Hunting for CPT symmetry and Quantum Mechanics violations in neutral meson systems

Hunting for CPT symmetry and Quantum Mechanics violations in neutral meson systems Antonio Di Domenico Dipartimento di Fisica, Sapienza Università di Roma and INFN sezione di Roma, Italy 30 Nov.- 2 Dec, 2012 Vienna

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.

CPT: introduction Consequences of CPT symmetry: equality of masses, lifetimes, q and µ of a particle and its anti-particle. Neutral meson systems are the most intriguing systems in nature; they offer 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 system neutral B system proton- anti-proton

Other important CPT tests: Hydrogen and Antihydrogen antiproton decelerator (AD) facility at CERN not discussed here

The neutral kaon: a two-level quantum system 0 and 0 can decay to common final states due to weak interactions: strangeness oscillations π 0 + π + 0 S=+1 0 0 s d "" s d S=-1 π π P[ 0 ( t = 0) " 0 ] S ω S L ω L P[ 0 ( t = 0) " 0 ] 0 ω=m 0 0 t( 1/" S )

The neutral kaon system: introduction The time evolution of a two-component state vector in the { 0, 0 } space is given by (Wigner-Weisskopf approximation): i t Ψ( t) = HΨ( t) Ψ = a 0 + b 0 H is the effective hamiltonian (non-hermitian), decomposed into a Hermitian part (mass matrix M) and an anti-hermitian part (i/2 decay matrix Γ) : Diagonalizing the effective Hamiltonian: eigenvalues λ S,L = m S,L i 2 Γ S,L S,L ( t) = e iλ S,L t S,L ( 0) τ S ~ 90 ps H = M i 2 Γ = m 11 m 12 i Γ 11 Γ 12 m 21 m 22 2 Γ 21 Γ 22 τ L ~ 51 ns S ππ L / ππ S,L = = 1 2( 1+ ε ) S,L 1 ( 1+ ε ) S,L S L ε S +ε L 0 eigenstates ( 1+ε S,L ) 0 ± 1 ε S,L ( ) 0 [ ] [ 1,2 +ε S,L ] 2,1 0 0 s d "" s d 1,2 > are CP=±1 states small CP impurity ~2 x 10-3

CPT violation: standard picture CP violation: T violation: " = H # H 12 21 2 ( $ S # $ L ) = #i%m # %& 2 12 12 'm + i'&/2 CPT violation: δ = H H 11 22 2( λ S λ L ) = 1 2 ( m 0 m ) 0 ( i 2) ( Γ 0 Γ ) 0 Δm + iδγ/2 δ 0 implies CPT violation ε 0 implies T violation ε 0 or δ 0 implies CP violation (with a phase convention ) Δm = m L m S, ΔΓ = Γ S Γ L Δm = 3.5 10 15 GeV ΔΓ Γ S 2Δm = 7 10 15 GeV

neutral B vs mesons B neutral B meson system m 5.3 GeV B 0 B 0 b d b d Δm m H m L 3.3 10 13 GeV Γ 4.3 10 13 GeV ΔΓ Γ H Γ L << Γ,Δm (QCD lattice calc. ΔΓ/Δm ~ 0.005) CPT violation parameter neutral meson system m 0.5 GeV Δm 3.5 10 15 GeV Γ S 7.3 10 15 GeV Γ L 1.3 10 17 GeV ΔΓ Γ S 2Δm ( ) i 2 z = m B 0 m B 0 ( ) Γ B 0 Γ B 0 Δm iδγ/2 ( ) δ Slightly different definition of the parameter than for : z = 2δ

1) Standard tests of CPT symmetry

Standard CPT test measuring the time evolution of a neutral kaon beam into semileptonic decays: Rδ = (0.30 ± 0.33 ± 0.06) 10-3 CPLEAR PLB444 (1998) 52 using the unitarity constraint (Bell-Steinberger relation) " = 1 2 ( m 0 # m ) 0 # ( i 2) ( $ 0 # $ ) 0 %m + i%$/2 Combining Reδ and Imδ results Assuming Im δ =( 1.5 ± 1.6) 10 5 TeV PRD 83, 092001 (2011) " * 2!! =!"# L S $ % =!* * # (" 0 # " ) 0 ( 10 #18 GeV), i.e. no CPT viol. in decay: 0 τ=0 τ ' f ( ) A S & f ( i (" S ) " L ) e + ν A L & f π ( ) ( $ + + + % m 0 " m 0 < 4.8 #10 "19 GeV at 95% c.l. ( m 0 " m 0 ) ( 10 "18 GeV)

Standard CPT test B From the study of the time evolution of neutral B mesons with opposite flavor (and also other) decays ( ) P( B 0 B 0 ) ( ) + P( B 0 B 0 ) A CPT = P B0 B 0 P B 0 B 0 PDG av. BABAR PRL 96, 251802 (2006) BELLE PRD85, 071105(R) (2012) Re z = (1.9± 3.7±3.3) 10-2 Im z = ( 0.8± 0.4) 10-2 Assuming ( Γ B 0 Γ ) B 0 = 0, i.e. no CPT viol. in decay: m B 0 m B 0 <~ 5 10 14 GeV at 95% c.l.

2) Entangled neutral mesons

Neutral kaons at a φ-factory Production of the vector meson φ in e + e - annihilations: e + e - φ σ φ 3 µb W = m φ = 1019.4 MeV BR(φ 0 0 ) ~ 34% ~10 6 neutral kaon pairs per pb -1 produced in an antisymmetric quantum state with J PC = 1 -- : p = 110 MeV/c λ S = 6 mm λ L = 3.5 m i = 1 2 0 p ( ) 0 ( p ) 0 ( p ) 0 ( p ) [ ] = N 2 S( p ) L p S,L e - L,S ( ) L ( p ) S ( p ) [ ] The detection of a kaon at large (small) times tags a S ( L ) possibility to select a pure S beam (unique at a φ-factory, not possible at fixed target experiments) e + N = 1+ ε S 2 φ ( )( 1+ ε 2 ) L 1 ε S ε L ( ) 1 ( are not perfectly back-to back in the lab because φ has a small momentum p(φ)~13 MeV)

Analogy with spin ½ particles C = 1 = 1 [ 2 0 0 0 0 ] S = 0 = 1 2 [ A A A A ] 0 (t 1 ) 0 (t 2 ) A B θ ab φ ideal case with Γ S = Γ L = 0 (no decay!) ( ) = 1 4 1 cos θ ab P A ;B Singlet (S=0) ( ) [ ] with Γ S and Γ L 0 (kaons decay!): ( ) = 1 8 e Γ L t 1 Γ S t 2 + e Γ S t 1 Γ L t 2 { P 0,t 1 ; 0,t 2 [ ( )]} 2e ( Γ S +Γ L )( t 1 +t 2 ) / 2 cos Δm t 2 t 1 - the time difference plays the same role as the angle between the spin analyzers - kaons change their identity with time, but remain correlated

The LOE detector at the Frascati φ-factory DAΦNE DAFNE collider Integrated luminosity (LOE) LOE detector Total LOE L dt ~ 2.5 fb -1 (2001-05) ~2.5 10 9 S L pairs

The LOE detector at the Frascati φ-factory DAΦNE DAFNE collider LOE detector Integrated luminosity (LOE) Total LOE L dt ~ 2.5 fb -1 (2001-05) ~2.5 10 9 S L pairs Lead/scintillating fiber calorimeter drift chamber 4 m diameter 3.3 m length helium based gas mixture

Correlated B meson pairs B

B-factories B BABAR @ PEP-II BELLE @ EB collected L=557 fb -1 collected L=1040 fb -1

Neutral kaon interferometry i = N 2 Double differential time distribution: ( ) = C 12 " 1 2e #$ L t 1 #$ S t 2 + " 2 I f 1,t 1 ; f 2,t 2! ( ) L "! {! ( ) " L ( ) S ("! ) [ S p p p p ] 2e #$ S t 1 #$ L t 2 f 1 t 1 S,L φ t 2 L,S Δt=t 1 - t 2 f 2 #2" 1 " 2 e # ( $ S +$ L )( t 1 +t 2 ) / 2 cos %m t 2 # t 1 [ ( ) + & 1 # & ]} 2 where t 1 (t 2 ) is the proper time of one (the other) kaon decay into f 1 (f 2 ) final state and: " i = " i e i# i = f i T L f i T S characteristic interference term at a φ-factory => interferometry C 12 = N 2 2 2 f 1 T S f 2 T S From these distributions for various final states f i one can measure the following quantities: " S, " L, #m, $ i, % i & arg ( $ ) i

Neutral kaon interferometry: main observables I(Δt) (a.u) I(Δt) (a.u) I(Δt) (a.u) Δt/τ S Δt/τ S Δt/τ S

i = 1 [ 2 0 0 " 0 0 ] Same final state for both kaons: f 1 = f 2 = π + π π π Δt= t 1 -t 2 φ t 1 t 2 π π I(Δt) (a.u) Δt/τ S

i = 1 [ 2 0 0 " 0 0 ] Same final state for both kaons: f 1 = f 2 = π + π π π Δt= t 1 -t 2 φ t 1 t 2 π π I(Δt) (a.u) EPR correlation: no simultaneous decays (Δt=0) in the same final state due to the destructive quantum interference π π t 1 φ t 2 =t 1 π π Δt/τ S

3) Search for decoherence and CPT violation in entangled neutral mesons

φ S L π + π π + π : test of quantum coherence ( ) = N 2 " + " #," + " # 0 0 $t I " + " #," + " # ;$t i = 1 [ 2 0 0 " 0 0 ] % &' #2( " + " #," + " # 0 0 $t ( ) 2 + " + " #," + " # 0 0 ( $t) 2 ( ( ) " + " #," + " # 0 0 ( $t) ) ) *, +

φ S L π + π π + π : test of quantum coherence ( ) = N 2 " + " #," + " # 0 0 $t I " + " #," + " # ;$t i = 1 [ 2 0 0 " 0 0 ] % &' #( 1 #( 00 )) 2* " + " #," + " # 0 0 $t ( ) 2 + " + " #," + " # 0 0 ( $t) 2 ( ( ) " + " #," + " # 0 0 ( $t) + ),. -

φ S L π + π π + π : test of quantum coherence ( ) = N 2 " + " #," + " # 0 0 $t I " + " #," + " # ;$t i = 1 [ 2 0 0 " 0 0 ] % &' #( 1 #( 00 )) 2* " + " #," + " # 0 0 $t ( ) 2 + " + " #," + " # 0 0 ( $t) 2 ( ( ) " + " #," + " # 0 0 ( $t) + ),. - Decoherence parameter: " 00 = 0 # QM " 00 =1 # total decoherence (also known as Furry's hypothesis or spontaneous factorization) [W.Furry, PR 49 (1936) 393] Bertlmann, Grimus, Hiesmayr PR D60 (1999) 114032 Bertlmann, Durstberger, Hiesmayr PRA 68 012111 (2003)

φ S L π + π π + π : test of quantum coherence ( ) = N 2 " + " #," + " # 0 0 $t I " + " #," + " # ;$t i = 1 [ 2 0 0 " 0 0 ] % &' ( ) 2 + " + " #," + " # 0 0 ( $t) 2 I(Δt) (a.u.) ( ( ) " + " #," + " # 0 0 ( $t) + ),. #( 1 #( 00 )) 2* " + " #," + " # 0 0 $t - " 00 > 0 Δt/τ S Decoherence parameter: " 00 = 0 # QM " 00 =1 # total decoherence (also known as Furry's hypothesis or spontaneous factorization) [W.Furry, PR 49 (1936) 393] Bertlmann, Grimus, Hiesmayr PR D60 (1999) 114032 Bertlmann, Durstberger, Hiesmayr PRA 68 012111 (2003)

φ S L π + π π + π : test of quantum coherence Analysed data: L=1.5 fb -1 Fit including Δt resolution and efficiency effects + regeneration LOE result: PLB 642(2006) 315 ( ) #10 $7 " 00 = 1.4 ± 9.5 STAT ± 3.8 SYST J.Phys.Conf.Ser.171:012008,2009. Observable suppressed by CP violation: η + 2 ε 2 10 6 => terms ζ 00 / η + 2 => high sensitivity to ζ 00 From CPLEAR data, Bertlmann et al. (PR D60 (1999) 114032) obtain:

Τest of quantum coherence in neutral B mesons B Δt dependent rates: opposite sign di-lepton vs same sign di-lepton A(Δt) = I( ±, ;Δt) I( ±, ± ;Δt) I( ±, ;Δt) + I( ±, ± ;Δt) = cos(δmδt) After correcting for Δt resolution and selection efficiency by a deconvolution procedure: QM prediction L~150 fb -1 BELLE PRL 99 131802 (2007) ζ 00 = 0.029 ± 0.057 no enhanced sensitivity due to CP violation here (η not very small) f CP T B H f CP T B L ~ O(1)

Decoherence and CPT violation Modified Liouville von Neumann equation for the density matrix of the kaon system: 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. α,β,γ: At most: [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]

φ S L π + π π + π : decoherence & CPTV Study of time evolution of single kaons decaying in π+π and semileptonic final state CPLEAR ( ) 10 17 GeV ( ) 10 19 GeV ( ) 10 21 GeV α = 0.5 ± 2.8 β = 2.5 ± 2.3 γ = 1.1 ± 2.5 PLB 364, 239 (1999) single kaons In the complete positivity hypothesis α = γ, β = 0 => only one independent parameter: γ The fit with I(π + π,π + π ;Δt,γ) gives: LOE result L=1.5 fb -1 γ = ( 0.7 ±1.2 STAT ± 0.3 ) SYST 10 21 GeV PLB 642(2006) 315 J.Phys.Conf.Ser.171:012008,2009. entangled kaons

φ S L π + π π + π : CPT violation in entangled 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, NPB744 (2006) 180]. i ( 0 0 0 0 ) +ω( 0 0 + 0 0 ) I(π + π, π + π ;Δt) (a.u.) at most one expects: ( S L L ) S +ω( S S L ) L ω = 3 10 3 φ ω = 0 Δt/τ S 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 ω is expected for f 1 =f 2 =π + π (again sensitivity boosted by CPV) All CPTV effects induced by QG (α,β,γ,ω) could be simultaneously disentangled.

φ S L π + π π + π : CPT violation in entangled states Im ω x10-2 Fit of I(π + π,π + π ;Δt,ω): Analysed data: 1.5 fb -1 LOE result: PLB 642(2006) 315 J.Phys.Conf.Ser.171:012008,2009. 0 ( ) 10 4 +3.0 Rω = 1.6 ± 0.4 2.1 STAT SYST ( ) 10 4 +3.3 Iω = 1.7 3.0 STAT ±1.2 SYST ω <1.0 10 3 at 95% C.L. 0 Re ω x10-2

CPT violation in entangled B states B Observable asymmetry of Δt dependent rates: same sign di-lepton A sl (Δt) = I( +, + ;Δt) I(, ;Δt) I( +, + ;Δt) + I(, ;Δt) For ω=0 equal sign di-lepton time asymmetry A sl is exactly time independent For ω 0 A sl acquires a time dependence A sl (0) ω 2 L~20 fb -1 Belle L~90 fb -1 Alvarez, Bernabeu, Nebot JHEP 0611, 087:

4) Search for Lorentz and CPT symmetry violations in neutral meson systems

CPT and Lorentz invariance violation (SME) ostelecky 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) [ostelecky PRD61, 016002, PRD64, 076001] CPT violation in neutral kaons according to SME: CPTV only in mixing, not in decay, at first order (i.e. B I = y = x - = 0) δ cannot be a constant (momentum dependence) δ = isinφ SW e iφ SW γ ( ) /Δm Δa 0 β Δa where Δa µ are four parameters associated to SME lagrangian terms and related to CPT and Lorentz violation.

CPT and Lorentz invariance violation (SME) δ = isinφ SW e iφ SW γ Δa 0 β Δa ( ) /Δm δ depends on sidereal time t since laboratory frame rotates with Earth. For a φ-factory there is an additional dependence on the polar and azimuthal angle θ, φ of the kaon momentum in the laboratory frame: γ Δm { Δa 0 +β Δa Z cosθ cos χ sinθ sinφ sin χ δ( p,t) = isinφ SW eiφ SW ( ) ( ) (in general z lab. axis is non-normal to Earth s surface) +β [ Δa X sinθ sinφ + Δa Y cosθ sin χ + sinθ cosφ cos χ ]sinωt +β [ +Δa Y sinθ sinφ + Δa X ( cosθ sin χ + sinθ cosφ cos χ) ]cosωt} Ω : Earth s sidereal frequency χ : angle between the z lab. axis and the Earth s rotation axis

CPT and Lorentz invariance violation (SME) δ = isinφ SW e iφ SW γ Δa 0 β Δa γ Δm { Δa 0 +β Δa Z cosθ cos χ sinθ sinφ sin χ δ( p,t) = isinφ SW eiφ SW ( ) /Δm δ depends on sidereal time t since laboratory frame rotates with Earth. For a φ-factory there is an additional dependence on the polar and azimuthal angle θ, φ of the kaon momentum in the laboratory frame: ( ) ( ) At DAΦNE mesons are produced with angular distribution dn/dω sin 2 θ e + e - +β [ Δa X sinθ sinφ + Δa Y cosθ sin χ + sinθ cosφ cos χ ]sinωt +β [ +Δa Y sinθ sinφ + Δa X ( cosθ sin χ + sinθ cosφ cos χ) ]cosωt} Ω : Earth s sidereal frequency χ : angle between the z lab. axis and the Earth s rotation axis

Measurement of Δa µ at LOE Δa 0 from S,L semileptonic asymmetries A S,L (with symmetric polar angle θ and sidereal time t integration) Δa X,Y,Z from cosθ<0 π + with L=400 pb -1 (preliminary): with L=2.5 fb -1 : σ(δa 0 ) ~ 7 10-18 GeV (analysis vs polar angle θ and sidereal time t) Fit to: I[π + π (cosθ>0),π + π (cosθ<0);δt] at Δt~τ s sensitive to Im(δ/ε) π S,L L,S θ π + cosθ>0 π With L=1 fb -1 (preliminary): TeV :Δa X, Δa Y < 9.2 10-22 GeV @ 90% CL

Measurement of Δa µ at LOE Δa 0 from S,L semileptonic asymmetries A S,L (with symmetric polar angle θ and sidereal time t integration) Δa X,Y,Z from cosθ<0 π + with L=400 pb -1 (preliminary): with L=2.5 fb -1 : σ(δa 0 ) ~ 7 10-18 GeV (analysis vs polar angle θ and sidereal time t) Fit to: 0. I[π - 4. + πsidereal (cosθ>0),π hours + π (cosθ<0);δt] at Δt~τ s sensitive to Im(δ/ε) π S,L L,S θ π + Δt/τcosθ>0 S π With L=1 fb -1 (preliminary): TeV :Δa X, Δa Y < 9.2 10-22 GeV @ 90% CL

Measurement of Δa µ at LOE Δa 0 from S,L semileptonic asymmetries A S,L (with symmetric polar angle θ and sidereal time t integration) Δa X,Y,Z from cosθ<0 π + with L=400 pb -1 (preliminary): with L=2.5 fb -1 : σ(δa 0 ) ~ 7 10-18 GeV (analysis vs polar angle θ and sidereal time t) Fit to: 0. I[π - 4. + πsidereal (cosθ>0),π hours + π (cosθ<0);δt] at Δt~τ s sensitive to Im(δ/ε) π S,L L,S θ π + Δt/τcosθ>0 S π With L=1 fb -1 (preliminary): TeV :Δa X, Δa Y < 9.2 10-22 GeV @ 90% CL new forthcoming LOE result: improvement precision of a factor ~5

CPT and Lorentz invariance violation (SME) ( a B ) z = γ Δa B 0 β Δ Δm i ΔΓ 2 boosted B s at B-factory (almost fixed direction) => cannot distinguish between Δa 0 B and Δa Z B B searching for a dependence of the form A CPT dilepton asymmetry Babar [PRL 100 (2008) 131802] Δa 0 B 0.30Δa Z B 3.0 ± 2.4 ( )( Δm /ΔΓ) 10 15 GeV Δa B X ( 22 ± 7) ( Δm /ΔΓ) 10 15 GeV L~232 fb -1 i.e. ~O(10-13 GeV) Δa B Y ( +10 14 ) 13 ( Δm /ΔΓ) 10 15 GeV

5) Future plans

LOE-2 at upgraded DAΦNE DAΦNE upgraded in luminosity: - new scheme of the interaction region (crabbed waist scheme) at DAΦNE (proposal by P. Raimondi) - increase L by a factor x 3 demonstrated by a successful experimental test LOE-2 experiment: - extend the LOE physics program at DAΦNE upgraded in luminosity - Collect O(10) fb 1 of integrated luminosity in the next 2-3 years Physics program (see EPJC 68 (2010) 619-681) Neutral kaon interferometry, CPT symmetry & QM tests aon physics, CM, LFV, rare S decays η,η physics Light scalars, γγ physics Hadron cross section at low energy, muon anomaly Detector upgrade: γγ tagging system: inner tracker: small angle and quad calorimeters: FEE maintenance and upgrade Computing and networking update etc.. (Trigger, software, )

Prospects for LOE-2 at upgraded DAΦNE Test of Param. Present best measurement LOE-2 (IT) L=20 fb -1 (stat. only) QM ζ 00 (0.1 ± 1.0) 10-6 ± 0.13 10-6 QM ζ SL (0.3 ± 1.9) 10-2 ± 0.25 10-2 CPT & QM α (-0.5 ± 2.8) 10-17 GeV ± 2.5 10-17 GeV CPT & QM β (2.5 ± 2.3) 10-19 GeV ± 0.25 10-19 GeV CPT & QM γ (1.1 ± 2.5) 10-21 GeV compl. pos. hyp. (0.7 ± 1.2) 10-21 GeV ± 0.38 10-21 GeV compl. pos. hyp. ± 0.16 10-21 GeV CPT & EPR corr. Re(ω) (-1.6 ± 2.6) 10-4 ± 0.35 10-4 CPT & EPR corr. Im(ω) (-1.7 ± 3.4) 10-4 ± 0.43 10-4 CPT & Lorentz Δa 0 [(0.4 ± 1.8) 10-17 GeV] ± 1.2 10-18 GeV CPT & Lorentz Δa Z [(2.4 ± 9.7) 10-18 GeV] ± 1.5 10-19 GeV CPT & Lorentz Δa X,Y [<10-21 GeV] ± 1.9 10-19 GeV [.] = preliminary

Super B-factories B Two projects: 1) BELLE-II at SuperEB (start ~2014) Goal: collect L~50 ab 1 2) SuperB at new Cabibbo Lab (start 2016?) Goal: collect L~75 ab 1

Prospect for Super B-factories B Test of Param. Present best measurement Super B-factory L~50 ab -1 (stat. only) CPT Re z (1.9± 4.9) 10 2 ± 0.4 10-2 CPT Im z ( 8 ± 4) 10 3 ± 0.4 10-3 QM ζ 00 (2.9 ± 5.7) 10-2 ± 3.6 10-3 QM ζ SL (0.4 ± 1.7) 10-2 ± 1 10-3 CPT & QM α,β,γ CPT & EPR corr. Re(ω) <0.01 ± 4 10-4 CPT & EPR corr. Im(ω) CPT & Lorentz Δa 0-0.3Δa Z (-3.0 ± 2.4) Δm/ΔΓ 10-15 GeV CPT & Lorentz Δa X (-22 ± 7) Δm/ΔΓ 10-15 GeV CPT & Lorentz Δa Y (-14 ± 12) Δm/ΔΓ 10-15 GeV ± 1.5 Δm/ΔΓ 10-16 GeV ± 4.4 Δm/ΔΓ 10-16 GeV ± 7.6 Δm/ΔΓ 10-16 GeV

Conclusions Neutral meson systems are unique and excellent laboratories for the study of CPT symmetry, and the basic principles of quantum mechanics. Several parameters related to possible CPT violation (within QM) Decoherence and CPT violation CPT violation and Lorentz symmetry breaking have been recently measured at LOE for mesons and at Belle and Babar for B mesons, with very high precision, especially for kaons. In some cases the precision reaches the interesting Planck s scale region. All results are consistent with no CPT violation. CPT symmetry and QM tests are one of the main issues of the LOE-2 physics program; a significant improvement in the precision is expected. Improvements in CPT tests are expected at Super B-factories

spare slides

Interferometry at LOE-2: φ S L π + π π + π Possible signal of decoherence concentrated at very small Δt I(π + π, π + π ;Δt) (a.u.) I(π + π, π + π ;Δt) (a.u.) Black hist. : σ(δt)~1τ S => 6mm (LOE) Red hist: σ(δt)~1/4 τ S => 1.5mm (LOE + inner tracker) Blue curve: ideal Theoretical distribution Δt/τ S Reconstructed distribution (MC) Δt/τ S

φ S L π + π π + π : test of quantum coherence The decoherence parameter ζ depends on the basis in which the spontaneous factorization mechanism is specified: ζ = 0 (QM) ζ = 1 (total decoherence) S L basis η + = π + π T L π + π T S ~ 10 3 i = 1 [ 2 S L L ] S S L or L S I π + π,π + π T i 2 I π + π T S π + π T L 2 suppressed by CP violation suppressed by CP violation 0 0 basis π + π T 0 π + π T 0 ~ 1 i = 1 [ 2 0 0 0 0 ] 0 0 or 0 0 I π + π,π + π T i 2 I π + π T 0 π + π T 0 2 suppressed by CP violation => intuitive explanation of the high sensitivity to not suppressed by CP violation

Neutral kaons more than 60 years history 1947 : first 0 observation in cloud chamber (V particle) 1955 : introduction of Strangeness (Gell-Mann, Nishijima) 0, 0 are two distinct particles (Gell-Mann, Pais) the θ 0 must be considered as a "particle mixture" exhibiting two distinct lifetimes, that each lifetime is associated with a different set of decay modes, and that no more than half of all θ 0 's undergo the familiar decay into two pions. (superposition principle) 1955 prediction of regeneration of short-lived particle (Pais, Piccioni) 1956 Observation of long lived L (BNL Cosmotron) 1960: Δm = m L -m S measured from regeneration 1964: discovery of CP violation (Cronin, Fitch, ) 1970 : suppression of FCNC, L à µµ - GIM mechanism/charm hypothesis 1972 : obayashi Maskawa six quark model: CP violation explained in SM 1992-2000 : CPLear: 0, 0 time evolution, decays, asymmetries 1999-2003 : TeV and NA48 : direct CP violation proved : ε /ε 0 2000 : DaΦne first Φ factory enters in operation: entangled pairs copiously produced 2000-2006: LOE: V us and precision tests of the SM CM unitarity and lepton universality, CPT and QM tests.

CPT test: standard picture Re(δ) Test of CPT in the time evolution of neutral kaons using the semileptonic asymmetry (CPLEAR experiment - CERN) 0 τ=0 τ e + ν π Rδ = (0.30 ± 0.33 ± 0.06) 10-3 PLB444 (1998) 52

CPT test: the Bell-Steinberger relation Unitarity constraint:

CPT test: the Bell-Steinberger relation Unitarity constraint: All measurable quantities: branching ratios of main kaon decays, τ S, τ L, (from LOE, CPLEAR, TeV, NA48 experiments)

CPT test: the Bell-Steinberger relation Unitarity constraint: Recent TeV result: Im δ =( 1.5 ± 1.6) 10 5 PRD 83, 092001 (2011) All measurable quantities: branching ratios of main kaon decays, τ S, τ L, (from LOE, CPLEAR, TeV, NA48 experiments)

CPT test: the standard picture " = 1 2 ( m 0 # m ) 0 # ( i 2) ( $ 0 # $ ) 0 %m + i%$/2 (" 0 # " ) 0 ( 10 #18 GeV) Combining Reδ and Imδ results Re δ =(0.30 ± 0.33) 10 3 Im δ =( 1.5 ± 1.6) 10 5 Assuming, i.e. no CPT viol. in decay: ( m 0 " m 0 ) ( 10 "18 GeV) m 0 " m 0 < 4.8 #10 "19 GeV at 95% c.l.

Exploiting neutral kaon interferometry i = 1 [ 2 0 0 " 0 0 ] η i = η i e iφ i = f i T L f i T S ( ) η 1 2 I f 1, f 2 ;Δt { e Γ L Δt + η 2 2e Γ S Δt 2η 1 η 2 e ( Γ S +Γ )Δt / 2 L cos ( ΔmΔt + φ φ )} 2 1 π + π t 1 t 2 ( 1) η + ( ) ε ( ) = ε 1 δ + p,t ( ) = ε 1 δ p,t η + 2 φ π + π ( ) ε ( ) I(Δt) (a.u) Δt/τ S

Exploiting neutral kaon interferometry i = 1 [ 2 0 0 " 0 0 ] η i = η i e iφ i = f i T L f i T S ( ) η 1 2 I f 1, f 2 ;Δt { e Γ L Δt + η 2 2e Γ S Δt 2η 1 η 2 e ( Γ S +Γ )Δt / 2 L cos ( ΔmΔt + φ φ )} 2 1 π + π t 1 t 2 ( 1) η + = ε 1 δ + p,t ( ) = ε 1 δ p,t η + 2 φ π + ( ) I Δδ ε π ( ) ε ( ) ( ) ε ( ) from the asymmetry at small Δt I(Δt) (a.u) R( Δδ ε) 0 because Δδ ε from the asymmetry at large Δt Δt/τ S

Refining method & techniques δ = isinφ SW e iφ SW γ ( ) /Δm Δa 0 β Δa Possible effects due to Δa 0 are washed out in the simple forward backward analysis (integration in φ). β Κ1 The quadrant analysis (kaons with γ Κ1 γ Κ2 ) recovers sensitivity to Δa 0 β Κ2 OLD Refined techniques used to select and analyse data: improvement in the Δt resolution tails, and improved sensitivity on CPTV parameters 42 LNF S.C. - 6/6/2011 66

From LOE to LOE-2: γγ taggers LET: E e ~ 160-230 MeV Ø Inside LOE detector Ø LYSO+SiPM Ø σ E <10% for E>150 MeV HET: E e > 400 MeV LOE Ø 11 m from IP Ø Scintillator hodoscopes Ø σ E ~ 2.5 MeV Ø σ T ~ 200 ps γγ taggers are installed and ready for the LOE-2 run

From LOE to LOE-2: IP detectors Major detector upgrades ready in fall 2012, start install. end 2012: INNER TRACER Ø 4 layers of cylindrical triple GEM Ø Better vertex reconstruction near IP Ø Larger acceptance for low p t tracks QCALT Ø W + scintillator tiles + SiPM/WLS Ø Low-beta quadrupoles: coverage for L decays CCALT Ø LYSO + SiPM Ø Increase acceptance for γ s from IP (21 10 )

DAΦNE luminosity upgrade Crabbed waist scheme at DAΦNE NEW COLLISION SCHEME: Large Piwinski angle Crab-Waist compensation SXTs Old collision scheme max. expected at LOE-2 : L int ~ 20 pb -1 /day x 200 dd/year = 4 fb -1 /year