 1.Finally, CP invariance requires both jq=pj 1 and z 0.
Inclusive dilepton events, where both B mesons decay semileptonically (b !Xl, with l e or ), represent 4% of all 4S !B B decays and provide a very large sample with which to study T, CPT, and CP violation in mixing.In the direct semileptonic neutral B decay, the flavor B 0 B 0 is tagged by the charge of the lepton l l ÿ .At the 4S resonance, neutral B mesons are produced in a coherent P-wave state.The B mesons remain in orthogonal flavor states until one decays, after which the flavor of the other B meson evolves with time.Neglecting second order terms in z, the decay rates for the three configurations (l l , l ÿ l ÿ , and l l ÿ ) are given by where t is the difference between the neutral B decay times, m is the B 0 -B 0 oscillation frequency, ÿ is the average neutral B decay rate and ÿ is the decay rate difference between the two physical states.The sign of t has a physical meaning only for opposite-sign dileptons and is given by t t ÿ t ÿ where t t ÿ corresponds to l l ÿ , respectively.
The same-sign dilepton asymmetry A T=CP , between the two oscillation probabilities P B 0 !B 0 and PB 0 !B 0 probes both T and CP symmetries and can be expressed in terms of jq=pj: ( Standard model calculations [4] predict the magnitude of this asymmetry to be at or below 10 ÿ3 .A large measured value would be an indication of new physics.
Similarly, the opposite-sign dilepton asymmetry, A CPT=CP , between events with t > 0 and t < 0 compares the B 0 !B 0 and B 0 !B 0 probabilities and is sensitive to CPT and CP violation.This asymmetry is given by As jÿj=ÿ 1 [3], we have Rez sinhÿt=2 ' ÿ Rez t=2 and this asymmetry is not sensitive to the CPT-violating term Rez alone, but to the product ÿ Rez.
In this Letter, we present measurements of jq=pj, Imz and ÿ Rez with a simultaneous likelihood fit to the observed t distributions of same-sign and opposite-sign dilepton events.In the coshÿt=2 term, we use jÿj 5 3 10 ÿ3 ps ÿ1 , the value reported in Ref. [3].
This study is performed with data collected by the BABAR detector [5] at the PEP-II asymmetric-energy B factory between October 1999 and July 2004.The integrated luminosity of this sample is 211 fb ÿ1 recorded at the 4S resonance (''on resonance'') (232 10 6 B B pairs) and about 16 fb ÿ1 recorded 40 MeV below the 4S resonance (''off resonance'').
The event selection is similar to that described in Ref. [6].Non-B B events, mainly e e ÿ !q qq udsc continuum events, are suppressed by applying requirements on the shape and the topology of the event.
Lepton candidate tracks must have at least 12 hits in the drift chamber, at least one z-coordinate hit in the silicon vertex tracker (SVT), and a momentum in the 4S center-of-mass system between 0.8 and 2:3 GeV=c.Electrons are selected by requirements on the ratio of the energy deposited in the electromagnetic calorimeter to the momentum measured in the drift chamber.Muons are identified through the energy released in the calorimeter, as well as the strip multiplicity, track continuity, and penetration depth in the instrumented flux return.Lepton candidates are rejected if their signal in the Cherenkov detector is consistent with that of a kaon or a proton.The electron and muon selection efficiencies are about 85% and 55%, with pion misidentification probabilities around 0.2% and 3%, respectively.Electrons from photon conversions are identified and rejected with a negligible loss of efficiency for signal events.Leptons from J= and 2S decays are identified by pairing them with other oppositely charged candidates of the same lepton species, selected with looser criteria.Events with at least two leptons are retained and the two highest momentum leptons in the 4S rest frame are used in the following.
The separation between direct leptons b !l and background from the b !c ! l decay chain (cascade leptons) is achieved with a neural network that combines five discriminating variables: the momenta and opening angle of the two lepton candidates, and the total visible energy and missing momentum of the event, all computed in the 4S rest frame.Of the original sample of 232 10 6 B B pairs, 1:4 10 6 pass this dilepton selection.
Since the asymmetry A T=CP is expected to be small, we have determined the possible charge asymmetries induced by charge-dependent differences in the reconstruction and identification of electrons and muons.The charge asymmetries are defined by a " ÿ " ÿ =" " ÿ where " " ÿ is the efficiency for positive and negative particles.As the lepton efficiencies and purities depend mainly on their momenta, we consider separately the asymmetry for the higher and lower momentum lepton, respectively, a l 1 and a l 2 .
The charge asymmetry of track reconstruction is measured in the data by comparing tracks reconstructed using only the SVT with those passing the dilepton track selection, obtaining a trk 0:8 0:2 10 ÿ3 .
The lepton identification efficiencies are measured as a function of total momentum and polar and azimuthal angles, with a control sample of radiative Bhabha events for electrons, and with a ee !control sample for muons.The misidentification probabilities are determined with control samples of kaons produced in D !D 0 !K ÿ (and charge conjugate) decays, pions produced in K S !ÿ decays, three-prong decays, and protons produced in decays.
The control samples show that the muon track reconstruction efficiency has a charge asymmetry reaching 5 10 ÿ3 and that positive kaons are 20%-30% more likely than negative kaons to be misidentified as muons.As a consequence, in the likelihood fit (described below), we float the charge asymmetries a dir and a casc for direct and cascade muons.
For electrons, the charge asymmetry averaged over the signal phase space is a e 0:4 0:2 10 ÿ3 and we find that antiprotons with momentum 1 GeV=c are significantly more likely than protons to be misidentified, due to annihilation with nucleons in the calorimeter material.Based on the charge asymmetry in tracking and in identification, we fix the charge asymmetry for the direct electrons with the higher momentum to a dir e 1 1:2 10 ÿ3 .For the lower momentum direct electrons and the cascade electrons, for which antiproton contamination is more important, we correct the initial charge asymmetry by the fraction of antiprotons estimated with B B Monte Carlo samples and the proton control sample.This gives the following charge asymmetries: a dir e 2 0:8 10 ÿ3 , a casc e 1 0:5 10 ÿ3 , and a casc e 2 0:2 10 ÿ3 .In the inclusive approach used here, the z coordinate of the B decay point is approximated by the z position of the point of closest approach between the lepton candidate and an estimate of the 4S decay point in the transverse plane.The 4S decay point is obtained by fitting the two lepton tracks to a common vertex, constrained to be consistent with the beam-spot position in the transverse plane.The proper time difference t between the two B meson decays is taken as t z=hic, where z is the difference between the z coordinates of the leptons, with the same-sign convention as for t, and hi 0:55 is the nominal Lorentz boost.For same-sign dileptons, the sign of t is chosen randomly.
We model the contributions to our sample from B B decays using five categories of events, i, each represented by a probability density function (PDF) in t, P n;c i .Their shapes are determined using the B 0 B 0 (n) and B B ÿ (c) Monte Carlo simulation separately, with the approach described in Ref. [7].
The five categories are the following.First, the pure signal events with two direct leptons (sig), which are 81% of the B B events, give information on the T, CPT, and CP parameters.Then, we consider two categories of cascade decays: those in which the direct lepton and the cascade lepton come from different B decays (obc), and those in which the direct lepton and the cascade lepton stem from the same B decay (sbc).According to B B Monte Carlo simulation, their contributions are around 9% and 4%, respectively.In addition, 3% of the dilepton events originate from the decay chain b !ÿ !l ÿ (1d1), which tags the B flavor correctly.Finally, the remaining events (other) consist mainly of one direct lepton and one lepton from the decay of a charmonium resonance from the other B decay.
The sig event PDF, P n;c sig , are obtained by the convolution of an oscillatory term containing the T, CPT, and CP parameters [Eq.( 1)] for neutral B decays (or an exponential function for charged B decays) with a resolution function which is the sum of three Gaussians.The widths of the core and tail Gaussians and the fractions of the core and outlier Gaussians are free parameters in the fit.The width of the outlier Gaussian is fixed to 8 ps.The means of the Gaussians are fixed to zero [8].
PRL 96, 251802 (2006)P H Y S I C A L R E V I E W L E T T E R

PRL 96 ,
251802 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending

TABLE I .
Summary of systematic uncertainties for jq=pj, Imz, and ÿ Rez measurements.