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. 2 Roma - 23 maggio 2008 A. Di Domenico CPT: introduction CPT theorem (Luders, Jost, Pauli, Bell 1955 -1957): Exact CPT invariance holds for any quantum field theory which assumes: (1) 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. 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.

3. 3 Roma - 23 maggio 2008 A. Di Domenico Consequences of CPT symmetry: equality of masses, lifetimes, |q| and | | 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 CPT: introduction

4. 4 Roma - 23 maggio 2008 A. Di Domenico 1)Standard tests of CPT symmetry in the neutral kaon system

5. 5 Roma - 23 maggio 2008 A. Di Domenico The time evolution of a two-component state vector 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 ) : The neutral kaon system Diagonalizing the effective Hamiltonian: eigenvalueseigenstates S ~ 90 ps L ~ 51 ns small CP impurity ~2 x 10 -3 m L -m S = 3.5 x 10 -15 GeV ~ S / 2 |K 1,2 > are CP=±1 states

6. 6 Roma - 23 maggio 2008 A. Di Domenico CPT violation in the neutral kaon system: standard picture CPT violation in the mixing: 0 implies CPT violation 0 implies T violation 0 or 0 implies CP violation (with a phase convention )

7. 7 Roma - 23 maggio 2008 A. Di Domenico CPT violation in the neutral kaon system: standard picture CPT violation in semileptonic decays CPT viol. CPT & S= Q viol. S= Q Viol. Standard Model prediction of S= Q rule violation is x=c/a ~ O(10 -7 ) Semileptonic charge asymmetry: S= Q rule CPTCPT S= Q a =0 b c d

8. 8 Roma - 23 maggio 2008 A. Di Domenico CPT violation in decays A I (B I ) CPT conserving (violating) K amplitudes for I=0,2 I strong phase shift for I=0,2) -2 S W Im Re - (not to scale) CPT violation in the neutral kaon system: standard picture

9. 9 Roma - 23 maggio 2008 A. Di Domenico Study of the time evolution of neutral kaons in semileptonic decays K0K0 e+e+ =0 PLB444 (1998) 52 Constraints on CPT violation in and semileptonic decays obtained combining KTeV and PDG results: A L =( 3322 58 47 ) 10 -6 PRL88, 181601(2002) K L semileptonic charge asymmetry: Study of regenerator beam two pion decay distribution +- - SW = 0.61º ±0.62º ± 1.01 º 00 - +- = 0.39º ± 0.22 º ±0.45 º PRD67,012005 (2003) Some results of CPT tests CPLEAR KTeV

10. 10 Roma - 23 maggio 2008 A. Di Domenico e + e b W = m = 1019.4 MeV BR( K 0 K 0 ) ~ 34% ~10 6 neutral kaon pairs per pb -1 produced in an antisymmetric quantum state with J PC = 1 Neutral kaons at a -factory p K = 110 MeV/c S = 6 mm L = 3.5 m The detection of a kaon at large (small) times tags a K S (K L ) possibility to select a pure K S beam (unique at a -factory, not possible at fixed target experiments) Production of the vector meson in e + e annihilations: K L,S K S,L e-e- e+e+

11. 11 Roma - 23 maggio 2008 A. Di Domenico Day performance: 7-8 pb -1 Best month L dt ~ 200 pb 1 Total KLOE L dt ~ 2.5 fb 1 (2001 - 05) ~2.5 10 9 K S K L pairs DA NE: the Frascati -factory Integrated luminosity (KLOE)

12. 12 Roma - 23 maggio 2008 A. Di Domenico Calorimeter Drift chamber E /E 5.7% / E(GeV) t 54 ps / E(GeV) 50 ps (relative time between clusters) ~ 2 cm ( 0 from K L ) p /p 0.4 % (tracks with > 45°) x hit 150 m (xy), 2 mm (z) x vertex ~ 1 mm The KLOE detector at DA NE 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 Superconducting coil B = 0.52 T

13. 13 Roma - 23 maggio 2008 A. Di Domenico K S tagged by K L interaction in EmC Efficiency ~ 30% (largely geometrical) K S angular resolution: ~ 1° (0.3 in ) K S momentum resolution: ~ 2 MeV K L crash = 0.22 (TOF) = 0.22 (TOF) K S e K S e K L tagged by K S vertex at IP Efficiency ~ 70% (mainly geometrical) K L angular resolution: ~ 1° K L momentum resolution: ~ 2 MeV K S K S K L 2 K L 2 K S and K L Tagging at KLOE

14. 14 Roma - 23 maggio 2008 A. Di Domenico K S e KLOE results Data sample: 410 pb -1 E miss -P miss A S = ( 1.5 9.6 2.9 ) 10 3 with 2.5 fb 1 : A S 3 10 3 2 Re PLB 636(2006) 173 x = ( 0.8 2.4 0.7) 10 y = ( 2.4 0.7) 10 CPT & S= Q viol. CPT viol. input from other experiments If CPT holds, A S =A L =2Re A S A L signals CPT violation in mixing and/or decay with S Q BR(K S e ) = (3.528 0.057 0.027) 10 4 BR(K S e ) = (3.517 0.051 0.029) 10 4 BR(K S e ) = (7.046 0.076 0.050) 10 4 BR( e ) [KLOE 02, 17 pb 1 ]: (6.91 0.34 0.15) 10 4 PLB 636(2006) 173

15. 15 Roma - 23 maggio 2008 A. Di Domenico CPT test: the Bell-Steinberger relation BR K S 00 BR K S kl3 S L BR(K L l3) (A S +A L )/4 i Im x S L BR K L Unitarity constraint: K S K L observables

16. 16 Roma - 23 maggio 2008 A. Di Domenico Experimental inputs to the Bell-Steinberger relation Main improvements done with KLOE measurements on K S semileptonic and 3 0 decays

17. 17 Roma - 23 maggio 2008 A. Di Domenico Re Im KLOE result: JHEP12(2006) 011 CPT test: the Bell-Steinberger relation Combining Re and Im results: Assuming, i.e. no CPT viol. in decay: at 95% c.l. Re Im

18. 18 Roma - 23 maggio 2008 A. Di Domenico 2) Tests of QM and CPT symmetry in the neutral kaon system

19. 19 Roma - 23 maggio 2008 A. Di Domenico Neutral kaon interferometry Double differential time distribution: where t 1 (t 2 ) is the proper time of one (the other) kaon decay into f 1 (f 2 ) final state and : f i = l etc characteristic interference term at a -factory => interferometry K L,S K S,L t1t1 t2t2 t=t 1 - t 2 f2f2 f1f1

20. 20 Roma - 23 maggio 2008 A. Di Domenico Integrating in (t 1 +t 2 ) we get the time difference ( t=t 1 -t 2 ) distribution (1-dim plot simpler to manipulate than 2-dim plot): Neutral kaon interferometry From these distributions for various final states f i one can measure the following quantities: Phases (difference of) from the interference term => interferometry

21. 21 Roma - 23 maggio 2008 A. Di Domenico Neutral kaon interferometry: main observables t/ S I( t) (a.u) t/ S

22. 22 Roma - 23 maggio 2008 A. Di Domenico Neutral kaon interferometry: main observables measured quantity parameters mode

23. 23 Roma - 23 maggio 2008 A. Di Domenico t/ S I( t) (a.u) Same final state for both kaons: f f t=|t 1 -t 2 | no simultaneous decays ( t=0) in the same final state due to the destructive quantum interference EPR correlation: t2t2 t1t1 t 2 =t 1 t1t1

24. 24 Roma - 23 maggio 2008 A. Di Domenico K S K L : test of quantum coherence Decoherence parameter: (also known as Furry's hypothesis or spontaneous factorization) [W.Furry, PR 49 (1936) 393]

25. 25 Roma - 23 maggio 2008 A. Di Domenico Analysed data: L=380 pb Fit including t resolution and efficiency effects + regeneration S, L, m fixed from PDG L=1 fb -1 (2005 data) From CPLEAR data, Bertlmann et al. (PR D60 (1999) 114032) obtain: KLOE result: PLB 642(2006) 315 In the B-meson system, BELLE coll. (PRL 99 (2007) 131802) obtains: KLOE preliminary: K S K L : test of quantum coherence Comparison with precision in quantum optics test as CP viol. O( high sensitivity to

26. 26 Roma - 23 maggio 2008 A. Di Domenico Modified Liouville – von Neumann equation for the density matrix of the kaon system: Decoherence and CPT violation extra term inducing decoherence: pure state => mixed state 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. : [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] At most: SPACE-TIME FOAM 10 -35 m

27. 27 Roma - 23 maggio 2008 A. Di Domenico A A m data fit 10 CPLEAR PLB 364, 239 (1999) at 90% CL Imposing >0 > 2 Using single kaons Decoherence and CPT violation induced by QG

28. 28 Roma - 23 maggio 2008 A. Di Domenico K S K L : decoherence & CPTV by QG KLOE preliminary The fit with I( t, ) gives: In the complete positivity hypothesis =, = 0 => only one independent parameter: Complete positivity guarantees the positivity of the eigenvalues of density matrices describing states of correlated kaons. KLOE preliminary L=1 fb -1 L=380 pb -1 KLOE result PLB 642(2006) 315 L=380 pb -1

29. 29 Roma - 23 maggio 2008 A. Di Domenico 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]. K S K L : CPT violation in correlated K states at most one expects: The maximum sensitivity to is expected for f 1 =f 2 = All CPTV effects induced by QG could be simultaneously disentangled. In some microscopic models of space-time foam arising from non-critical string theory: [Bernabeu, Mavromatos, Sarkar PRD 74 (2006) 045014]

30. 30 Roma - 23 maggio 2008 A. Di Domenico KLOE preliminary : Analysed data: 1 fb -1 (2005 data) K S K L : CPT violation in correlated K states Fit of I( t, ): Analysed data: 380 pb -1 KLOE result : PLB 642(2006) 315 Re x10 -2 Im x10 -2 0 0 ( measured for the first time)

31. 31 Roma - 23 maggio 2008 A. Di Domenico 3) Tests of Lorentz invariance and CPT symmetry in the neutral kaon system

32. 32 Roma - 23 maggio 2008 A. Di Domenico 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 => and exhibits a kaon momentum dependence: Possible hidden momentum dependence in other parameters, e.g., m,, SW, is suppressed w.r.t.. cannot be a constant No CPT viol. in decays where a are four parameters related to CPT and Lorentz violation a = r q1 a q1 – r q2 a q2, with a qi CPT and Lorentz violating coupling constants for the two valence quarks in the kaon; r qi factors for quark binding or other normalization effects. a q have mass dimension and are associated to SME lagrangian terms of the form

33. 33 Roma - 23 maggio 2008 A. Di Domenico at 6 A.M. at 6 P.M. Rotation axis Z costant vector For a fixed target experiment (fixed momentum direction) depends on sidereal time t since laboratory frame rotates with Earth. CPT and Lorentz invariance violation (SME) Earths sidereal frequency angle between the z lab. axis and the Earths rotation axis For a -factory there is an additional dependence on the polar and azimuthal angle of the kaon momentum in the laboratory frame: (in general z axis is non-normal to Earths surface) At DA NE K mesons are produced with angular distribution dN/d sin 2 KLOE is a kind of telescope, able to explore with a kaon beam almost any direction in space e+e+ e-e-

34. 34 Roma - 23 maggio 2008 A. Di Domenico a 0 from K S and K L semileptonic charge asymmetries tagged K S and K L (symmetric polar angle and sidereal time t integration) with L=400 pb -1 (preliminary): with L=2.5 fb -1 : a 0 ~ 7 10 -18 GeV Measurement of a 0 at KLOE ( a 0 evaluated for the first time)

35. 35 Roma - 23 maggio 2008 A. Di Domenico Measurement of a X,Y,Z at KLOE With L=1 fb -1 (preliminary): a X,Y,Z from + K S,L K L,S cos (analysis vs polar angle and sidereal time t) I[ ( cos ), ( cos <0 ) t] at t>> s sensitive to Re( )=0 at t~ s sensitive to Im( ) 2 /dof=131/117 t/ S 0. - 4. sidereal hours KTeV : a X, a Y < 9.2 10 -22 GeV @ 90% CL BABAR a B x,y, ( a B 0 – 0.30 a B Z ) ~O(10 -13 GeV)

36. 36 Roma - 23 maggio 2008 A. Di Domenico 4) Future plans

37. 37 Roma - 23 maggio 2008 A. Di Domenico Physics issues: Neutral kaon interferometry, CPT symmetry & QM tests Kaon physics, CKM, LFV, rare K S decays, physics Light scalars, physics Hadron cross section at low energy, muon anomaly (baryon electromagnetic form factors, e + e - pp, nn, KLOE-2 at upgraded DA NE Detector upgrade issues: Inner tracker R&D tagging system Calorimeter, increase of granularity FEE maintenance and upgrade Computing and networking update etc.. (Trigger,software, …) Proposals to upgrade DA NE in luminosity (and energy): Crabbed waist scheme at DA NE (proposal by P. Raimondi) - increase L by a factor O(5) - requires minor modifications - relatively low cost - Experimental test at DA NE in progress KLOE-2 Expression of Interest: [ L=50 fb -1 at peak (and s up to 2.5 GeV) ]

38. 38 Roma - 23 maggio 2008 A. Di Domenico ModeTest ofParam.Present best published measurement KLOE-2 L=50 fb -1 K S e CP, CPTASAS (1.5 11) 10 -3 1 10 -3 e CP, CPTALAL ( 3322 58 47 ) 10 -6 25 10 -6 CP Re (1.47 0.22) 10 -3 0.2 10 -3 CP, CPT Im (2.3 2.9) 10 -3 3 10 -3 e e CPT Re( )+Re(x - )Re( (0.29 0.27) 10 -3 Re(x - ) (-0.8 2.5) 10 -3 0.2 10 -3 e e CPT Im( )+Im(x + )Im( ) = (0.4 2.1) 10 -5 Im(x + ) = (0.8 0.7) 10 -2 3 10 -3 m(5.288 0.043) 10 9 s -1 0.03 10 9 s -1 Perspectives with KLOE-2 at upgraded DA NE

39. 39 Roma - 23 maggio 2008 A. Di Domenico Perspectives with KLOE-2 at upgraded DA NE ModeTest ofParam.Present best published measurement KLOE-2 L=50 fb -1 QM 00 (1.0 2.1) 10 -6 0.1 10 -6 QM SL (1.8 4.1) 10 -2 0.2 10 -2 CPT & QM (-0.5 2.8) 10 -17 GeV 2 10 -17 GeV CPT & QM (2.5 2.3) 10 -19 GeV 0.1 10 -19 GeV CPT & QM (1.1 2.5) 10 -21 GeV 0.2 10 -21 GeV compl. pos. hyp. 0.1 10 -21 GeV CPT & EPR corr. Re (1.1 7.0) 10 -4 2 10 -5 CPT & EPR corr. Im (3.4 4.9) 10 -4 2 10 -5 K S,L e CPT & Lorentz a 0 [(0.4 1.8) 10 -17 GeV] 2 10 -18 GeV CPT & Lorentz a Z [(2.4 9.7) 10 -18 GeV] 7 10 -19 GeV e CPT & Lorentz a X,Y [<10 -21 GeV]O(10 -19 )GeV

40. 40 Roma - 23 maggio 2008 A. Di Domenico 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 Plancks scale region; All results are consistent with no CPT violation The full KLOE data set analysis is almost completed; KLOE and DA NE 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. 41 Roma - 23 maggio 2008 A. Di Domenico http://www.roma1.infn.it/people/didomenico/roadmap/handbook.html More detailed information can be found in: Handbook on neutral kaon interferometry at a -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:

42. 42 Roma - 23 maggio 2008 A. Di Domenico A. Di Domenico Neutral kaon interferometry at a phi-factory J. Bernabeu, J. Ellis, N. Mavromatos, D. Nanopoulos, J. Papavassiliou CPT and quantum mechanics tests with kaons S. Sarkar Methods and models for the study of decoherence F. Benatti, R. Floreanini Open quantum dynamics: complete positivity and correlated kaons R. Lehnert CPT and Lorentz symmetry breaking: a review G. Amelino-Camelia, M. Arzano, A. Marciano' On the quantum gravity phenomenology of multiparticle states G. Isidori Testing CPT in the neutral kaon system by means of the Bell-Steinberger relation R. Bertlmann, B. Hiesmayr Strangeness measurements of kaon pairs, CP violation and Bell inequalities A. Bramon, R. Escribano, G. Garbarino A 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

43. 43 Roma - 23 maggio 2008 A. Di Domenico Spare

44. 44 Roma - 23 maggio 2008 A. Di Domenico EFFECTS OF CRAB SEXTUPOLES ON LUMINOSITY Crab on Crab off Transverse beam dimensions at the Synchrotron Light Monitor LUMINOMETERS A huge work on machine optimization has been done and is still in progress in term of feedbacks systems tuning, background minimization and tuning of the machine luminosity… P. Raimondi May 6, 2008

45. 45 Roma - 23 maggio 2008 A. Di Domenico Black hist. : ( t)~1 S => 6mm (KLOE) Red hist: ( t)~1/4 S => 1.5mm (KLOE + inner tracker) Blue curve: ideal Example of interferometry at KLOE-2: K S K L t/ S I(, ; t) (a.u.) t/ S I(, ; t) (a.u.) Possible signal of decoherence concentrated at very small t Theoretical distribution Reconstructed distribution (MC)