weak arrow of time IFIC Universitat de València CSIC SLAC Seminar 23 rd October 2012

Transcription

1 Observing directly the weak arrow of time F. Martínez Vidal IFIC Universitat de València CSIC 23 rd October 2012

2 Introduction ti Outline Time reversal symmetries in the laws of Physics Scenarios for T violation o T violation in unstable systems T violation and entanglement: strategy at a B factory Data sample and fitting strategy The BaBar data set Signal and backgrounds Fitting strategy Results and interpretation Results Cross checks and systematic uncertainties Significance of T violation The raw T asymmetries Summary 2

3 Introduction 24

4 Time reversal symmetries in the laws of Physics The dynamical laws of Physics have an intrinsic t t symmetry Microscopic t symmetry, or T symmetry CP violation exists in the Standard Model or any extension of it All field theories with local Lorentz invariance have CPT symmetry y Straightforward connection between CP violation and T violation Observed weak CP violation in K and B mesons T should be violated as well in weak interactions Can T violation be directly observed, independently of CP violation? 4

5 Universe and Macroscopic t asymmetries Effects in Physics t t asymmetric are not necessarily T violating Universe t asymmetry Macroscopic t asymmetry, or arrow of time The Universe is expanding, even accelerating Time is asymmetric with respect to the Compatible with the t symmetry in the amount of order in an isolated system underlying laws of Physics (Lorentz (Nature of Thermodynamics, Eddigton) symmetry of general relativity) 3000 BC to 2000 BC Today Due to the initial conditions of our? Universe (Inflation?) Consistent with uniform average (same temperature) and its fluctuations in the cosmic background radiation map Probably connected with the Universe t asymmetry: the initial condition was improbable (more ordered) In particle physics, particle decays are an example of time asymmetric process: Mismatch between P 1+ +n and 1+ +n P 5

6 Scenarios for time reversal violation Non-zero expected value of a T-odd observable for stationary, non-degenerate states, like the permanent electric dipole moment (EDM) of a particle (with spin) Also violates parity, P EDM of the neutron or electron: PDGLive.org d n < e-cm; d e = (0.7±0.7) e-cm For a reaction a b, P(a b) P(b a), once the initial conditions, namely a in one case and b in the other, have been precisely realized! Detailed balance when there are no spins With stable particles: e vs. e but needs future facility with a long baseline With unstable particles: a decay products vs. decay products a, very difficult or impossible A A Time T Time B C B C 26

7 T violation in unstable systems Compare a b vs. b a in decay processes BaBar and Belle have observed large direct CP violation in B K PRL93, (2004) X Can we observe KB? CP CPT Preparation of the initial state difficult (unfeasible). The strong process will swamp the feeble weak process, (Khadrons)>>(KB) d B) Impossible rather than merely unfeasible. 27

8 T violation in unstable systems (cont d) Compare a b vs. b a in mixing processes Mixing has been observed in K, B, and more recently in D neutral systems CPT Kabir, PRD2, 540 (1970) CP T K 0 K 0 vs. K 0 K 0 asymmetry observed by CPLEAR But, T and CP transformations lead to the same observation CPLEAR, PLB444, 43 (1998) o Can not distinguish T and CP e.g. Wolfenstein, PRL83, 911 (1999); Int. Jour. Mod. Phys. E8, 501 (1999) o Not a direct observation of T violation [Wolfenstein, Quinn, Bernabeu] The flavor mixing asymmetry is independent of time and requires 0 o Various criticisms in the interpretation of this observable Gerber, and references therein, Eur. Phys. Jour. C 35, 195 (2004) 28

9 T violation picture (from PDG) 29

10 CP violation in mixing-decay interference Large CP violation observed in the interference between mixing and decay in B mesons, measured precisely with golden channels mixing decay decay Cannot be interpreted as T violation: Assume CPT invariance and = 0 No exchanges t t and in out states How could we directly observe T violation in this privileged system of Nature? 210

11 T violation i and entanglement: strategy at a B factory 24

12 T violation and quantum entanglement Quantum (EPR) entanglement at B factories (4S) decay yields an entangled state tt of fb mesons Bañuls & Bernabeu, PLB464, 117 (1999) Antisymmetric wave function (P-wave particle system) States 1 and 2 are defined by the time of their decay with t 1 < t 2 Can be expressed in terms of any linear combination of flavor eigenstates Time evolution (including mixing) preserves only B 0 B 0, or B + B terms Flavor tag: e.g. B semileptonic decay to l + X (l X) projects B 0 (B 0 ) B 0 (B 0 )tag CP tag: B decay to J/K L projects B 1/ 2 [B 0 + B 0 ] B tag g( ( CP-odd ) B decay to J/K S projects B 1/ 2 [B 0 B 0 ] B + tag ( CP-even ) Conclusion: ability to prepare a quantum state without destroying it ( tag ), and then study its time evolution 122

13 T violation: strategy at a B factory βγ ~ 0.56 Υ(4S) Entangled t1 t1 B Tag projects B l 0 J/ψ 0 t2 projects B Inclusive B meson flavor Identification K L T Υ(4S) Entangled t1 projects B J/ψ It is NOT the exchange t2 B t 1 t Tag 2 Exclusive B-meson reconstruction t1 Time reconstruction K S projects 0 B l

14 T violation analysis at a glance Completely reconstructed B + Inclusive reconstructed B: flavor identification (extract features to determine b or b quark content) etc. etc. 14 2

15 T violation analysis at a glance (cont d) Tag B flavor final state e- e+ Υ(4S) βγ ~ 0.56 (BABAR) B of opposite tag starts Opp B CP final state In B factory CP violation canonical analysis, we define t t t z/ c CP flav Signed decay time difference If t<0, we can exchange the roles of the two B s in above picture 15 2

16 T violation: strategy at a B factory βγ ~ 0.56 Υ(4S) Entangled t1 t1 B Tag projects B l 0 J/ψ 0 t2 projects B Inclusive B meson flavor Identification K L T Υ(4S) Entangled t1 projects B J/ψ It is NOT the exchange t2 B t 1 t Tag 2 Exclusive B-meson reconstruction t1 Time reconstruction K S projects 0 B l 0 t 0 0 t t

17 T-transformed processes Define processes of interest and their T-transformed counterparts JHEP08 (2012)

18 Signal parameters S ± and C ± 8 Signal PDFs: g, ( ) e {1 S, sin( m d ) C, cos( m d )} for "flavor tag" t tcp tflav for "CP tag" Assumes =0 For T violation In interference ΔS + T 0, ΔS - T 0 In decay ΔC + T 0, ΔC - T

19 Properties of the B + and B states Let s call the state B as the one defined by the B decay to J (JK S, K S ) [a pure CP-odd final state] 0 JHEP08 (2012) 064 B is the state orthogonal to B, B B, defined by entanglement, thus cannot decay to J, i.e., J / T B 0 Since and are linear combinations of flavor eigenstates, B B B N B B, B N B B 0 J / T B 0 J / T B * B B NN if 1 Analogously, the state B is defined by the B decay to JK L [a CPeven final state at O(10( -3 )], * B N B B, B N B B if 1 J / K T B L J / K T B / L

20 Properties of the B + and B states (cont d) B B and B, and B B and B have to be the same states in order to define * processes and their T-transformed counterparts, so It then follows that B and B are too orthogonal, B B NN * * 1 0 Property 1: B and B are orthogonal linear combinations of flavor eigenstates, not necessarily defined through CP final states Property 2: B and B states defined through the B decays to JK L and J final states are orthogonal iff We neglect the J component in JK L final states, i.e. neglect CPV in K 0 -K 0 mixing, O(10-3 ) = =1, i.e., there is no direct CPV in the B decay to JK 0 (one single weak decay amplitude) Next largest amplitude ( 2 ) has same weak phase Other CKM corrections are Cabibbo suppressed O( 4 ) 20 2

21 Data sample and fitting strategy 24

22 BaBar data set 530 fb -1 recorded in the 9 years of operation 14.5 fb fb fb -1 Reconstructed modes 54 fb -1 Off-(nS) 4 fb -1 above (4S) sign nal sampl e BB (0.5Belle) cc (3S) (7Belle+Cleo) (2S) (0.5Belle+Cleo) 222

23 Signal and backgrounds Select B candidates using Beam-energy substituted mass where and Energy difference * ~ MeV E E B Choose best B candidates based on masses of daughters Background rejection Depends on B decay channel Veto dangerous or significant backgrounds m ES ~ ~ 2.7 MeV Suppress continuum u, d, s backgrounds using angular distributions and event shape variables beam 23 2

24 m ES and E for the signal sample Identical sample to that used in our most recent (canonical) CP violation measurement with BccK (*)0 events, but excluding c K S and J/K *0 (K S 0 ) PRD 79, (2009) 7796 events, purity 87 96% 5813 events, purity 56% 24 2

25 Fitting strategy Overall procedure very similar il to that t followed in the most recent CP violation study with BccK (*)0 decays PRD 79, (2009) Use the B flav sample to determine Decay time difference resolution model and parameters CP flav Wrong-flavor ID fractions Perform simultaneous, unbinned ML fit to the 4 signal samples t t t Signed decay time difference Normalization is common for B 0, B 0, and t>0 and t<0 But independent for cck S and J/K L Signal and background probabilities biliti defined d as a function of m ES and E Sample composition and time-dependent background description identical to the CP violation analysis 11 parameters allow for possible T and CP violation in background But the signal model is quite different Time ordering is the key!

26 Signal PDF Fitting strategy: signal model Step function Resolution function H ( t) g ( t ) H( t ) ( t; ),, true true t t tt true Flavor tagged events () g, ( ttru e) H( t true ) ( t; t) CP tagged events () g e m d d, ( ) {1S, sin( ) C, cos( m )} Fit has to unfold t true >0 and t true <0 events (mixed due to limited time resolution), to obtain 8 sets of S, C parameters Flavor misid fractions w (not shown here) dilute the S,C parameters by a factor (1-2w) In practice, we directly fit to the T-, CP- and CPT-violating parameters S T ±, C T ± S CP ±, C CP ± S CPT ±, C CPT ± In canonical CP violation studies (assume CPT and =0), one single S, C set In SM, S~ and C~0 e.g. PRD 79, (2009)

27 Results and interpretation 24

28 Results T-violating parameters 95% 95% 68% 68% (S T,C T ) (S T,C T ) (0,0)=no violation Large significance for T violation

29 Results (cont d) CP-violating parameters (S CP,C CP ) (S CP,C CP ) CP violation significance largest than for T violation CPT-violating parameters No sign of CPT violation Observed T violation as due to compensate CP violation

30 Cross checks Study using simulation data shows asymmetry y parameters ΔS ± T, ΔC ± T are unbiased and have Gaussian errors Studies of data segmented by running period or flavor mode are consistent With appropriate constraints, obtain same S,C parameters as the latest BaBar CP violation study PRD 79, (2009) Fitting BccK ± and B J/ψK* ψ ± control samples yield asymmetry y parameters consistent with zero BccK ± used as J/ψK S B J/ψK* ± used as J/ψK L (S T,C T ) (S T,C T ) 68% 95%

31 Systematic uncertainties Systematic uncertainties are evaluated similarly as in our last CP analysis Effect of treating cck S and J/ψK L as orthogonal states negligible

32 Significance of T violation Repeat the standard fit, applying constraints to the parameters for T-conjugate processes Difference in likelihood lih with the standard d fit yields the significance of T violation CP and CPT significance can be estimated this way using appropriate constraints Include systematics variations in significance estimations Take max(m j2 ), scale significance by [1+max(m j2 )]=

33 Building raw T asymmetries Construct asymmetry for each of the four reference transitions For the 1 st reference (and similarly for the other three) where 22 Signal region: 5.27<m ES <5.29 GeV/c 2 E < GV GeV Projection of the fit without T violation For perfect reconstruction, is Projection of the fit with T violation Elapsed time (ps)

34 The four independent T asymmetries

35 The four independent CP asymmetries

36 The four independent CPT asymmetries

37 Summary 24

38 Summary has measured for the first time T-violating parameters in the time evolution of neutral B mesons, by comparing conjugate processes that can only be achieved by T reversal, not CP This novel approach does not need CPT invariance to link T and CP violation The significance of the effect exceeds 10 level Flip 6 often in one time direction than the other Elapsed time (ps) The result is consistent with CP-violating measurements assuming CPT invariance This is the first direct observation of Time Reversal Violation, in any system, through processes that can only be related by a T transformation This somehow closes the cycle of the CPT theorem

39 Summary Paper (arxiv: v3 [hep-ex]) ex]) is now in press

40 Summary Added bonus: article in The Economist (1 st September) A press release is now under review by SLAC and DOE,,plan to release once the paper will be published online Plan for an article in Physics Today

41 Thank you for your attention 24

42 The BaBar detector DIRC PID) 144 quartz bars PMs 15T 1.5T solenoid EMC 6580 CsI(Tl) crystals e + (3.1 GeV) Drift Chamber 40 stereo layers e - (8-9 GeV) Instrumented Flux Return iron / RPCs / LSTs (muon / neutral hadrons) Asymmetric B-factory: E cms = GeV Silicon Vertex Tracker 5 layers, double sided strips Performed a wide range of flavor physics results in B, Cham and sectors General purpose detector in e + e - environment: precision tracking, photon/electron detection, particle ID, muon/k L identification. Very stable over the 9 years of operation 25 3