CPT symmetry, entanglement, and neutral kaons

Transcription

1 CPT symmetry, entanglement, and neutral kaons Antonio Di Domenico Dipartimento di Fisica, Sapienza Università di Roma and INFN sezione di Roma, Italy Seminar at Dipartimento di Fisica, Università di Trieste April 22, 2015

2 Outline - Introduction - Standard test of CPT symmetry in the neutral kaon system - Test of QM: test of quantum coherence of the entangled state - Search for decoherence and CPT violation effects - Test of Lorentz invariance and CPT symmetry - Future plans

3 CPT: introduction The three discrete symmetries of QM, C (charge conjugation: q! -q), P (parity: x! -x), and T (time reversal: t! -t) are known to be violated in nature both singly and in pairs. Only CPT appears to be an exact symmetry of nature. CPT theorem : J. Schwinger (1951) G. Lüders (1954) R. Jost (1957) W. Pauli (1952) J. Bell (1955) Exact CPT invariance holds for any quantum field theory (like the Standard Model) formulated on flat space-time 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. 3

4 CPT: introduction The three discrete symmetries of QM, C (charge conjugation: q! -q), P (parity: x! -x), and T (time reversal: t! -t) are known to be violated in nature both singly and in pairs. Only CPT appears to be an exact symmetry of nature. Intuitive justification of CPT symmetry [1]: For an even-dimensional space => reflection of all axes is equivalent to a rotation e.g. in 2-dim. space: reflection of 2 axes = rotation of π around the origin In 4-dimensional pseudo-euclidean space-time PT reflection is NOT equivalent to a rotation. Time coordinate is not exactly equivalent to space coordinate. Charge conjugation is also needed to change sign to e.g. 4-vector current j µ. (or axial 4-v). CPT (and not PT) is equivalent to a rotation in the 4-dimensional space-time [1] Khriplovich, I.B., Lamoreaux, S.K.: CP Violation Without Strangeness.

5 CPT: introduction Extension of CPT theorem to a theory of quantum gravity far from obvious. (e.g. CPT violation appears in several QG models) No predictive theory incorporating CPT violation => only phenomenological models to be constrained by experiments. Consequences of CPT symmetry: equality of masses, lifetimes, q and µ of a particle and its anti-particle. Neutral meson systems 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 K system m K 0 m K 0 m K < neutral B system m B 0 m B 0 m B < proton- anti-proton m p m p m p <10 8 Other interesting CPT tests: e.g. the study of anti-hydrogen atoms, etc.. 5

6 K mesons a 70 years history 1944 : first indication of a new charged particle with mass ~0.5 GeV/c 2 in cosmic rays (Leprince-Ringuet, Lheritier) 1947 : first K 0 observation in cloud chamber - V particle (Rochester, Butler) 1955 : introduction of Strangeness (Gell-Mann, Nishijima) K 0, K 0 are two distinct particles (Gell-Mann, Pais) 1955 prediction of regeneration of short-lived particle (Pais, Piccioni) 1956 Observation of long lived K L (BNL Cosmotron) 1957 τ-θ puzzle on spin-parity assignment, P violation in weak interactions 1960: Δm = m L -m S measured from regeneration 1964: discovery of CP violation (Cronin, Fitch, ) 1970 : suppression of FCNC, K L!µµ - GIM mechanism/charm hypothesis 1972 : Kobayashi Maskawa six quark model: CP violation explained in SM : CPLear: K 0, K 0 time evolution and decays, T, CP, CPT tests : KTeV and NA48 (prev. E731 and NA31): direct CP violation proven : ε /ε : NA48/2: charged kaon beam, search for direct CP viol : KLOE at DaΦne: first Φ factory enters in operation, V us and precision tests of the SM, entangled neutral K pairs and CPT and QM tests. 6

7 The neutral kaon: a two-level quantum system S=+1 K 0 K 0 s d s d S=-1 T. D. Lee One of the most intriguing physical systems in Nature Neutral K mesons are a unique physical system which appears to be created by nature to demonstrate, in the most impressive manner, a number of spectacular phenomena.... If the K mesons did not exist, they should have been invented on purpose in order to teach students the principles of quantum mechanics Lev B. Okun 7

8 The neutral kaon: a two-level quantum system K 0 and K 0 can decay to common final states due to weak interactions: strangeness oscillations π K 0 + π + K 0 S=+1 K 0 K 0 s d ππ s d S=-1 π - π - P[ K 0 ( t = 0) K 0 ] P( K 0 (0) K 0 (t)) = 1 4 e Γ Lt + e Γ St { +2e ( Γ S+Γ )t/2 L cos[ Δm t]} P[ K 0 ( t = 0) K 0 ] P( K 0 (0) K 0 (t)) = 1 4 e Γ Lt + e Γ St { 2e ( Γ S+Γ )t/2 L cos[ Δm t]} t( 1/Γ S ) 8

9 The neutral kaon: a two-level quantum system K 0 and K 0 can decay to common final states due to weak interactions: strangeness oscillations π K 0 + π + K 0 S=+1 K 0 K 0 s d ππ s d S=-1 π - π - P[ K 0 ( t = 0) K 0 ] K S ω S K L ω L P[ K 0 ( t = 0) K 0 ] K 0 ω=m 0 K 0 t( 1/Γ S ) 9

10 The neutral kaon: a two-level quantum system ψ( 0) = a( 0) K 0 + b( 0) K 0 ψ( t) = a( t) K 0 + b( t) K 0 initial state { K 0,K 0 } The time evolution of a two-component state vector Φ in the subspace (for times >> the strong interaction formation time) is given by (Wigner-Weisskopf approximation): i t Φ( t) = HΦ( t) 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 H = M i # 2 Γ = M 11 M 12 % $ M 21 M 22 λ S = m S i 2 Γ S, λ L = m L i 2 Γ L!# #" ### $ + c k t & ( i # ' 2 % $ ( ) Φ t Γ 11 Γ 12 Γ 21 Γ 22 eigenstates K S,L & ( ' k ( ) f k decay final states ( t) = e iλ S,L t K S,L ( 0) 10

11 The neutral kaon: a two-level quantum system ψ( 0) = a( 0) K 0 + b( 0) K 0 ψ( t) = a( t) K 0 + b( t) K 0 initial state { K 0,K 0 } The time evolution of a two-component state vector Φ in the subspace (for times >> the strong interaction formation time) is given by (Wigner-Weisskopf approximation): i t Φ( t) = HΦ( t) 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) : M ij = M 0 δ ij + i H wk j + P ( ) i Hwk f f H wk j M 0 E H f f Γ ij = 2π ij = M ij i 2 Γ ij i H wk f f H wk j δ(m 0 E f ) f Diagonalizing the effective Hamiltonian: eigenvalues λ S = m S i 2 Γ S, λ L = m L i 2 Γ L!# #" ### $ + c k t ( ) Φ t eigenstates K S,L k ( ) f k decay final states ( t) = e iλ S,L t K S,L ( 0) 11

12 The neutral kaon: a two-level quantum system Strangeness (flavor) eigenstates: K 0, K 0 K S = 1 2( 2 1+ ε ) S CP eigenstates: K 1 = 1 [ 2 K 0 + K 0 ], K 2 = 1 [ 2 K 0 K 0 ] S = +1 S = -1 CP = +1 CP = -1 The physical states (eigenstates of H): ( 1+ε S ) K ε S ( ) K 0 [ ] = 1 ( 2 1+ ε ) S [ K 1 +ε S K 2 ] K L = 1 2( 2 1+ ε ) L ( 1+ε L ) K 0 1 ε L ( ) K 0 [ ] = 1 ( 2 1+ ε ) L [ K 2 +ε L K 1 ] Short lifetime τ S ~ 90 ps ε S = ε +δ CP violation: K S K L ε S +ε L 0 ε L = ε δ Long lifetime τ L ~ ps ε CPT violation: δ <~

13 K-spin Z K 0 How to detect a K-spin? Active measurement strong interactions with a thin absorber Passive measurement semileptonic decay (ΔS=ΔQ rule) Passive measurement K 1 or K 2 can be identified via 2π or 3π decay (ε neglected) Z K 0 X K 1 = K 0 (K 0 ) K 0 K 1 K + (K - or Λ) π + (π 0 ) π - (π 0 ) e + ν π - K K K K 2 p p K + n K K 0 ( 12 K 0 + K 0 ) X K 2 = 1 ( 2 K 0 K 0 ) + + Λ + n p + ( p + π ) + π π + ν e - π 0 π 0 π 0 13

14 CPT violation: standard picture CP violation: T violation: ε S, L = ε ± δ ε = H H ( λ S λ L ) = iim IΓ Δm + iδγ / 2 CPT violation: δ = H H ( λ S λ L ) = 1 2 ( m K 0 m ) K 0 ( i 2) ( Γ K 0 Γ ) K 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 IΓ 12 = 0 ) Δm = m L m S, ΔΓ = Γ S Γ L Δm = GeV ΔΓ Γ S 2Δm = GeV 14

15 neutral kaons vs other oscillating meson systems <m> (GeV) Δm (GeV) <Γ> (GeV) ΔΓ/2 (GeV) K x x x10-15 D x x x10-14 B 0 d 5.3 3x x10-13 O(10-15 ) (SM prediction) B 0 s 5.4 1x x x10-14

16 Standard CPT tests 16

17 The Bell-Steinberger relationship (1965) J. Bell J. Steinberger Unitarity constraint: K dt = f yields two trivial relations: d 2 2 ( t) = a f T K + Γ S,L = f T K S,L 2 f and a not trivial one, i.e. the B-S relationship: K L K S = 2( Rε + iiδ) = t 0 S K = a K + a S S S a L L f K T L K f T K S f T K L f Sum over all possible decay products (sum over few decay products for kaons; many for B and D mesons => not easy to evaluate) i( λ S λ ) L L All observables quantities

18 Neutral kaons at CPLEAR (CERN) K 0, K 0 Pure initial are produced from antiproton annihilation at rest with a hydrogen target ( p + p) REST 0 K + K ( p + p) REST 0 + K + K ( p + p) 0 0 K + K REST + π + π + P K ~500 MeV The detection of a charged kaon tags the strangeness of the accompanying neutral kaon

19 CPT test at CPLEAR Test of CPT in the time evolution of neutral kaons using the semileptonic asymmetry Rδ = (0.30 ± 0.33 ± 0.06) 10-3 CPLEAR PLB444 (1998) 52 ( ) ( ) R + = = = = = + + = + = + + = L t t t t v e K R R v e K R R R R R R R R R R A ε α π τ π τ τ α τ τ α τ τ α τ τ α τ τ τ τ δ 4 1 ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 0 0 ) ( ) ( ) ( 0 0 ) ( δ τ τ δ R = >> 8 ) ( S A K 0 e + π - ν τ=0 τ K 0

20 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) PDG fit (2014) ( m K 0 m ) K 0 ( i 2) ( Γ K 0 Γ ) K 0 δ = 1 2 Δm + iδγ/2 Combining Reδ and Imδ results Assuming Im δ =(-0.7 ± 1.4) 10-5 ( Γ ) K 0 Γ 0 = 0 K ( Γ K 0 Γ ) K 0 ( GeV), i.e. no CPT viol. in decay: K 0 τ=0 τ e + ν π - " f T K S f T K $ ) L * 2Iδ = I"# K L K S $ f % = I) * ) i( λ S λ L ) * # % m K 0 m K 0 < GeV at 95% c.l. ( m K 0 m K 0 ) ( GeV) 20

21 Entangled neutral kaon pairs 21

22 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 = MeV BR(φ K 0 K 0 ) ~ 34% ~10 6 neutral kaon pairs per pb -1 produced in an antisymmetric quantum state with J PC = 1 -- : e + i = 1 2 K 0 p K S,L e - φ K L,S ( ) K 0 ( p ) K 0 ( p ) K 0 ( p ) [ ] p K = 110 MeV/c λ S = 6 mm λ L = 3.5 m = N 2 K S( p ) K L p ( ) K L ( p ) K S ( p ) [ ] ( )( 1+ ε 2 ) L 1 ε S ε L N = 1+ ε S 2 ( ) 1 22

23 Analogy with spin ½ particles 1 = 1 [ 2 K 0 K 0 K 0 K 0 ] K 0 (t 1 ) K 0 (t 2 ) b! S = 0 = 1 2 a! A [ A A A A ] B a! θ ab b! φ ( ) = cos Δm(t 1 t 2 ) P K 0,t 1 ;K 0,t 2 ( ) [ ] ideal case with Γ S = Γ L = 0 (no decay!) ( ) = cos θ ab P A ;B Singlet (S=0) ( ) [ ] with the actual Γ S and Γ L (kaons decay!): ( ) = 1 8 e Γ L t 1 Γ S t 2 + e Γ S t 1 Γ L t 2 { P K 0,t 1 ;K 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 23

24 The KLOE detector at the Frascati φ-factory DAΦNE DAFNE collider Integrated luminosity (KLOE) KLOE detector Total KLOE L dt ~ 2.5 fb -1 ( ) ~ K S K L pairs 24

25 The KLOE detector at the Frascati φ-factory DAΦNE DAFNE collider KLOE detector Integrated luminosity (KLOE) Total KLOE L dt ~ 2.5 fb -1 ( ) ~ K S K L pairs Lead/scintillating fiber calorimeter drift chamber 4 m diameter 3.3 m length helium based gas mixture 25

26 Neutral kaon interferometry i = N 2 ( ) K L ( ) K L ( ) K S ( ) [ K S p p p p ] f 1 t 1 K S,L φ t 2 Double differential time distribution: Δt=t 1 - t 2 K L,S f2 ( ) = C 12 η 1 2e Γ L t 1 Γ S t 2 + η 2 I f 1,t 1 ; f 2,t 2 { 2e Γ S t 1 Γ L t 2 2η 1 η 2 e ( Γ S +Γ L )( t 1 +t 2 ) / 2 cos Δm t 2 t 1 [ ( ) + φ 1 φ ]} 2 where t 1 (t 2 ) is the proper time of one (the other) kaon decay into f 1 (f 2 ) final state and: η i = η i e iφ i = f i T K L f i T K S characteristic interference term at a φ-factory => interferometry C 12 = N f 1 T K S f 2 T K S From these distributions for various final states f i one can measure the following quantities: Γ S, Γ L, Δm, η i, φ i arg( η ) i

27 Neutral kaon interferometry: main observables I(Δt) (a.u) Rδ +Rx Iδ + Ix + + φ K K S L π l ν I(Δt) (a.u) π l + ν I(Δt) (a.u) φ K K S L ε ʹ R ε Δt/τ S + 0 π π π 0 π εʹ I ε Δt/τ S φ K K S L A L φ ππ ππ = 2Rε Rδ Δt/τ S Ry Rx πlν

28 Direct test of CPT symmetry in neutral kaon transitions EPR correlations at a φ-factory (or B-factory) can be exploited to study other transitions involving also orthogonal CP states K + and K - K + = K 1 (CP = +1) K = K 2 (CP = 1) π + l - ν i = 1 2 K! 0 p K 0 ( ) K 0 ( p!! [ ) K 0 ( p ) K 0 ( p! ) ]! [ ( ) K p ( ) K + ( p! ) ] = 1 2 K p! + ( ) K p! φ K 0 K - decay as filtering measurement entanglement -> preparation of state 3π 0 t 1 t 1 Δt=t 2 -t 1 28

29 Direct test of CPT symmetry in neutral kaon transitions EPR correlations at a φ-factory (or B-factory) can be exploited to study other transitions involving also orthogonal CP states K + and K - K + = K 1 (CP = +1) K = K 2 (CP = 1) π + l - ν i = 1 2 K! 0 p K 0 ( ) K 0 ( p!! [ ) K 0 ( p ) K 0 ( p! ) ]! [ ( ) K p ( ) K + ( p! ) ] = 1 2 K p! + ( ) K p! φ K 0 K - decay as filtering measurement entanglement -> preparation of state 3π 0 t 1 t 1 Δt=t 2 -t 1 K 0 K reference process 29

30 Direct test of CPT symmetry in neutral kaon transitions EPR correlations at a φ-factory (or B-factory) can be exploited to study other transitions involving also orthogonal CP states K + and K - K + = K 1 (CP = +1) K = K 2 (CP = 1) π + l - ν i = 1 2 K! 0 p K 0 ( ) K 0 ( p!! [ ) K 0 ( p ) K 0 ( p! ) ]! [ ( ) K p ( ) K + ( p! ) ] = 1 2 K p! + ( ) K p! φ K 0 K - decay as filtering measurement entanglement -> preparation of state 3π 0 t 1 t 1 Δt=t 2 -t 1 K 0 K reference process ππ K + φ K - K 0 π + l - ν t 1 t 1 Δt=t 2 -t 1 30

31 Direct test of CPT symmetry in neutral kaon transitions EPR correlations at a φ-factory (or B-factory) can be exploited to study other transitions involving also orthogonal CP states K + and K - K + = K 1 (CP = +1) K = K 2 (CP = 1) π + l - ν i = 1 2 K! 0 p K 0 ( ) K 0 ( p!! [ ) K 0 ( p ) K 0 ( p! ) ]! [ ( ) K p ( ) K + ( p! ) ] = 1 2 K p! + ( ) K p! φ K 0 K - decay as filtering measurement entanglement -> preparation of state 3π 0 t 1 t 1 Δt=t 2 -t 1 K 0 K reference process K K 0 CPT-conjugated process ππ K + φ K - K 0 π + l - ν t 1 t 1 Δt=t 2 -t 1 31

32 Direct test of CPT symmetry in neutral kaon transitions EPR correlations at a φ-factory (or B-factory) can be exploited to study other transitions involving also orthogonal CP states K + and K - K + = K 1 (CP = +1) K = K 2 (CP = 1) π + l - ν i = 1 2 K! 0 p K 0 ( ) K 0 ( p!! [ ) K 0 ( p ) K 0 ( p! ) ]! [ ( ) K p ( ) K + ( p! ) ] = 1 2 K p! + ( ) K p! φ K 0 K - decay as filtering measurement entanglement -> preparation of state 3π 0 Note: CP and T conjugated process t 1 K 0 K K K 0 ππ K + φ t 1 Δt=t 2 -t 1 K 0 K K K 0 K - K 0 reference process CPT-conjugated process π + l - ν t 1 t 1 Δt=t 2 -t 1 32

33 Direct test of CPT symmetry in neutral kaon transitions EPR correlations at a φ-factory (or B-factory) can be exploited to study other transitions involving also orthogonal CP states K + and K - K + = K 1 (CP = +1) K = K 2 (CP = 1) π + l - ν i = 1 2 K! 0 p K 0 ( ) K 0 ( p!! [ ) K 0 ( p ) K 0 ( p! ) ]! [ ( ) K p ( ) K + ( p! ) ] = 1 2 K p! + ( ) K p! φ K 0 K - decay as filtering measurement entanglement -> preparation of state 3π 0 t 1 t 1 Δt=t 2 -t 1 K 0 K reference process In general with f X decayng before f Y, i.e. Δt>0 (K X,Y = K 0, K 0, K +, K - ) : with 33

34 Direct test of CPT symmetry in neutral kaon transitions CPT symmetry test Reference CPT CPT -conjugate Transition Decay products Transition Decay products K 0 K + (l, ππ) K + K 0 (3π 0, l ) K 0 K (l, 3π 0 ) K K 0 (ππ, l ) K 0 K + (l +, ππ) K + K 0 (3π 0, l + ) K 0 K (l +, 3π 0 ) K K 0 (ππ, l + ) One can define the following ratios of probabilities: [ ] [ ] Any deviation from R i,cpt =1 constitutes a violation of CPT-symmetry J. Bernabeu, A.D.D., P. Villanueva: NPB 868 (2013) 102 J. Bernabeu, A.D.D. in preparation 34

35 Direct test of CPT symmetry in neutral kaon transitions for visualization purposes, plots with Re(δ)= Im(δ)= R exp 2,CPT R exp 2,CPT ( t) I(`, 3 0 ; t) I(, ` ; t) R exp CPT I(`+, 4,CPT ( t) 3 0 ; t) I(, `+; t) R exp 2,CPT ( t) =R 2,CPT ( t) D CPT R exp 4,CPT ( t) =R 4,CPT ( t) D CPT R exp 4,CPT R exp 2,CPT ( t) =R 1,CPT ( t ) D CPT R exp 4,CPT ( t) =R 3,CPT ( t ) D CPT, coefficients: Δt/τ S Test feasible at KLOE-2, studies in progress!! 35

36 Test of Quantum Coherence 36

37 EPR correlations in entangled neutral kaon pairs from φ i = 1 [ 2 K 0 K 0 K 0 K 0 ] Same final state for both kaons: f 1 = f 2 = π + π - π π π π t 1 t 1 φ φ t 2 t 2 =t 1 π π π π I(Δt) (a.u) EPR correlation: no simultaneous decays (Δt=0) in the same final state due to the fully destructive quantum interference Δt=t 1 -t 2 Δt/τ S 37

38 EPR correlations in entangled neutral kaon pairs from φ i = 1 [ 2 K 0 K 0 K 0 K 0 ] Same final state for both kaons: f 1 = f 2 = π + π - π π π π t 1 t 1 φ φ t 2 t 2 =t 1 π π π π I(Δt) (a.u) EPR correlation: no simultaneous decays (Δt=0) in the same final state due to the fully destructive quantum interference Δt= t 1 -t 2 Δt/τ S 38

39 EPR correlations in entangled neutral kaon pairs from φ i = 1 [ 2 K 0 K 0 K 0 K 0 ] Same final state for both kaons: f 1 = f 2 = π + π - π π π π t 1 t 1 φ φ t 2 t 2 =t 1 π π π π I(Δt) (a.u) Interference effects are a key feature of QM, the only mystery according to Feynman EPR correlation: no simultaneous decays (Δt=0) in the same final state due to the fully destructive quantum interference Δt= t 1 -t 2 => Experimental test Δt/τ S 39

40 φ K S K L π + π - π + π - : test of quantum coherence ( ) = N 2 π + π,π + π K 0 K 0 Δt I π + π,π + π ;Δt i = 1 [ 2 K 0 K 0 K 0 K 0 ] % &' ( ) 2 + π + π,π + π K 0 K 0 ( Δt) 2 ( ( ) ) *, 2R π + π,π + π K 0 K 0( Δt ) π + π,π + π K 0 K 0 Δt + 40

41 φ K S K L π + π - π + π - : test of quantum coherence ( ) = N 2 π + π,π + π K 0 K 0 Δt I π + π,π + π ;Δt i = 1 [ 2 K 0 K 0 K 0 K 0 ] % &' ( 1 ζ 00 ) 2R π + π,π + π K 0 K 0 Δt ( ) 2 + π + π,π + π K 0 K 0 ( Δt) 2 ( ( ) π + π,π + π K 0 K 0 ( Δt) ),. - 41

42 φ K S K L π + π - π + π - : test of quantum coherence ( ) = N 2 π + π,π + π K 0 K 0 Δt I π + π,π + π ;Δt i = 1 [ 2 K 0 K 0 K 0 K 0 ] % &' ( 1 ζ 00 ) 2R π + π,π + π K 0 K 0 Δt ( ) 2 + π + π,π + π K 0 K 0 ( Δt) 2 ( ( ) π + π,π + π K 0 K 0 ( Δt) ),. - Decoherence parameter: ζ 00 = 0 ζ 00 =1 QM total decoherence (also known as Furry's hypothesis or spontaneous factorization) [W.Furry, PR 49 (1936) 393] Bertlmann, Grimus, Hiesmayr PR D60 (1999) Bertlmann, Durstberger, Hiesmayr PRA (2003) 42

43 φ K S K L π + π - π + π - : test of quantum coherence ( ) = N 2 π + π,π + π K 0 K 0 Δt I π + π,π + π ;Δt i = 1 [ 2 K 0 K 0 K 0 K 0 ] % &' ( ) 2 + π + π,π + π K 0 K 0 ( Δt) 2 I(Δt) (a.u.) ( ( ) π + π,π + π K 0 K 0 ( Δt) ),. ( 1 ζ 00 ) 2R π + π,π + π K 0 K 0 Δt - ζ 00 = ζ 0 = 0 0 Δt/τ S Decoherence parameter: ζ 00 = 0 ζ 00 =1 QM total decoherence (also known as Furry's hypothesis or spontaneous factorization) [W.Furry, PR 49 (1936) 393] Bertlmann, Grimus, Hiesmayr PR D60 (1999) Bertlmann, Durstberger, Hiesmayr PRA (2003) 43

44 φ K S K L π + π - π + π - : test of quantum coherence ( ) = N 2 π + π,π + π K 0 K 0 Δt I π + π,π + π ;Δt i = 1 [ 2 K 0 K 0 K 0 K 0 ] % &' ( ) 2 + π + π,π + π K 0 K 0 ( Δt) 2 I(Δt) (a.u.) ( ( ) π + π,π + π K 0 K 0 ( Δt) ),. ( 1 ζ 00 ) 2R π + π,π + π K 0 K 0 Δt - ζ 00 = ζ 0 = 0 0 Δt/τ S Decoherence parameter: ζ 00 = 0 ζ 00 =1 QM total decoherence (also known as Furry's hypothesis or spontaneous factorization) [W.Furry, PR 49 (1936) 393] Bertlmann, Grimus, Hiesmayr PR D60 (1999) Bertlmann, Durstberger, Hiesmayr PRA (2003) 44

45 φ K S K L π + π - π + π - : test of quantum coherence Analysed data: L=1.5 fb -1 Fit including Δt resolution and efficiency effects + regeneration KLOE result: PLB 642(2006) 315 Found. Phys. 40 (2010) 852 ( ) 10 7 ζ 00 = 1.4 ± 9.5 STAT ± 3.8 SYST Observable suppressed by CP violation: η +- 2 ε => terms ζ 00 / η +- 2 => high sensitivity to ζ 00 From CPLEAR data, Bertlmann et al. (PR D60 (1999) ) obtain: ζ = 0.4 ± In the B-meson system, BELLE coll. (PRL 99 (2007) ) obtains: ζ B 00 = ±

46 φ K S K L π + π - π + π - : test of quantum coherence Analysed data: L=1.5 fb -1 Fit including Δt resolution and efficiency effects + regeneration KLOE result: PLB 642(2006) 315 Found. Phys. 40 (2010) 852 ( ) 10 7 ζ 00 = 1.4 ± 9.5 STAT ± 3.8 SYST Observable suppressed by CP violation: η +- 2 ε => terms ζ 00 / η +- 2 => high sensitivity to ζ 00 From CPLEAR data, Bertlmann et al. (PR D60 (1999) ) obtain: ζ = 0.4 ± In the B-meson system, BELLE coll. (PRL 99 (2007) ) obtains: B Best precision achievable in an entangled system ζ 00 = ±

47 φ K S K L π + π - π + π - : test of quantum coherence Analysed data: L=1.5 fb -1 Fit including Δt resolution and efficiency effects + regeneration KLOE result: PLB 642(2006) 315 Found. Phys. 40 (2010) 852 ( ) 10 7 ζ 00 = 1.4 ± 9.5 STAT ± 3.8 SYST Observable suppressed by CP violation: η +- 2 ε => terms ζ 00 / η +- 2 => high sensitivity to ζ 00 Cinelli et al. PHYSICAL REVIEW A 70, (2004) From CPLEAR data, Bertlmann et al. (PR D60 (1999) ) obtain: ζ = 0.4 ± In the B-meson system, BELLE coll. (PRL 99 (2007) ) obtains: B Best precision achievable in an entangled system ζ 00 = ± FIG. 2. Bell inequalities test. The selected state is = 1/ 2 H1,H 2 V 1,V 2. 47

48 Search for decoherence and CPT violation effects 48

49 Decoherence and CPT violation S. Hawking (1975) Possible decoherence due quantum gravity effects (BH evaporation) (apparent loss of unitarity): Black hole information loss paradox => ( like candy rolling Possible decoherence near a black hole. on the tongue by J. Wheeler ) 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]. Modified Liouville von Neumann equation for the density matrix of the kaon system with 3 new CPTV parameters α,β,γ [3]: ( ) = ihρ + iρh +!ρ t! #" ## $ QM + L( ρ;α, β,γ) extra term inducing decoherence: pure state => mixed state [1] Hawking, Comm.Math.Phys.87 (1982) 395; [2] Wald, PR D21 (1980) 2742;[3] Ellis et. al, NP B241 (1984) 381; Ellis, Mavromatos et al. PRD53 (1996)3846; Handbook on kaon interferometry [hep-ph/ ] 49

50 Decoherence and CPT violation S. Hawking (1975) Possible decoherence due quantum gravity effects (BH evaporation) (apparent loss of unitarity): Black hole information loss paradox 10 => -35 m ( like candy rolling Possible decoherence near a black hole. on the tongue by J. Wheeler ) 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]. Modified Liouville von Neumann equation for the density matrix of the kaon system with 3 new CPTV parameters α,β,γ [3]: ( ) = ihρ + iρh +!ρ t! #" ## $ QM + L( ρ;α, β,γ) extra term inducing decoherence: pure state => mixed state [1] Hawking, Comm.Math.Phys.87 (1982) 395; [2] Wald, PR D21 (1980) 2742;[3] Ellis et. al, NP B241 (1984) 381; Ellis, Mavromatos et al. PRD53 (1996)3846; Handbook on kaon interferometry [hep-ph/ ] 50

51 Decoherence and CPT violation S. Hawking (1975) Possible decoherence due quantum gravity effects (BH evaporation) (apparent loss of unitarity): Black hole information loss paradox => ( like candy rolling Possible decoherence near a black hole. on the tongue by J. Wheeler ) 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]. Modified Liouville von Neumann equation for the density matrix of the kaon system with 3 new CPTV parameters α,β,γ [3]: ( ) = ihρ + iρh +!ρ t! #" ## $ QM + L( ρ;α, β,γ) M α, β, γ = O M 2 10 [1] Hawking, Comm.Math.Phys.87 (1982) 395; [2] Wald, PR D21 (1980) 2742;[3] Ellis et. al, NP B241 (1984) 381; Ellis, Mavromatos et al. PRD53 (1996)3846; Handbook on kaon interferometry [hep-ph/ ] 2 K PLANCK 20 GeV 51

52 φ K S K L π + π - π + π - : decoherence and CPT violation Study of time evolution of single kaons decaying in π+π- and semileptonic final state CPLEAR ( ) GeV ( ) GeV ( ) 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: KLOE result L=1.5 fb -1 γ = ( 0.7 ±1.2 STAT ± 0.3 ) SYST GeV PLB 642(2006) 315 Found. Phys. 40 (2010) 852 entangled kaons 52

53 φ K S K L π + π - π + π - : CPT violation in entangled 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) , NPB744 (2006) 180]. at most one expects: i ( K 0 K 0 K 0 K 0 ) +ω( K 0 K 0 + K 0 K 0 ) ( K S K L K L K ) S +ω( K S K S K L K ) L ω 2 E M ΔΓ 2 PLANCK 5 = O 10 ω ~ 10 The maximum sensitivity to ω is expected for f 1 =f 2 =π + π - All CPTV effects induced by QG (α,β,γ,ω) could be simultaneously disentangled. 3 ω ~10 I(π + π -, π + π - ;Δt) (a.u.) 10 ω = 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) ]

54 φ K S K L π + π - π + π - : CPT violation in entangled K states Im ω x10-2 Fit of I(π + π -,π + π - ;Δt,ω): Analysed data: 1.5 fb -1 KLOE result: PLB 642(2006) 315 Found. Phys. 40 (2010) ( ) Rω = 1.6 ± STAT SYST ( ) Iω = In the B system [Alvarez, Bernabeu, Nebot JHEP 0611, 087]: Rω STAT ±1.2 SYST ω < at 95% C.L at 95% C.L. 0 Re ω x

55 CPT symmetry and Lorentz invariance test 55

56 CPT and Lorentz invariance violation (SME) " CPT theorem : Exact CPT invariance holds for any quantum field theory which assumes: (1) Lorentz invariance (2) Locality (3) Unitarity (i.e. conservation of probability). " Anti-CPT theorem (Greenberger 2002): Any unitary, local, point-particle quantum field theory that violates CPT invariance necessarily violates Lorentz invariance. " 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, , PRD64, ] CPT violation in neutral kaons according to SME: At first order CPTV appears only in mixing parameter δ (no direct CPTV in decay) δ cannot be a constant (momentum dependence) ε S, L = ε ± δ ( ) /Δm δ = isinφ SW e iφ SW γ K Δa 0! β K Δ a! where Δa µ are four parameters associated to SME lagrangian terms and related to CPT and Lorentz violation. 56

57 The Earth as a moving laboratory SUN EARTH A. Di Domenico Seminar at Dipartimento di Fisica, Università di Trieste - April 22,

58 Search for CPT and Lorentz invariance violation (SME) δ = isinφ SW e iφ SW γ K Δa 0! β K Δ a! γ Δm K { Δa 0 +β K 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: ( ) ( ) (in general z lab. axis is non-normal to Earth s surface) +β [ K Δa X sinθ sinφ + Δa Y cosθ sin χ + sinθ cosφ cos χ ]sinωt +β [ K +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 58

59 Search for CPT and Lorentz invariance violation (SME) δ = isinφ SW e iφ SW γ K Δa 0! β K Δ a! γ Δm K { Δa 0 +β K 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 K mesons are produced with angular distribution dn/dω sin 2 θ e + e - +β [ K Δa X sinθ sinφ + Δa Y cosθ sin χ + sinθ cosφ cos χ ]sinωt +β [ K +Δa Y sinθ sinφ + Δa X ( cosθ sin χ + sinθ cosφ cos χ) ]cosωt} ẑ Ω : Earth s sidereal frequency χ : angle between the z lab. axis and the Earth s rotation axis 59

60 Search for CPTV and LV: exploiting EPR correlations i = 1 [ 2 K 0 K 0 K 0 K 0 ] η i = η i e iφ i = f i T K L f i T K S ( ) η 1 2 I f 1, f 2 ;Δt { e ΓLΔt 2 + η e ΓSΔt 2 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 60

61 Search for CPTV and LV: exploiting EPR correlations i = 1 [ 2 K 0 K 0 K 0 K 0 ] η i = η i e iφ i = f i T K L f i T K S ( ) η 1 2 I f 1, f 2 ;Δt { e ΓLΔt 2 + η e ΓSΔt 2 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 61

62 Search for CPTV and LV: exploiting EPR correlations i = 1 [ 2 K 0 K 0 K 0 K 0 ] η i = η i e iφ i = f i T K L f i T K S ( ) η 1 2 I f 1, f 2 ;Δt { e ΓLΔt 2 + η e ΓSΔt 2 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 δ ε π - ( ) ε ( ) ( ) ε ( ) from the asymmetry at small Δt I(Δt) (a.u) R( δ ε) 0 because δ ε from the asymmetry at large Δt Δt/τ S 62

63 Search for CPTV and LV: results ( ) /Δm δ = isinφ SW e iφ SW γ K Δa 0! β K Δ a! Data divided in 4 sidereal time bins x 2 angular bins Simultaneous fit of the Δt distributions to extract Δa µ parameters 63

64 Search for CPTV and LV: results ( ) /Δm δ = isinφ SW e iφ SW γ K Δa 0! β K Δ a! Data divided in 4 sidereal time bins x 2 angular bins Simultaneous fit of the Δt distributions to extract Δa µ parameters with L=1.7 fb -1 KLOE final result PLB 730 (2014) Δa 0 = ( 6.0 ± 7.7 STAT ± 3.1 ) SYST GeV Δa X = ( 0.9 ±1.5 STAT ± 0.6 ) SYST GeV Δa Y = ( 2.0 ±1.5 STAT ± 0.5 ) SYST GeV Δa Z = ( 3.1±1.7 STAT ± 0.6 ) SYST GeV presently the most precise measurements in the quark sector of the SME B meson system: Δa B x,y, (ΔaB ΔaB Z ) ~O(10-13 GeV) [Babar PRL 100 (2008) ] D meson system: Δa D x,y, (ΔaD ΔaD Z ) ~O(10-13 GeV) [Focus PLB 556 (2003) 7] 64

65 Future perspectives 65

66 KLOE-2 at upgraded DAΦNE DAΦNE upgraded in luminosity: - a new scheme of the interaction region has been implemented (crabbed waist scheme) - increase of L by a factor ~ 3 demonstrated by an experimental test (without KLOE solenoid), PRL104, , KLOE-2 experiment: - extend the KLOE 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) ) Neutral kaon interferometry, CPT symmetry & QM tests Kaon physics, CKM, LFV, rare K S decays η,η physics Light scalars, γγ physics Hadron cross section at low energy, a µ Dark forces: search for light U boson Detector upgrade: γγ tagging system inner tracker small angle and quad calorimeters FEE maintenance and upgrade Computing and networking update etc.. (Trigger, software, ) 66

67 Inner tracker at KLOE I(Δt) (a.u.) MC Black: KLOE res. Red: KLOE + inner tracker res Blue: ideal Δt/τ S - Construction and installation inside KLOE completed (July 2013) - Data taking (started on Nov. 2014) and commissioning in progress 67

68 Prospects for KLOE-2 Param. Present best published measurement KLOE-2 (IT) L=5 fb -1 KLOE-2 (IT) L=10 fb -1 ζ 00 (0.1 ± 1.0) 10-6 ± ± ζ SL (0.3 ± 1.9) 10-2 ± ± α (-0.5 ± 2.8) GeV ± GeV ± GeV β (2.5 ± 2.3) GeV ± GeV ± GeV γ (1.1 ± 2.5) GeV compl. pos. hyp. ± GeV compl. pos. hyp. ± GeV compl. pos. hyp. (0.7 ± 1.2) GeV ± GeV ± GeV Re(ω) (-1.6 ± 2.6) 10-4 ± ± Im(ω) (-1.7 ± 3.4) 10-4 ± ± Δa 0 (-6.2 ± 8.8) GeV ± GeV ± GeV Δa Z (-0.7 ± 1.0) GeV ± GeV ± GeV Δa X (3.3 ± 2.2) GeV ± GeV ± GeV Δa Y (-0.7 ± 2.0) GeV ± GeV ± GeV 68

69 Conclusions The entangled neutral kaon system at a φ-factory is an excellent laboratory for the study of CPT symmetry, discrete symmetries in general, and the basic principles of Quantum Mechanics; Several parameters related to possible CPT violation Decoherence Decoherence and CPT violation CPT violation and Lorentz symmetry breaking have been measured at KLOE, in same cases with a precision reaching the interesting Planck s scale region; All results are consistent with no CPT symmetry violation and no decoherence Neutral kaon interferometry, CPT symmetry and QM tests are one of the main issues of the KLOE-2 physics program. (G. Amelino-Camelia et al. EPJC 68 (2010) ) The precision of several tests could be improved by about one order of magnitude 69