Observation of Time Reversal Violation in the B^{0} Meson System

Observation of Time Reversal Violation in the Meson System

J. P. Lees    V. Poireau    V. Tisserand Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Université de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France    J. Garra Tico    E. Grauges Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain    A. Palano INFN Sezione di Bari; Dipartimento di Fisica, Università di Bari, I-70126 Bari, Italy    G. Eigen    B. Stugu University of Bergen, Institute of Physics, N-5007 Bergen, Norway    D. N. Brown    L. T. Kerth    Yu. G. Kolomensky    G. Lynch Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA    H. Koch    T. Schroeder Ruhr Universität Bochum, Institut für Experimentalphysik 1, D-44780 Bochum, Germany    D. J. Asgeirsson    C. Hearty    T. S. Mattison    J. A. McKenna    R. Y. So University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1    A. Khan Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom    V. E. Blinov    A. R. Buzykaev    V. P. Druzhinin    V. B. Golubev    E. A. Kravchenko    A. P. Onuchin    S. I. Serednyakov    Yu. I. Skovpen    E. P. Solodov    K. Yu. Todyshev    A. N. Yushkov Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia    M. Bondioli    D. Kirkby    A. J. Lankford    M. Mandelkern University of California at Irvine, Irvine, California 92697, USA    H. Atmacan    J. W. Gary    F. Liu    O. Long    G. M. Vitug University of California at Riverside, Riverside, California 92521, USA    C. Campagnari    T. M. Hong    D. Kovalskyi    J. D. Richman    C. A. West University of California at Santa Barbara, Santa Barbara, California 93106, USA    A. M. Eisner    J. Kroseberg    W. S. Lockman    A. J. Martinez    B. A. Schumm    A. Seiden University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA    D. S. Chao    C. H. Cheng    B. Echenard    K. T. Flood    D. G. Hitlin    P. Ongmongkolkul    F. C. Porter    A. Y. Rakitin California Institute of Technology, Pasadena, California 91125, USA    R. Andreassen    Z. Huard    B. T. Meadows    M. D. Sokoloff    L. Sun University of Cincinnati, Cincinnati, Ohio 45221, USA    P. C. Bloom    W. T. Ford    A. Gaz    U. Nauenberg    J. G. Smith    S. R. Wagner University of Colorado, Boulder, Colorado 80309, USA    R. Ayad Now at the University of Tabuk, Tabuk 71491, Saudi Arabia    W. H. Toki Colorado State University, Fort Collins, Colorado 80523, USA    B. Spaan Technische Universität Dortmund, Fakultät Physik, D-44221 Dortmund, Germany    K. R. Schubert    R. Schwierz Technische Universität Dresden, Institut für Kern- und Teilchenphysik, D-01062 Dresden, Germany    D. Bernard    M. Verderi Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France    P. J. Clark    S. Playfer University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom    D. Bettoni    C. Bozzi    R. Calabrese    G. Cibinetto    E. Fioravanti    I. Garzia    E. Luppi    M. Munerato    L. Piemontese    V. Santoro INFN Sezione di Ferrara; Dipartimento di Fisica, Università di Ferrara, I-44100 Ferrara, Italy    R. Baldini-Ferroli    A. Calcaterra    R. de Sangro    G. Finocchiaro    P. Patteri    I. M. Peruzzi Also with Università di Perugia, Dipartimento di Fisica, Perugia, Italy    M. Piccolo    M. Rama    A. Zallo INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy    R. Contri    E. Guido    M. Lo Vetere    M. R. Monge    S. Passaggio    C. Patrignani    E. Robutti INFN Sezione di Genova; Dipartimento di Fisica, Università di Genova, I-16146 Genova, Italy    B. Bhuyan    V. Prasad Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India    C. L. Lee    M. Morii Harvard University, Cambridge, Massachusetts 02138, USA    A. J. Edwards Harvey Mudd College, Claremont, California 91711, USA    A. Adametz    U. Uwer Universität Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany    H. M. Lacker    T. Lueck Humboldt-Universität zu Berlin, Institut für Physik, Newtonstr. 15, D-12489 Berlin, Germany    P. D. Dauncey Imperial College London, London, SW7 2AZ, United Kingdom    U. Mallik University of Iowa, Iowa City, Iowa 52242, USA    C. Chen    J. Cochran    W. T. Meyer    S. Prell    A. E. Rubin Iowa State University, Ames, Iowa 50011-3160, USA    A. V. Gritsan    Z. J. Guo Johns Hopkins University, Baltimore, Maryland 21218, USA    N. Arnaud    M. Davier    D. Derkach    G. Grosdidier    F. Le Diberder    A. M. Lutz    B. Malaescu    P. Roudeau    M. H. Schune    A. Stocchi    G. Wormser Laboratoire de l’Accélérateur Linéaire, IN2P3/CNRS et Université Paris-Sud 11, Centre Scientifique d’Orsay, B. P. 34, F-91898 Orsay Cedex, France    D. J. Lange    D. M. Wright Lawrence Livermore National Laboratory, Livermore, California 94550, USA    C. A. Chavez    J. P. Coleman    J. R. Fry    E. Gabathuler    D. E. Hutchcroft    D. J. Payne    C. Touramanis University of Liverpool, Liverpool L69 7ZE, United Kingdom    A. J. Bevan    F. Di Lodovico    R. Sacco    M. Sigamani Queen Mary, University of London, London, E1 4NS, United Kingdom    G. Cowan University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom    D. N. Brown    C. L. Davis University of Louisville, Louisville, Kentucky 40292, USA    A. G. Denig    M. Fritsch    W. Gradl    K. Griessinger    A. Hafner    E. Prencipe Johannes Gutenberg-Universität Mainz, Institut für Kernphysik, D-55099 Mainz, Germany    R. J. Barlow Now at the University of Huddersfield, Huddersfield HD1 3DH, UK    G. Jackson    G. D. Lafferty University of Manchester, Manchester M13 9PL, United Kingdom    E. Behn    R. Cenci    B. Hamilton    A. Jawahery    D. A. Roberts University of Maryland, College Park, Maryland 20742, USA    C. Dallapiccola University of Massachusetts, Amherst, Massachusetts 01003, USA    R. Cowan    D. Dujmic    G. Sciolla Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA    R. Cheaib    D. Lindemann    P. M. Patel    S. H. Robertson McGill University, Montréal, Québec, Canada H3A 2T8    P. Biassoni    N. Neri    F. Palombo    S. Stracka INFN Sezione di Milano; Dipartimento di Fisica, Università di Milano, I-20133 Milano, Italy    L. Cremaldi    R. Godang Now at University of South Alabama, Mobile, Alabama 36688, USA    R. Kroeger    P. Sonnek    D. J. Summers University of Mississippi, University, Mississippi 38677, USA    X. Nguyen    M. Simard    P. Taras Université de Montréal, Physique des Particules, Montréal, Québec, Canada H3C 3J7    G. De Nardo    D. Monorchio    G. Onorato    C. Sciacca INFN Sezione di Napoli; Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126 Napoli, Italy    M. Martinelli    G. Raven NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands    C. P. Jessop    J. M. LoSecco    W. F. Wang University of Notre Dame, Notre Dame, Indiana 46556, USA    K. Honscheid    R. Kass Ohio State University, Columbus, Ohio 43210, USA    J. Brau    R. Frey    N. B. Sinev    D. Strom    E. Torrence University of Oregon, Eugene, Oregon 97403, USA    E. Feltresi    N. Gagliardi    M. Margoni    M. Morandin    A. Pompili    M. Posocco    M. Rotondo    G. Simi    F. Simonetto    R. Stroili INFN Sezione di Padova; Dipartimento di Fisica, Università di Padova, I-35131 Padova, Italy    S. Akar    E. Ben-Haim    M. Bomben    G. R. Bonneaud    H. Briand    G. Calderini    J. Chauveau    O. Hamon    Ph. Leruste    G. Marchiori    J. Ocariz    S. Sitt Laboratoire de Physique Nucléaire et de Hautes Energies, IN2P3/CNRS, Université Pierre et Marie Curie-Paris6, Université Denis Diderot-Paris7, F-75252 Paris, France    M. Biasini    E. Manoni    S. Pacetti    A. Rossi INFN Sezione di Perugia; Dipartimento di Fisica, Università di Perugia, I-06100 Perugia, Italy    C. Angelini    G. Batignani    S. Bettarini    M. Carpinelli Also with Università di Sassari, Sassari, Italy    G. Casarosa    A. Cervelli    F. Forti    M. A. Giorgi    A. Lusiani    B. Oberhof    E. Paoloni    A. Perez    G. Rizzo    J. J. Walsh INFN Sezione di Pisa; Dipartimento di Fisica, Università di Pisa; Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy    D. Lopes Pegna    J. Olsen    A. J. S. Smith    A. V. Telnov Princeton University, Princeton, New Jersey 08544, USA    F. Anulli    R. Faccini    F. Ferrarotto    F. Ferroni    M. Gaspero    L. Li Gioi    M. A. Mazzoni    G. Piredda INFN Sezione di Roma; Dipartimento di Fisica, Università di Roma La Sapienza, I-00185 Roma, Italy    C. Bünger    O. Grünberg    T. Hartmann    T. Leddig    H. Schröder    C. Voss    R. Waldi Universität Rostock, D-18051 Rostock, Germany    T. Adye    E. O. Olaiya    F. F. Wilson Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom    S. Emery    G. Hamel de Monchenault    G. Vasseur    Ch. Yèche CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France    D. Aston    D. J. Bard    R. Bartoldus    J. F. Benitez    C. Cartaro    M. R. Convery    J. Dorfan    G. P. Dubois-Felsmann    W. Dunwoodie    M. Ebert    R. C. Field    M. Franco Sevilla    B. G. Fulsom    A. M. Gabareen    M. T. Graham    P. Grenier    C. Hast    W. R. Innes    M. H. Kelsey    P. Kim    M. L. Kocian    D. W. G. S. Leith    P. Lewis    B. Lindquist    S. Luitz    V. Luth    H. L. Lynch    D. B. MacFarlane    D. R. Muller    H. Neal    S. Nelson    M. Perl    T. Pulliam    B. N. Ratcliff    A. Roodman    A. A. Salnikov    R. H. Schindler    A. Snyder    D. Su    M. K. Sullivan    J. Va’vra    A. P. Wagner    W. J. Wisniewski    M. Wittgen    D. H. Wright    H. W. Wulsin    C. C. Young    V. Ziegler SLAC National Accelerator Laboratory, Stanford, California 94309 USA    W. Park    M. V. Purohit    R. M. White    J. R. Wilson University of South Carolina, Columbia, South Carolina 29208, USA    A. Randle-Conde    S. J. Sekula Southern Methodist University, Dallas, Texas 75275, USA    M. Bellis    P. R. Burchat    T. S. Miyashita    E. M. T. Puccio Stanford University, Stanford, California 94305-4060, USA    M. S. Alam    J. A. Ernst State University of New York, Albany, New York 12222, USA    R. Gorodeisky    N. Guttman    D. R. Peimer    A. Soffer Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel    P. Lund    S. M. Spanier University of Tennessee, Knoxville, Tennessee 37996, USA    J. L. Ritchie    A. M. Ruland    R. F. Schwitters    B. C. Wray University of Texas at Austin, Austin, Texas 78712, USA    J. M. Izen    X. C. Lou University of Texas at Dallas, Richardson, Texas 75083, USA    F. Bianchi    D. Gamba    S. Zambito INFN Sezione di Torino; Dipartimento di Fisica Sperimentale, Università di Torino, I-10125 Torino, Italy    L. Lanceri    L. Vitale INFN Sezione di Trieste; Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy    J. Bernabeu    F. Martinez-Vidal    A. Oyanguren    P. Villanueva-Perez IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain    H. Ahmed    J. Albert    Sw. Banerjee    F. U. Bernlochner    H. H. F. Choi    G. J. King    R. Kowalewski    M. J. Lewczuk    I. M. Nugent    J. M. Roney    R. J. Sobie    N. Tasneem University of Victoria, Victoria, British Columbia, Canada V8W 3P6    T. J. Gershon    P. F. Harrison    T. E. Latham Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom    H. R. Band    S. Dasu    Y. Pan    R. Prepost    S. L. Wu University of Wisconsin, Madison, Wisconsin 53706, USA
July 20, 2012
Abstract

Although violation in the meson system has been well established by the B factories, there has been no direct observation of time reversal violation. The decays of entangled neutral mesons into definite flavor states ( or ), and or final states (referred to as or ), allow comparisons between the probabilities of four pairs of -conjugated transitions, for example, and , as a function of the time difference between the two decays. Using 468 million  pairs produced in decays collected by the BABAR detector at SLAC, we measure -violating parameters in the time evolution of neutral mesons, yielding and . These nonzero results represent the first direct observation of violation through the exchange of initial and final states in transitions that can only be connected by a -symmetry transformation.

pacs:
13.25.Ft, 11.30.Er, 12.15.Ff, 14.40.Lb

BABAR-PUB-12/011        SLAC-PUB-15192

thanks: Deceasedthanks: Deceased

The BABAR Collaboration

The observations of -symmetry breaking, first in neutral decays ref:christenson:1964 () and more recently in mesons ref:mixingInducedCP-Bs (); ref:directCP-Bs (), are consistent with the standard model (SM) mechanism of the three-family Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix being the dominant source of violation ref:CKM:1963:1973 (). Local Lorentz invariant quantum field theories imply invariance ref:CPTtheorem (), in accordance with all experimental evidence ref:CPTtests (); ref:TestsConservationLaws (). Hence, it is expected that the -violating weak interaction also violates time reversal invariance.

To date, the only evidence related to violation has been found in the neutral system, where a difference between the probabilities of and transitions for a given elapsed time has been measured ref:Angelopoulos (). This flavor mixing asymmetry is both - and -violating (the two transformations lead to the same observation), independent of time, and requires a nonzero decay width difference between the neutral mass eigenstates to be observed ref:Kabir (); ref:Wolfenstein (); ref:Wolfenstein2 (). The dependence with has aroused controversy in the interpretation of this observable ref:Wolfenstein (); ref:Wolfenstein2 (); ref:Gerber (); ref:TestsConservationLaws (). In the neutral and systems, where and are negligible and significantly smaller, respectively, the flavor mixing asymmetry is much more difficult to detect ref:TviolationBs (). Experiments that could provide direct evidence supporting non-invariance, without using an observation which also violates , involve either nonvanishing expectation values of -odd observables, or the exchange of initial and final states, which are not conjugates to each other, in the time evolution for transition processes. Among the former, there exist upper limits for electric dipole moments of the neutron and the electron ref:edm (). The latter, requiring neutrinos or unstable particles, are particularly difficult to implement.

In this letter, we report the direct observation of violation in the meson system, through the exchange of initial and final states in transitions that can only be connected by a -symmetry transformation. The method is described in Ref. ref:method2012 (), based on the concepts proposed in Ref. ref:bernabeuPLB-NPB () and further discussed in Refs. ref:Wolfenstein2 (); ref:QuinnDiscrete (); ref:BernabeuDiscrete (). We use a data sample of 426  of integrated luminosity at the resonance, corresponding to   pairs, and 45  at a center-of-mass (c.m.) energy 40  below the , recorded by the BABAR detector ref:Aubert:2001tu () at the PEP-II asymmetric-energy collider at SLAC. The experimental analysis exploits identical reconstruction algorithms, selection criteria, calibration techniques, and meson samples to our most recent time-dependent asymmetry measurement in decays ref:Aubert:2009yr (), with the exception of and final states. The “flavor tagging” is combined here, for the first time, with the “ tagging” ref:bernabeuPLB-NPB (), as required for the construction of -transformed processes. Whereas the descriptions of the sample composition and time-dependent backgrounds are the same as described in Ref. ref:Aubert:2009yr (), the signal giving access to the -violating parameters needs a different data treatment. This echoes the fundamental differences between observables for and symmetry breaking. The procedure to determine the -violating parameters and their significance is thus novel ref:method2012 ().

In the decay of the , the two mesons are in an entangled, antisymmetric state, as required by angular momentum conservation for a P-wave particle system. This two-body state is usually written in terms of flavor eigenstates, such as and , but can be expressed in terms of any linear combinations of and , such as the and states introduced in Ref. ref:method2012 (). They are defined as the neutral states filtered by the decay to -eigenstates (-even) and , with (-odd), respectively. The and states are orthogonal to each other when there is only one weak phase involved in the decay amplitude, as it occurs in decays to final states ref:CPVreview (), and violation in neutral kaons is neglected.

We select events in which one candidate is reconstructed in a or state, and the flavor of the other is identified, referred to as flavor identification (ID). We generically denote reconstructed final states that identify the flavor of the as for and for . The notation is used to indicate the flavor or final states that are reconstructed at corresponding times and , where , i.e., is the first decay in the event and is the second decay. For later use in Eq. (1), we define . Once the state is filtered at time , the living partner is prepared (“tagged”) by entanglement as its orthogonal state. The notation describes the transition of the which decays at , having tagged its state at . For example, an event reconstructed in the time-ordered final states identifies the transition for the second to decay. We compare the rate for this transition to its -reversed (exchange of initial and final states) by reconstructing the final states . Any difference in these two rates is evidence for -symmetry violation. There are three other independent comparisons that can be made between , , and transitions and their -conjugates, , , and , respectively. Similarly, four different () comparisons can be made, e.g., between the transition and its ()-transformed (ref:method2012 ().

Assuming , each of the eight transitions has a general, time-dependent decay rate given by

(1)

where indices and stand for and final states, respectively, and the symbol or indicates whether the decay to the flavor final state occurs before or after the decay to the final state . Here, is the average decay width, is the mass difference between the neutral mass eigenstates, and and are model independent coefficients. The sine term, expected to be large in the SM, results from the interference between direct decay of the neutral to the final state and decay after - oscillation, while the cosine term arises from the interference between decay amplitudes with different weak and strong phases, and is expected to be negligible ref:CPVreview (). violation would manifest itself through differences between the or values for -conjugated processes, for example between and .

In addition to , states are reconstructed through the and final states (denoted generically as ), with , , , and (the latter only for ). states are identified through . The candidates are characterized by the difference between the reconstructed energy of the and the beam energy in the c.m. frame, , while for the modes we use the beam-energy substituted invariant mass , where is the momentum in the c.m. frame.

The flavor ID of the other neutral meson in the event, not associated with the reconstructed or , is made on the basis of the charges of prompt leptons, kaons, pions from mesons, and high-momentum charged particles. These flavor ID inputs are combined using a neural network (NN), trained with Monte Carlo (MC) simulated data. The output of the NN is then divided into six hierarchical, mutually exclusive flavor categories of increasing misidentification (misID) probability . Events for which the NN output indicates very low discriminating power are excluded from further analysis. We determine the signed difference of proper time between the two decays from the measured separation of the decay vertices along the collision axis. Events are accepted if the reconstructed and its estimated uncertainty, , are lower than   and  , respectively. The performances of the flavor ID and reconstruction algorithms are evaluated by using a large sample of flavor-specific neutral decays to and final states (referred to as sample). The resolution function is the same as in Ref. ref:Aubert:2009yr () except that all Gaussian offsets and widths are modeled to be proportional to .

The composition of the final sample is determined through fits to the and distributions, using parametric forms and distributions extracted from MC simulation and dilepton mass sidebands in data to describe the signal and background components. Figure 1 shows the and data distributions for events that satisfy the flavor ID and vertexing requirements, overlaid with the fit projections. The final sample contains 7796 events, with purities in the signal region ( ) ranging between 87% and 96%, and 5813 events, with a purity of 56% in the   region.

Figure 1: (color online). Distributions of (a) and (b) for the neutral decays reconstructed in the and final states, respectively, after flavor ID and vertexing requirements. In each plot, the shaded region is the estimated background contribution. The two samples of events are identical to those used in our most recent -violation study ref:Aubert:2009yr (), but excluding and final states.

We perform a simultaneous, unbinned maximum likelihood fit to the distributions for flavor identified and events, split by flavor category. The signal probability density function () is ref:method2012 ()

where is the signed difference of proper time between the two decays in the limit of perfect reconstruction, is the Heaviside step function, with is the resolution function, and are given by Eq. (1). Note that is equivalent to () when a true flavor () tag occurs. Because of the convolution with the resolution function, the distribution for contains predominantly true flavor-tagged events, with contribution from true -tagged events at low , and conversely for . Mistakes in the flavor ID algorithm mix correct and incorrect flavor assignments, and dilute the -violating asymmetries by a factor of approximately . Backgrounds are accounted for by adding terms to Eq. ( Observation of Time Reversal Violation in the Meson System ref:Aubert:2009yr (). Events are assigned signal and background probabilities based on the or distributions, for or events, respectively.

A total of 27 parameters are varied in the likelihood fit: eight pairs of coefficients for the signal, and 11 parameters describing possible and violation in the background. All remaining signal and background parameters are fixed to values taken from the sample, -candidate sidebands in , world averages for and  ref:pdg2010 (), or MC simulation ref:Aubert:2009yr (). From the 16 signal coefficients ref:epaps (), we construct six pairs of independent asymmetry parameters , , and , as shown in Table 1. The -asymmetry parameters have the advantage that -symmetry breaking would directly manifest itself through any nonzero value of or , or any difference between and , or between and (analogously for - or -symmetry breaking). The measured values for the asymmetry parameters are reported in Table 1. There is another two times three pairs of -, -, and -asymmetry parameters, but they are not independent and can be derived from Table 1 or Ref. ref:epaps ().

Parameter Result
=
=
=
=
=
=
=
=
=
=
=
=
Table 1: Measured values of the -, -, and -asymmetry parameters, defined as the differences in and between symmetry-transformed transitions. The values of reference coefficients are also given at the bottom. The first uncertainty is statistical and the second systematic. The indices , , , and stand for reconstructed final states that identify the meson as , , , and , respectively.

We build time-dependent asymmetries to visually demonstrate the -violating effect. For transition ,

(3)

where . With this construction, is defined only for positive values. Neglecting reconstruction effects, . We introduce the other three -violating asymmetries similarly. Figure 2 shows the four observed asymmetries, overlaid with the projection of the best fit results to the distributions with and without the eight -invariance restrictions: , , and  ref:epaps ().

Figure 2: (color online). The four independent -violating asymmetries for transition a) , b) , c) , d) , for combined flavor categories with low misID (leptons and kaons), in the signal region (  for modes and   for ). The points with error bars represent the data, the red solid and dashed blue curves represent the projections of the best fit results with and without violation, respectively.

Using large samples of MC simulated data, we determine that the asymmetry parameters are unbiased and have Gaussian errors. Splitting the data by flavor category or data-taking period give consistent results. Fitting a single pair of coefficients, reversing the sign of under , or or exchanges, and the sign of under exchange, we obtain identical results to those obtained in Ref. ref:Aubert:2009yr (). Performing the analysis with decays to and final states instead of the signal and , respectively, we find that all the asymmetry parameters are consistent with zero.

In evaluating systematic uncertainties in the asymmetry parameters, we follow the same procedure as in Ref. ref:Aubert:2009yr (), with small changes ref:epaps (). We considered the statistical uncertainties on the flavor misID probabilities, resolution function, and parameters. Differences in the misID probabilities and resolution function between and final states, uncertainties due to assumptions in the resolution for signal and background components, compositions of the signal and backgrounds, the and , and the branching fractions for the backgrounds and their properties, have also been accounted for. We also assign a systematic uncertainty corresponding to any deviation of the fit for MC simulated asymmetry parameters from their generated MC values, taking the largest between the deviation and its statistical uncertainty. Other sources of uncertainty such as our limited knowledge of , , and other fixed parameters, the interaction region, the detector alignment, and effects due to a nonzero value in the time dependence and the normalization of the , are also considered. Treating and as orthogonal states and neglecting violation for flavor categories without leptons, has an impact well below the statistical uncertainty. The total systematic uncertainties are shown in Table 1 ref:epaps ().

The significance of the -violation signal is evaluated based on the change in log-likelihood with respect to the maximum (). We reduce by a factor to account for systematic errors in the evaluation of the significance. Here, , where is the maximum log-likelihood, is the log-likelihood with asymmetry parameter fixed to its total systematic variation and maximized over all other parameters, and is the change in at confidence level () for one degree of freedom (d.o.f). Figure 3 shows contours calculated from the change in two dimensions for the -asymmetry parameters and . The difference in the value of at the best fit solution with and without violation is with eight d.o.f., including systematic uncertainties. Assuming Gaussian errors, this corresponds to a significance equivalent to standard deviations (), and thus constitutes direct observation of violation. The significance of and violation is determined analogously, obtaining and , respectively, equivalent to and , consistent with violation and invariance.

Figure 3: (color online). The central values (blue point and red square) and two-dimensional contours for , , , , , and , calculated from the change in the value of compared with its value at maximum (), for the pairs of -asymmetry parameters (blue dashed curves) and (red solid curves). Systematic uncertainties are included. The -invariance point is shown as a sign.

In summary, we have measured -violating parameters in the time evolution of neutral mesons, by comparing the probabilities of , , , and transitions, to their conjugate. We determine for the main -violating parameters and , and observe directly for the first time a departure from invariance in the meson system, with a significance equivalent to . Our results are consistent with current -violating measurements obtained invoking invariance. They constitute the first observation of violation in any system through the exchange of initial and final states in transitions that can only be connected by a -symmetry transformation.

We are grateful for the excellent luminosity and machine conditions provided by our PEP-II colleagues, and for the substantial dedicated effort from the computing organizations that support BABAR. The collaborating institutions wish to thank SLAC for its support and kind hospitality. This work is supported by DOE and NSF (USA), NSERC (Canada), CEA and CNRS-IN2P3 (France), BMBF and DFG (Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MES (Russia), MINECO (Spain), STFC (United Kingdom). Individuals have received support from the Marie Curie EIF (European Union), the A. P. Sloan Foundation (USA) and the Binational Science Foundation (USA-Israel).

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Observation of Time Reversal Violation in the Meson System

The BABAR Collaboration

The following includes supplementary material for the Electronic Physics Auxiliary Publication Service.

Systematic source
Interaction region 0.011 0.035 0.02 0.029 0.012 0.024 0.015 0.026
Flavor misID probabilities 0.022 0.042 0.022 0.022 0.016 0.040 0.020 0.020
resolution 0.030 0.050 0.048 0.062 0.057 0.033 0.012 0.011
background 0.033 0.038 0.052 0.010 0.002 0.001 0.001 0.002
Background fractions and content 0.029 0.021 0.020 0.026 0.013 0.012 0.008 0.009
parameterization 0.011 0.002 0.005 0.002 0.016 0.008 0.005 0.004
and 0.001 0.005 0.011 0.008 0.003 0.007 0.011 0.012
violation for flavor ID categories 0.018 0.019 0.001 0.001 0.009 0.008 0.006 0.006
Fit bias 0.010 0.072 0.013 0.010 0.010 0.007 0.007 0.014
0.004 0.003 0.002 0.002 0.004 0.003 0.001 0.001
normalization 0.013 0.019 0.005 0.004 0.017 0.012 0.006 0.007
Total 0.064 0.112 0.08 0.077 0.068 0.061 0.033 0.041
Systematic source
Interaction region 0.015 0.024 0.023 0.026 0.014 0.009 0.015 0.008
Flavor misID probabilities 0.018 0.008 0.009 0.009 0.013 0.020 0.012 0.010
resolution 0.062 0.033 0.051 0.072 0.051 0.030 0.045 0.012
background 0.046 0.021 0.029 0.015 0.002 0.001 0.001 0.001
Background fractions and content 0.024 0.020 0.024 0.016 0.012 0.004 0.007 0.007
parameterization 0.011 0.002 0.005 0.002 0.011 0.002 0.005 0.002
and 0.004 0.001 0.002 0.003 0.003 0.003 0.009 0.008
violation for flavor ID categories 0.026 0.010 0.007 0.005 0.014 0.005 0.003 0.002
Fit bias 0.018 0.026 0.007 0.021 0.005 0.017 0.006 0.015
0.003 0.002 0.002 0.001 0.002 0.001 0.001 0.001
normalization 0.019 0.015 0.007 0.004 0.008 0.002 0.003 0.003
Total 0.092 0.058 0.067 0.083 0.059 0.041 0.051 0.026
Table 1: Breakdown of main systematic uncertainties on the -, -, and -asymmetry parameters and the coefficients for and transitions. The indices and stand for reconstructed final states that identify the meson as and , respectively. The first nine rows in each panel are evaluated using similar procedures as in Ref. ref:Aubert:2009yr (). The tenth and eleventh rows ( and normalization) are estimated by varying by , while the and coefficients of the most general time-dependent decay rate  ref:method2012 () are changed around their reference model values, 0 and 1, respectively. The normalization also accounts for systematic effects related to the range used to normalize the . The total systematic uncertainty (last row in each panel) is calculated adding the individual systematic uncertainties in quadrature.
Figure 1: (color online). The four independent -violating asymmetries for transition a) , b) , c) , d) , for combined flavor categories with low misID (leptons and kaons), in the signal region (  for modes and   for ). The points with error bars represent the data, the red solid and dashed blue curves represent the projections of the best fit results with and without violation, respectively.
Figure 2: (color online). The four independent -violating asymmetries for transition a) , b) , c) , d) , for combined flavor categories with low misID (leptons and kaons), in the signal region (  for modes and   for ). The points with error bars represent the data, the red solid and dashed blue curves represent the projections of the best fit results with and without violation, respectively.
Figure 3: (color online). The central values (blue point and red square) and two-dimensional contours for , , , , , and , calculated from the change in the value of