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Test della simmetria CPT e della meccanica quantistica nel sistema dei mesoni K neutri a KLOE

Test della simmetria CPT e della meccanica quantistica nel sistema dei mesoni K neutri a KLOE. Antonio Di Domenico. Roma, 23 maggio 2008. CPT: introduction. The three discrete symmetries of QM, C (charge conjugation), P (parity),

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Test della simmetria CPT e della meccanica quantistica nel sistema dei mesoni K neutri a KLOE

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  1. Test della simmetria CPT e della meccanica quantistica nel sistema dei mesoni K neutri a KLOE Antonio Di Domenico Roma, 23 maggio 2008

  2. CPT: introduction The three discrete symmetries of QM, C (charge conjugation), P (parity), and T (time reversal) are known to be violated in nature both singly and in pairs. Only CPT appears to be an exact symmetry of nature. • CPT theorem (Luders, Jost, Pauli, Bell 1955 -1957): • Exact CPT invariance holds for any quantum field theory which assumes: • Lorentz invariance (2) Locality (3) Unitarity (i.e. conservation of probability). Testing the validity of the CPT symmetry probes the most fundamental assumptions of our present understanding of particles and their interactions. Extension of CPT theorem to a theory of quantum gravity far from obvious (e.g. CPT violation appears in some models with space-time foam backgrounds). No predictive theory incorporating CPT violation => only phenomenological models to be constrained by experiments.

  3. CPT: introduction Consequences of CPT symmetry: equality of masses, lifetimes, |q| and |m| of a particle and its anti-particle. The neutral kaon system is one of the most intriguing systems in nature; it offers unique possibilities to test CPT invariance; e.g. taking as figure of merit the fractional difference between the masses of a particle and its anti-particle: neutral K system neutral B system proton- anti-proton

  4. “Standard” tests of CPT symmetry in the neutral kaon system

  5. The neutral kaon system The time evolution of a two-component state vector Y in the space is given by (Wigner-Weisskopf approximation): H is the effective hamiltonian (non-hermitian), decomposed into a Hermitian Part (mass matrix M) and an anti-Hermitian part (i/2 decay matrix G) : Diagonalizing the effective Hamiltonian: eigenvalues eigenstates |K1,2> are CP=±1 states tS~ 90 ps tL~ 51 ns mL-mS= 3.5 x 10-15 GeV ~ GS / 2 small CP impurity ~2 x 10-3

  6. CPT violation in the neutral kaon system: “standard” picture CPT violation in the mixing: • d ≠ 0 implies CPT violation • e ≠ 0 implies T violation • e ≠ 0 or d ≠ 0 implies CP violation (with a phase convention )

  7. CPT violation in the neutral kaon system: “standard” picture CPT violation in semileptonic decays DS=DQ rule Standard Model prediction of DS=DQ rule violation is x=c/a ~ O(10-7) Semileptonic charge asymmetry:

  8. Im (not to scale) e -2e -D h+- h00 e fSW f+- f00 Re CPT violation in the neutral kaon system: “standard” picture CPT violation in pp decays AI(BI) CPT conserving (violating) Kpp amplitudes for I=0,2 (dI strong phase shift for I=0,2)

  9. Some results of CPT tests e+ K0 t=0 t p- n CPLEAR Study of the time evolution of neutral kaons in semileptonic decays d= (0.30  0.33  0.06) 10-3 PLB444 (1998) 52 KTeV f+- - fSW = 0.61º ±0.62º ± 1.01 º f00-f+- = 0.39º ± 0.22 º ±0.45 º PRL88, 181601(2002) Study of regenerator beam two pion decay distribution AL=( 3322  58  47 ) 10-6 KL semileptonic charge asymmetry: Constraints on CPT violation in pp and semileptonic decays obtained combining KTeV and PDG results: KTeV PRD67,012005 (2003)

  10. Neutral kaons at a f-factory KS,L e+ e- f KL,S Production of the vector meson f in e+e annihilations: • e+e f sf~3 mb • W = mf = 1019.4 MeV • BR(f  K0K0) ~ 34% • ~106 neutral kaonpairs per pb-1 produced in an antisymmetric quantum state with JPC = 1 : pK = 110 MeV/c lS = 6 mm lL = 3.5 m • The detection of a kaon at large (small) times tags a KS (KL) • possibility to select a pure KS beam (unique at a f-factory, not possible at fixed target experiments)

  11. DANE: the Frascati f-factory Integrated luminosity (KLOE) Day performance: 7-8 pb-1 Bestmonth L dt ~ 200 pb1 Total KLOE L dt ~ 2.5 fb1 (2001 - 05)  ~2.5109 KSKL pairs

  12. The KLOE detector at DAFNE Superconducting coil B = 0.52 T Drift chamber Calorimeter 4 m diameter × 3.3 m length 90% helium, 10% isobutane 12582/52140 sense/total wires All-stereo geometry Lead/scintillating fiber 4880 PMTs 98% coverage of solid angle sE/E  5.7% /E(GeV) st 54 ps /E(GeV)  50 ps (relative time between clusters) sgg ~ 2 cm(p0from KLp+p-p0) sp/p  0.4 % (tracks with q > 45°) sxhit 150 mm (xy), 2 mm (z) sxvertex ~ 1 mm

  13. KS and KL Tagging at KLOE KL“crash” b= 0.22 (TOF) KS p+p- KS p-e+n KL 2p0 KS tagged by KL interaction in EmC Efficiency ~ 30% (largely geometrical) KS angular resolution: ~ 1° (0.3 in f) KS momentum resolution: ~ 2 MeV KL tagged by KS  p+p- vertex at IP Efficiency ~ 70% (mainly geometrical) KL angular resolution: ~ 1° KL momentum resolution: ~ 2 MeV

  14. KSpen: KLOE results PLB 636(2006) 173 BR(KSp-e+n) = (3.528  0.057  0.027)  10-4 BR(KSp+e-n) = (3.517  0.051  0.029)  10-4 BR(KSpen) = (7.046  0.076  0.050)  10-4 AS = (1.5  9.6  2.9 )  10-3 with 2.5 fb-1: dAS  3 10-3  2 Re e BR(pen) [KLOE ’02, 17 pb-1]: (6.91  0.34  0.15)  10-4 If CPT holds, AS=AL =2ReeASAL signals CPT violation in mixing and/or decay with DSDQ x- = ( -0.8  2.4  0.7) 10-3 CPT & DS=DQ viol. y = ( 0.4 2.4  0.7) 10-3 CPT viol. PLB 636(2006) 173 input from other experiments Data sample: 410 pb-1 Emiss-Pmiss

  15. CPT test: the Bell-Steinberger relation a+-= h+- BR(KSp+p-) a+-0= tS/tL h+- 0* BR(KLp+p-p0) a000= tS/tL h 000* BR(KLp0p0p0) a00= h00 BR(KSp0p0) akl3 = 2tS/tL BR(KLl3) [(AS+AL)/4i Im x+] Unitarity constraint: KS KL observables

  16. Experimental inputs to the Bell-Steinberger relation Main improvements done with KLOE measurements on KS semileptonic and 3p0 decays

  17. CPT test: the Bell-Steinberger relation KLOE result: JHEP12(2006) 011 Re  = (159.6  1.3) 10-5 Im  =(0.4  2.1)  10-5 Combining Red and Imd results: Imd Assuming , i.e. no CPT viol. in decay: Red at 95% c.l.

  18. 2) Tests of QM and CPT symmetry in the neutral kaon system

  19. Neutral kaon interferometry f1 t1 t2 KS,L f KL,S Dt=t1- t2 f2 Double differential time distribution: where t1(t2) is the proper time of one (the other) kaon decay into f1 (f2) final state and: characteristic interference term at a f-factory => interferometry fi = p+p-, p0p0, pln, p+p-p0, 3p0, p+p-g ..etc

  20. Neutral kaon interferometry Integrating in (t1+t2) we get the time difference (Dt=t1-t2) distribution (1-dim plot simpler to manipulate than 2-dim plot): From these distributions for various final states fi one can measure the following quantities: Phases (difference of) from the interference term => interferometry

  21. Neutral kaon interferometry: main observables I(Dt) (a.u) I(Dt) (a.u) I(Dt) (a.u) Dt/tS Dt/tS Dt/tS

  22. Neutral kaon interferometry: main observables parameters mode measured quantity

  23. p p f p t1 t2 p EPR correlation: no simultaneous decays (Dt=0) in the same final state due to the destructive quantum interference p p f p t1 t2=t1 p Same final state for both kaons: f1 = f2 = p+p- Dt=|t1-t2| I(Dt) (a.u) Dt/tS

  24. fKSKLp+p- p+p-: test of quantum coherence Decoherence parameter: (also known as Furry's hypothesis or spontaneous factorization) [W.Furry, PR 49 (1936) 393]

  25. fKSKLp+p- p+p-: test of quantum coherence • Analysed data: L=380 pb-1 • Fit including Dt resolution and efficiency effects + regeneration • GS, GL , Dm fixed from PDG L=1 fb-1 (2005 data) KLOE preliminary: KLOE result: PLB 642(2006) 315 as CP viol. O(|h+-|2) ~ 10-6 => high sensitivity to From CPLEAR data, Bertlmann et al. (PR D60 (1999) 114032) obtain: In the B-meson system, BELLE coll. (PRL 99 (2007) 131802) obtains: Comparison with precision in quantum optics test

  26. Decoherence and CPT violation SPACE-TIME FOAM Possible decoherence due quantum gravity effects: Black hole information loss paradox => Possible decoherence near a black hole. Hawking [1] suggested that at a microscopic level, in a quantum gravity picture, non-trivial space-time fluctuations (generically space-time foam) could give rise to decoherence effects, which would necessarily entail a violation of CPT [2]. J. Ellis et al.[3-6] => model of decoherence for neutral kaons => 3 new CPTV param. a,b,g: At most: 10-35 m [1] Hawking, Comm.Math.Phys.87 (1982) 395; [2] Wald, PR D21 (1980) 2742;[3] Ellis et. al, NP B241 (1984) 381; PRD53 (1996)3846 [4] Huet, Peskin, NP B434 (1995) 3; [5] Benatti, Floreanini, NPB511 (1998) 550 [6] Bernabeu, Ellis, Mavromatos, Nanopoulos, Papavassiliou: Handbook on kaon interferometry [hep-ph/0607322] Modified Liouville – von Neumann equation for the density matrix of the kaon system: extra term inducing decoherence: pure state => mixed state

  27. Decoherence and CPT violation induced by QG Using single kaons CPLEAR PLB 364, 239 (1999) ADm(t) A+-(t) data fit a, b, g 10 Imposing a, g >0 a g > b2 at 90% CL

  28. fKSKLp+p- p+p-: decoherence & CPTV by QG KLOE result KLOE preliminary L=1 fb-1 L=380 pb-1 PLB 642(2006) 315 The fit with I(p+p-,p+p-;Dt,a,b,g) gives: KLOE preliminary L=380 pb-1 In the complete positivity hypothesis a = g , b = 0 => only one independent parameter: g Complete positivity guarantees the positivity of the eigenvalues of density matrices describing states of correlated kaons.

  29. fKSKLp+p- p+p-: CPT violation in correlated K states at most one expects: In some microscopic models of space-time foam arising from non-critical string theory: [Bernabeu, Mavromatos, Sarkar PRD 74 (2006) 045014] The maximum sensitivity to w is expected for f1=f2=p+p- All CPTV effects induced by QG (a,b,g,w) could be simultaneously disentangled. In presence of decoherence and CPT violation induced by quantum gravity (CPT operator “ill-defined”) the definition of the particle-antiparticle states could be modified. This in turn could induce a breakdown of the correlations imposed by Bose statistics (EPR correlations) to the kaon state: [Bernabeu, et al. PRL 92 (2004) 131601, NPB744 (2006) 180].

  30. fKSKLp+p- p+p-: CPT violation in correlated K states Im w x10-2 Fit of I(p+p-,p+p-;Dt,w): • Analysed data: 1 fb-1 (2005 data) • Analysed data: 380 pb-1 0 KLOE result : KLOE preliminary : PLB 642(2006) 315 0 Re w x10-2 (w measured for the first time)

  31. 3) Tests of Lorentz invariance and CPT symmetry in the neutral kaon system

  32. CPT and Lorentz invariance violation (SME) Kostelecky et al. developed a phenomenological effective model providing a framework for CPT and Lorentz violations, based on spontaneous breaking of CPT and Lorentz symmetry, which might happen in quantum gravity (e.g. in some models of string theory) Standard Model Extension (SME) [Kostelecky PRD61 (1999) 016002, PRD 64 (2001) 076001] CPT violation in SME manifests to lowest order only in d => and exhibits a kaon momentum dependence: No CPT viol. in decays d cannot be a constant where Dam are four parameters related to CPT and Lorentz violation Dam = rq1 amq1 – rq2 amq2 , with amqi CPT and Lorentz violating coupling constants for the two valence quarks in the kaon; rqi factors for quark binding or other normalization effects. amq have mass dimension and are associated to SME lagrangian terms of the form Possible hidden momentum dependence in other parameters, e.g. e, Dm, DG, fSW , is suppressed w.r.t. d.

  33. CPT and Lorentz invariance violation (SME) At DAFNE K mesons are produced with angular distribution dN/dW sin2q costant vector KLOE is a kind of telescope, able to explore with a kaon beam almost any direction in space Rotation axis Z e+ e- (in general z axis is non-normal to Earth’s surface) at 6 A.M. at 6 P.M. For a fixed target experiment (fixed momentum direction) d depends on sidereal time t since laboratory frame rotates with Earth. For a f-factory there is an additional dependence on the polar and azimuthal angle q,f of the kaon momentum in the laboratory frame: • : Earth’s sidereal frequency c : angle between the z lab. axis and the Earth’s rotation axis

  34. Measurement of Da0 at KLOE Da0 from KS and KL semileptonic charge asymmetries tagged KS and KL (symmetric polar angle q and sidereal time t integration) with L=400 pb-1 (preliminary): (Da0 evaluated for the first time) with L=2.5 fb-1 :s(Da0)~ 7 10-18 GeV

  35. Measurement of DaX,Y,Z at KLOE p+ KL,S p- cosq<0 q p+ KS,L p- cosq>0 DaX,Y,Z from (analysis vs polar angle q and sidereal time t) • I[p+p-(cosq>0),p+p- (cosq<0);Dt] • at Dt>>ts sensitive to Re(d/e)=0 • at Dt~ts sensitive to Im(d/e) 0. - 4. sidereal hours With L=1 fb-1 (preliminary): c2/dof=131/117 Dt/tS KTeV :DaX , DaY < 9.2 10-22GeV @ 90% CL BABAR DaBx,y , (DaB0 – 0.30 DaBZ )~O(10-13 GeV)

  36. 4) Future plans

  37. KLOE-2 at upgraded DAFNE Proposals to upgrade DAFNE in luminosity (and energy): • Crabbed waist scheme at DAFNE (proposal by P. Raimondi) • - increase L by a factor O(5) • requires minor modifications • relatively low cost • Experimental test at DAFNE in progress KLOE-2 Expression of Interest: [ L=50 fb-1 at f peak (and s up to 2.5 GeV) ] • Physics issues: • Neutral kaon interferometry, CPT symmetry & QM tests • Kaon physics, CKM, LFV, rare KS decays • h,h’ physics • Light scalars, gg physics • Hadron cross section at low energy, muon anomaly • (baryon electromagnetic form factors, e+e-pp, nn, ) • Detector upgrade issues: • Inner tracker R&D • gg tagging system • Calorimeter, increase of granularity • FEE maintenance and upgrade • Computing and networking update • etc.. (Trigger,software, …)

  38. Perspectives with KLOE-2 at upgraded DAFNE

  39. Perspectives with KLOE-2 at upgraded DAFNE

  40. Conclusions • The neutral kaon system is an excellent laboratory for the study of CPT symmetry and the basic principles of Quantum Mechanics; • Several parameters related to possible • CPT violation (within QM) • CPT violation and decoherence • CPT violation and Lorentz symmetry breaking • have been measured by KLOE, in same cases with a precision reaching the interesting Planck’s scale region; • All results are consistent with no CPT violation • The full KLOE data set analysis is almost completed; • KLOE and DAFNE are going to be upgraded; • Neutral kaon interferometry, CPT symmetry and QM tests are one of the main issues of the KLOE-2 physics program

  41. More detailed information can be found in: Handbook on neutral kaon interferometry at a f-factory G. Amelino-Camelia, M. Arzano, F. Benatti, J. Bernabeu, R. Bertlmann, A. Bramon, A. Di Domenico, R. Floreanini, A. Go, B. Hiesmayr, G. Isidori, R. Lehnert, N. Mavromatos J. Ellis, G. Garbarino, A. Marcianò, D. Nanopoulos, J. Papavassiliou, S. Sarkar published in Frascati Physics Series, Vol. 43, 2007 also available at: http://www.roma1.infn.it/people/didomenico/roadmap/handbook.html

  42. A. Di Domenico Neutral kaon interferometry at a phi-factory J. Bernabeu, J. Ellis, N. Mavromatos, D. Nanopoulos, J. PapavassiliouCPT and quantum mechanics tests with kaons S. SarkarMethods and models for the study of decoherence F. Benatti, R. Floreanini Open quantum dynamics: complete positivity and correlated kaons R. LehnertCPT and Lorentz symmetry breaking: a review G. Amelino-Camelia, M. Arzano, A. Marciano'On the quantum gravity phenomenology of multiparticle states G. IsidoriTesting CPT in the neutral kaon system by means of the Bell-Steinberger relation R. Bertlmann, B. HiesmayrStrangeness measurements of kaon pairs, CP violation and Bell inequalities A. Bramon, R. Escribano, G. GarbarinoA review of Bell inequality tests with neutral kaons A. Bramon, G. Garbarino, B. Hiesmayr Kaonic quantum erasers at a phi-factory: "erasing the present, changing the past" A. Go Kaon interferometry at CPLEAR http://www.roma1.infn.it/people/didomenico/roadmap/handbook.html

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