Test della simmetria CPT e della meccanica quantistica

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), 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: (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. A. Di Domenico Roma - 23 maggio 2008 2

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 A. Di Domenico Roma - 23 maggio 2008 3

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

The neutral kaon system The time evolution of a two-component state vector Y in the given by (Wigner-Weisskopf approximation): space is 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 |K 1, 2> are CP=± 1 states t. S ~ 90 ps t. L ~ 51 ns m. L-m. S= 3. 5 x 10 -15 Ge. V ~ GS / 2 A. Di Domenico small CP impurity ~2 x 10 -3 Roma - 23 maggio 2008 5

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 A. Di Domenico ) Roma - 23 maggio 2008 6

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

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 (d. I strong phase shift for I=0, 2) Im (not to scale) e -2 e h 00 -D h+ e f 00 A. Di Domenico f+ f. SW Re Roma - 23 maggio 2008 8

Some results of CPT tests CPLEAR Study of the time evolution of neutral kaons in semileptonic decays d = (0. 30 0. 33 0. 06) 10 -3 KTe. V Study of regenerator beam two pion decay distribution KTe. V t=0 p t PLB 444 (1998) 52 f+- - f. SW = 0. 61º ± 0. 62º ± 1. 01 º f 00 -f+- = 0. 39º ± 0. 22 º ± 0. 45 º KL semileptonic charge asymmetry: e+ K 0 n PRL 88, 181601(2002) AL=( 3322 58 47 ) 10 -6 Constraints on CPT violation in pp and semileptonic decays obtained combining KTe. V and PDG results: PRD 67, 012005 (2003) A. Di Domenico Roma - 23 maggio 2008 9

Neutral kaons at a f-factory Production of the vector meson f in e+e annihilations: • e+e f sf 3 mb W = mf = 1019. 4 Me. V • BR(f K 0 K 0) ~ 34% • ~106 neutral kaon pairs per pb-1 produced in an antisymmetric quantum state with JPC = 1 : p. K = 110 Me. V/c l. S = 6 mm l. L = 3. 5 m e+ KS, L e- f KL, S The detection of a kaon at large (small) times tags a KS (KL) Þ possibility to select a pure KS beam (unique at a f-factory, not possible at fixed target experiments) A. Di Domenico Roma - 23 maggio 2008 10

DA NE: the Frascati f-factory Integrated luminosity (KLOE) Day performance: 7 -8 pb-1 Best month L dt ~ 200 pb 1 Total KLOE L dt ~ 2. 5 fb 1 (2001 - 05) ~2. 5 109 KSKL pairs A. Di Domenico Roma - 23 maggio 2008 11

The KLOE detector at DA NE 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 s. E/E 5. 7% / E(Ge. V) st 54 ps / E(Ge. V) 50 ps (relative time between clusters) sgg ~ 2 cm (p 0 from A. Di Domenico KL p+p-p 0) sp/p 0. 4 % (tracks with q > 45°) sxhit 150 mm (xy), 2 mm (z) sxvertex ~ 1 mm Roma - 23 maggio 2008 12

KS and KL Tagging at KLOE KL “crash” b= 0. 22 (TOF) K S p +p K S p -e +n KS tagged by KL interaction in Em. C Efficiency ~ 30% (largely geometrical) KS angular resolution: ~ 1° (0. 3 in f) KS momentum resolution: ~ 2 Me. V A. Di Domenico KL 2 p 0 KL tagged by KS p+p- vertex at IP Efficiency ~ 70% (mainly geometrical) KL angular resolution: ~ 1° KL momentum resolution: ~ 2 Me. V Roma - 23 maggio 2008 13

KS pen: KLOE results Data sample: 410 pb-1 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 AS = ( 1. 5 9. 6 2. 9 ) 10 -3 BR(KS pen) = (7. 046 0. 076 0. 050) 10 -4 with 2. 5 fb 1: d. AS 3 10 3 2 Re e BR(pen) [KLOE ’ 02, 17 pb 1]: (6. 91 0. 34 0. 15) 10 4 Emiss-Pmiss If CPT holds, AS=AL =2 Re e AS 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 PLB 636(2006) 173 input from other experiments A. Di Domenico CPT viol. Roma - 23 maggio 2008 14

CPT test: the Bell-Steinberger relation Unitarity constraint: KS K L observables a+ = h+ BR(KS p+p ) a+ 0= t. S/t. L h+ 0* BR(KL p+p p 0) a 00= h 00 BR(KS p 0 p 0) a 000= t. S/t. L h 000* BR(KL p 0 p 0 p 0) akl 3 = 2 t. S/t. L BR(KLl 3) [(AS+AL)/4 i Im x+] A. Di Domenico Roma - 23 maggio 2008 15

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

CPT test: the Bell-Steinberger relation JHEP 12(2006) 011 KLOE result: 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. A. Di Domenico Roma - 23 maggio 2008 17

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

Neutral kaon interferometry f 1 t 1 KS, L f Dt=t 1 - t 2 Double differential time distribution: t 2 KL, S f 2 where t 1(t 2) is the proper time of one (the other) kaon decay into f 1 (f 2) final state and: characteristic interference term at a f-factory => interferometry fi = p+p , p 0 p 0, pln, p+p p 0, 3 p 0, p+p g. . etc A. Di Domenico Roma - 23 maggio 2008 19

Neutral kaon interferometry Integrating in (t 1+t 2) we get the time difference (Dt=t 1 -t 2) 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 A. Di Domenico Roma - 23 maggio 2008 20

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

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

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

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

f KSKL p+p- : test of quantum coherence 1 • Analysed data: L=1 L=380 fb-1 pb(2005 data) • Fit including Dt resolution and efficiency effects + regeneration • GS, GL , Dm fixed from PDG KLOE preliminary: result: PLB 642(2006) 315 as CP viol. O(|h+ |2) 10 6 => high sensitivity to From CPLEAR data, Bertlmann et al. (PR D 60 (1999) 114032) obtain: In the B-meson system, BELLE coll. (PRL 99 (2007) 131802) obtains: Comparison with precision in quantum optics test A. Di Domenico Roma - 23 maggio 2008 25

Decoherence and CPT violation Modified Liouville – von Neumann equation for the density matrix of the kaon system: SPACE-TIME FOAM 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, nontrivial 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 D 21 (1980) 2742; [3] Ellis et. al, NP B 241 (1984) 381; PRD 53 (1996)3846 [4] Huet, Peskin, NP B 434 (1995) 3; [5] Benatti, Floreanini, NPB 511 (1998) 550 [6] Bernabeu, Ellis, Mavromatos, Nanopoulos, Papavassiliou: Handbook on kaon interferometry [hep-ph/0607322] A. Di Domenico Roma - 23 maggio 2008 26

Decoherence and CPT violation induced by QG Usingle kaons CPLEAR A+ (t) ADm(t) data fit a, b, g 10 A. Di Domenico Roma - 23 maggio 2008 PLB 364, 239 (1999) Imposing a, g >0 a g > b 2 at 90% CL 27

f KSKL p+p- : decoherence & CPTV by QG 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 -1 -1 preliminary L=1 fb KLOE result L=380 pb PLB 642(2006) 315 of correlated kaons. A. Di Domenico Roma - 23 maggio 2008 28

f KSKL p+p- : CPT violation in correlated K states 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, NPB 744 (2006) 180]. 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 f 1=f 2=p+p All CPTV effects induced by QG (a, b, g, w) could be simultaneously disentangled. A. Di Domenico Roma - 23 maggio 2008 29

f KSKL p+p- : CPT violation in correlated K states Im w x 10 -2 Fit of I(p+p-, p+p-; Dt, w): -1 • Analysed data: 1380 fb-1 pb(2005 data) 0 result : KLOE preliminary : 642(2006) 315 PLB 0 (w measured for the first time) A. Di Domenico Roma - 23 maggio 2008 Re w x 10 -2 30

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

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 PRD 61 (1999) 016002, PRD 64 (2001) 076001] No CPT viol. in decays CPT violation in SME manifests to lowest order only in d => and exhibits a kaon momentum dependence: cannot be a constant where Dam are four parameters related to CPT and Lorentz violation Dam = rq 1 amq 1 – rq 2 amq 2 , 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, f. SW , is suppressed w. r. t. d. A. Di Domenico Roma - 23 maggio 2008 32

CPT and Lorentz invariance violation (SME) 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: At DAFNE K mesons are producedcostant with Rotation Z 2 q angularaxis distribution d. N/d. W sinvector KLOE is a kind of telescope, able to explore with a kaon beam almost any direction in space at 6 A. M. (in general z axis is non-normal + e surface) to Earth’s at 6 P. M. W: Earth’s sidereal frequency c : angle between the z lab. axis and the Earth’s rotation axis A. Di Domenico Roma - 23 maggio 2008 33 e-

Measurement of Da 0 at KLOE Da 0 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): (Da 0 evaluated for the first time) with L=2. 5 fb-1 : A. Di Domenico s(Da 0) ~ 7 10 -18 Ge. V Roma - 23 maggio 2008 34

Measurement of Da. X, Y, Z at KLOE Da. X, Y, Z from (analysis vs polar angle q and sidereal time t) KL, S cosq<0 p+ p q 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) With L=1 fb-1 (preliminary): p+ p KS, L cosq>0 0. - 4. sidereal hours c 2/dof=131/117 KTe. V : Da. X , Da. Y < 9. 2 10 -22 Ge. V @ 90% CL Dt/t. S BABAR Da. Bx, y , (Da. B 0 – 0. 30 Da. BZ ) ~O(10 -13 Ge. V) A. Di Domenico Roma - 23 maggio 2008 35

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

KLOE-2 at upgraded DA NE Proposals to upgrade DAFNE in luminosity (and energy): Crabbed waist scheme at DAFNE (proposal by P. Raimondi) - Experimental test at DAFNE in progress - increase L by a factor O(5) - requires minor modifications - relatively low cost KLOE-2 Expression of Interest: [ L=50 fb-1 at f peak (and s up to 2. 5 Ge. V) 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, ) A. Di Domenico ] 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, …) Roma - 23 maggio 2008 37

Perspectives with KLOE-2 at upgraded DA NE Mode Test of Param. Present best published measurement KLOE-2 L=50 fb-1 KS pen CP, CPT AS (1. 5 11) 10 -3 1 10 -3 p+p- pen CP, CPT AL ( 3322 58 47 ) 10 -6 25 10 -6 p+p- p 0 p 0 CP Re( ’/ ) (1. 47 0. 22) 10 -3 0. 2 10 -3 p+p- p 0 p 0 CP, CPT Im( ’/ ) (2. 3 2. 9) 10 -3 3 10 -3 pen CPT Re( )+Re(x-) Re( ) = (0. 29 0. 27) 10 -3 Re(x-) = (-0. 8 2. 5) 10 -3 0. 2 10 -3 pen CPT Im( )+Im(x+) Im( ) = (0. 4 2. 1) 10 -5 Im(x+) = (0. 8 0. 7) 10 -2 3 10 -3 Dm (5. 288 0. 043) 109 s-1 0. 03 109 s-1 p+p- A. Di Domenico Roma - 23 maggio 2008 38

Perspectives with KLOE-2 at upgraded DA NE Mode Test of Param. Present best published measurement KLOE-2 L=50 fb-1 p+p- QM z 00 (1. 0 2. 1) 10 -6 0. 1 10 -6 p+p- QM z. SL (1. 8 4. 1) 10 -2 0. 2 10 -2 p+p- CPT & QM a (-0. 5 2. 8) 10 -17 Ge. V 2 10 -17 Ge. V p+p- CPT & QM b (2. 5 2. 3) 10 -19 Ge. V 0. 1 10 -19 Ge. V p+p- CPT & QM g (1. 1 2. 5) 10 -21 Ge. V 0. 2 10 -21 Ge. V compl. pos. hyp. 0. 1 10 -21 Ge. V p+p- CPT & EPR corr. Re(w) (1. 1 7. 0) 10 -4 2 10 -5 p+p- CPT & EPR corr. Im(w) (3. 4 4. 9) 10 -4 2 10 -5 KS, L pen CPT & Lorentz Da 0 [(0. 4 1. 8) 10 -17 Ge. V] 2 10 -18 Ge. V p+p- CPT & Lorentz Da. Z [(2. 4 9. 7) 10 -18 Ge. V] 7 10 -19 Ge. V p+p- pen CPT & Lorentz Da. X, Y [<10 -21 Ge. V] O(10 -19)Ge. V A. Di Domenico Roma - 23 maggio 2008 39

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 A. Di Domenico Roma - 23 maggio 2008 40

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. roma 1. infn. it/people/didomenico/roadmap/handbook. html A. Di Domenico Roma - 23 maggio 2008 41

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. roma 1. infn. it/people/didomenico/roadmap/handbook. html Roma - 23 maggio 2008 42 A. Di Domenico

Spare A. Di Domenico Roma - 23 maggio 2008 43

EFFECTS OF CRAB SEXTUPOLES ON LUMINOSITY 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… Crab off Transverse beam dimensions at the Synchrotron Light Monitor Crab on P. Raimondi May 6, 2008 A. Di Domenico Roma - 23 maggio 2008 44

Example of interferometry at KLOE-2: f KSKL p+p- p+p. Possible signal of decoherence concentrated at very small Dt I(p+p , p+p ; Dt) (a. u. ) Black hist. : s(Dt)~1 t. S => 6 mm (KLOE) Red hist: s(Dt)~1/4 t. S => 1. 5 mm (KLOE + inner tracker) Blue curve: ideal Dt/t. S Theoretical distribution A. Di Domenico Dt/t. S Reconstructed distribution (MC) Roma - 23 maggio 2008 45