Experimental tests of CPT symmetry and quantum mechanics in the neutral kaon system

Transcription

1 Experimental tests of CPT symmetry and quantum mechanics in the neutral kaon system Antonio Di Domenico Dipartimento di Fisica Università di Roma a apienza and INFN sezione di Roma Italy eminar at Institute of Physics Jagiellonian University October 8 th 8 Cracow Poland

2 CPT: introduction The three discrete symmetries of QM C (charge conjugation) P (parity) and T (time reversal) are known to be violated in nature both singly and in pairs. Only CPT appears to be an exact symmetry of nature. CPT theorem (uders Jost Pauli Bell ): Exact CPT invariance holds for any quantum field theory (flat space-time) which assumes: () orentz invariance () ocality (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 neutral kaon system offers unique possibilities to test CPT invariance e.g. : m m m < 8 m m B B m B < 4 m p m p m p < 8 eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

3 ) tandard tests of CPT symmetry in the neutral kaon system eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

4 The neutral kaon system { } The time evolution of a two-component state vector Ψ in the space is given by (Wigner-Weisskopf approximation): i Ψ() t HΨ() t t H is the effective hamiltonian (non-hermitian) decomposed into a Hermitian Part (mass matrix M) and an anti-hermitian part (i/ decay matrix Γ) : Diagonalizing the effective Hamiltonian: eigenvalues λ m Γ iλ t () t e ( ) i H τ ~ 9 ps τ ~ 5 ns m -m 3.5 x -5 GeV ~ Γ / M i Γ m m m m [ ] ( ) ( ) ε ( ) ± ε ε Γ i Γ ( ) [ ] ε ε Γ Γ eigenstates > are CP± states small CP impurity ~ x -3 eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

5 CPT violation in the neutral kaon system: standard picture CPT violation in the mixing: ε ε ± δ ε H H iim IΓ ( λ λ ) Δm iδγ/ δ H ( λ λ ) ( m m ) ( i )( Γ Γ ) H Δm iδγ/ δ implies CPT violation ε implies T violation ε or δ implies CP violation (with a phase convention IΓ ) m Γ Δm m Γ m m Γ m Γ m ΔΓ Γ Γ eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

6 eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland CPT violation in the neutral kaon system: standard picture d c T b a T d c T b a T l l l l CPT violation in semileptonic decays tandard Model prediction of ΔΔQ rule violation is xc/a ~ O( -7 ) ( ) ( ) ( ) ( ) R ± R R ± R Γ Γ Γ Γ x y e e e e A δ ε emileptonic charge asymmetry: l l l l ΔΔQ rule ( ) R R x A A δ 4 CP T CPT ΔΔQ a I I b R I c I I d R I

7 eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland CPT violation in the neutral kaon system: standard picture d c T b a T d c T b a T l l l l CPT violation in semileptonic decays a c x a d x a b y CPT viol. CPT & ΔΔQ viol. ΔΔQ Viol. tandard Model prediction of ΔΔQ rule violation is xc/a ~ O( -7 ) ( ) ( ) ( ) ( ) R ± R R ± R Γ Γ Γ Γ x y e e e e A δ ε emileptonic charge asymmetry: l l l l ΔΔQ rule ( ) R R x A A δ 4

8 CPT violation in the neutral kaon system: standard picture CPT violation in decays ; I ; I T T ( A B ) iδi ( A B ) e A I (B I ) CPT conserving (violating) amplitudes for I (δ I strong phase shift for I) Im (not to scale) I I -ε η η ε ε φ φ φ W I I e -Δ iδ I Re φ φ η η φ η e iφ iφ η e ε Δ T RB Δ δ RA φ W 3 η - η RA RA T φ T T m m Δm ε Δ ε ε ( Δ ΔΓ) arctan m W RB RA RB RA RB RA ε 3I ε eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

9 ome results of CPT tests tudy of the time evolution of CPEAR neutral kaons in semileptonic decays e Rδ (.3 ±.33 ±.6) 3 PB444 (998) 5 τ τ TeV tudy of regenerator beam two pion decay distribution φ - - φ W.6º ±.6º ±. º φ -φ -.39º ±. º ±.45 º PR88 86() semileptonic charge asymmetry: A ( 33 ± 58 ± 47 ) -6 TeV Constraints on CPT violation in and semileptonic decays obtained combining TeV and PDG results: R A η η R 3 3 y x RA RB 6 ( 3± 35) PRD675 (3) eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

10 ome results of CPT tests tudy of the time evolution of CPEAR neutral kaons in semileptonic decays e Rδ (.3 ±.33 ±.6) 3 PB444 (998) 5 τ τ TeV tudy of regenerator beam two pion decay distribution φ ε - φ W.4º ±.56º φ -φ -.3º ±.35º Presented at Moriond8 HQ8 semileptonic charge asymmetry: A ( 33 ± 58 ± 47 ) -6 TeV Constraints on CPT violation in and semileptonic decays obtained combining TeV and PDG results: R A η η R 3 3 y x RA RB 6 ( 3± 35) PRD675 (3) eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

11 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 9.4 MeV BR(φ ) ~ 34% ~ 6 neutral kaon pairs per pb - produced in an i antisymmetric quantum state with J PC : p MeV/c λ 6 mm λ 3.5 m N e [ ( p) ( p) ( p) ( p) ] r r r r [ ( p) ( p) ( p) ( p) ] r N e - φ r ( )( ) ε ε ( ε ε ) r r The detection of a kaon at large (small) times tags a ( ) possibility to select a pure beam (unique at a φ-factory not possible at fixed target experiments) eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

12 DAΦNE: the Frascati φ-factory Integrated luminosity (OE) Day performance: 7-8 pb - Best month dt ~ pb Total OE dt ~.5 fb ( - 5) ~.5 9 pairs eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

13 The OE detector at DAΦNE uperconducting coil B.5 T Calorimeter ead/scintillating fiber 488 PMTs 98% coverage of solid angle σ E /E 5.7% / E(GeV) σ t 54 ps / E(GeV) 5 ps (relative time between clusters) σ γγ ~ cm ( from ) Drift chamber σ p /p.4 % (tracks with θ > 45 ) σ x hit 5 μm (xy) mm (z) σ x vertex ~ mm 4 m diameter 3.3 m length 9% helium % isobutane 58/54 sense/total wires All-stereo geometry eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

14 and Tagging at OE crash β. (TOF) e tagged by interaction in EmC Efficiency ~ 3% (largely geometrical) angular resolution: ~ (.3 in φ) momentum resolution: ~ MeV tagged by vertex at IP Efficiency ~ 7% (mainly geometrical) angular resolution: ~ momentum resolution: ~ MeV eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

15 e: OE results Data sample: 4 pb - PB 636(6) 73 BR( e ) (3.58 ±.57 ±.7) 4 BR( e ) (3.57 ±.5 ±.9) 4 BR( e) (7.46 ±.76 ±.5) 4 BR(e) [OE 7 pb ]: (6.9 ±.34 ±.5) 4 E miss -P miss eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

16 e: OE results Data sample: 4 pb - PB 636(6) 73 BR( e ) (3.58 ±.57 ±.7) 4 BR( e ) (3.57 ±.5 ±.9) 4 BR( e) (7.46 ±.76 ±.5) 4 A A A 4 E miss -P miss A 4 ε ( Rδ x ) R ( R Ry ) input from other experiments BR(e) [OE 7 pb ]: (6.9 ±.34 ±.5) 4 A Γ Γ ( ) ( ) e Γ e ( ) ( e Γ e ) A (.5 ± 9.6 ±.9 ) 3 with.5 fb : δa 3 3 Re ε Rx (.8 ±.4 ±.7) 3 Ry (.4 ±.4 ±.7) 3 eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland CPT & ΔΔQ viol. CPT viol.

17 eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland CPT test: the Bell-teinberger relation ( ) ( ) ( ) ( ) I R I R i i i i W W k k k b k N δ ε ε α α φ φ tan tan α η BR( ) α η BR( ) α kl3 τ /τ BR( l3) [(A A )/4 i Im x ] α τ /τ η BR( ) α τ /τ η BR( ) ( ) ( ) ( ) ( ) k bk k k N BR b k W tan φ τ τ l i i i T f T f η () f t T f a T f a t dt d a a Γ Γ I R Γ Γ Γ Γ f W T f T f i i tan δ ε ε φ Unitarity constraint: observables

18 Experimental inputs to the Bell-teinberger relation Main improvements done with OE measurements on semileptonic and 3 decays eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

19 CPT test: the Bell-teinberger relation OE result: JHEP(6) Re ε (59.6 ±.3) 5 Im δ (.4 ±.) 5 CPEAR: study of the time evolution of neutral kaons in semileptonic decays Rδ (.3 ±.33 ±.6) 3 PB444 (998) 5 Combining Reδ and Imδ results: δ ( m m ) ( i )( Γ Γ ) Δm iδγ/ ( Γ ) Γ GeV C C Imδ ( Γ ) Γ Assuming i.e. no CPT viol. in decay: < m m < GeV at 95% c.l. ( m ) m M Reδ GeV - eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

20 CPT test: the Bell-teinberger relation M. Palutan presented at FAVIANET aon ws 8 (prelim.): Re ε (6. ±.6) 5 Im δ (. ±.4) 5 ( using new TeV results on φ : Moriond EW 8 HQ8) Combining Reδ and Imδ results: δ ( m m ) ( i )( Γ Γ ) Δm iδγ/ CPEAR: study of the time evolution of neutral kaons in semileptonic decays Rδ (.3 ±.33 ±.6) 3 ( Γ ) Γ PB444 (998) 5 Imδ ( Γ ) Γ Assuming i.e. no CPT viol. in decay: m m < 4. 9 GeV at 95% C.. ( m ) m Reδ eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

21 ) earch for decoherence and CPT violation in the neutral kaon system eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

22 Neutral kaon interferometry Double differential time distribution: I ( ) { f t ; f t C η η η e e Γ t Γ t η e Γ ( Γ )( )/ cos ( ) Γ t t Δm t t t Γ t [ φ φ ]} where t (t ) is the proper time of one (the other) kaon decay into f (f ) final state and: η η i i C N i iφ e i N r r r r [ ( p) ( p) ( p) ( p) ] f f T i T f f i l 3 γ..etc T f i T f t t φ Δtt -t characteristic interference term at a φ-factory > interferometry f eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

23 Neutral kaon interferometry Integrating in (t t ) we get the time difference (Δtt -t ) distribution (-dim plot simpler to manipulate than -dim plot): I ( ) { C f f ; Δt for Δt η < Γ Γ η η Δt e e Γ ( Γ Γ ) Δt / cos( ΔmΔt )} φ φ Δt Δt η and e Γ From these distributions for various final states f i one can measure the following quantities: Phases (difference of) from the ( ) interference term > Γ Γ Δm η i φi arg η i interferometry Δt eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

24 Neutral kaon interferometry: main observables I(Δt) (a.u) I(Δt) (a.u) φ l l I(Δt) (a.u) l l φ Δt/τ φ Δt/τ l Δt/τ eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

25 i φ Δt t -t [ ] t t φ I(Δt) (a.u) ame final state for both kaons: f f Δt/τ eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

26 i φ Δt t -t EPR correlation: [ ] t φ t no simultaneous decays (Δt) in the same final state due to the destructive quantum interference I(Δt) (a.u) ame final state for both kaons: f f t φ t t Δt/τ eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

27 i φ Δt t -t EPR correlation: [ ] t φ t no simultaneous decays (Δt) in the same final state due to the destructive quantum interference I(Δt) (a.u) ame final state for both kaons: f f t φ t t Δt/τ eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

28 eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland ( ) ( ) ( ) ( ) ( ) Δ Δ R Δ Δ Δ t t t t t I N ; φ : test of quantum coherence [ ] i Feynman described the phenomenon of interference as containing the only mistery of quantum mechanics

29 eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland ( ) ( ) ( ) ( ) ( ) ( ) Δ Δ R Δ Δ Δ t t t t t I N ; ζ φ : test of quantum coherence [ ] i Feynman described the phenomenon of interference as containing the only mistery of quantum mechanics

30 eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland ( ) ( ) ( ) ( ) ( ) ( ) Δ Δ R Δ Δ Δ t t t t t I N ; ζ φ : test of quantum coherence [ ] i decoherence total QM ζ ζ Decoherence parameter: (also known as Furry's hypothesis or spontaneous factorization) [W.Furry PR 49 (936) 393] Feynman described the phenomenon of interference as containing the only mistery of quantum mechanics

31 φ : test of quantum coherence Analysed data: 38 pb Fit including Δt resolution and efficiency effects regeneration Γ Γ Δm fixed from PDG OE result: ζ PB 64(6) 35 6 (. ±. ±.4 ) TAT YT as CP viol. O( η ) 6 > high sensitivity to ζ Data - - inc. regeneration e e From CPEAR data Bertlmann et al. (PR D6 (999) 43) obtain: ζ.4 ±.7 In the B-meson system BEE coll. (PR 99 (7) 38) obtains: ζ B.9 ± t/ s eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

32 φ : test of quantum coherence Analysed data: 38 pb Fit including Δt resolution and efficiency effects regeneration Γ Γ Δm fixed from PDG OE result: ζ PB 64(6) 35 6 (. ±. ±.4 ) TAT YT as CP viol. O( η ) 6 > high sensitivity to ζ Data - - inc. regeneration e e From CPEAR data Bertlmann et al. (PR D6 (999) 43) obtain: ζ.4 ±.7 In the B-meson system BEE coll. (PR 99 (7) 38) obtains: ζ B.9 ± t/ s eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

33 φ : test of quantum coherence Analysed data: 38 pb Fit including Δt resolution and efficiency effects regeneration Γ Γ Δm fixed from PDG OE result: ζ PB 64(6) 35 6 (. ±. ±.4 ) TAT YT as CP viol. O( η ) 6 > high sensitivity to ζ Data - - inc. regeneration e e From CPEAR data Bertlmann et al. (PR D6 (999) 43) obtain: ζ.4 ±.7 In the B-meson system BEE coll. (PR 99 (7) 38) obtains: ζ B.9 ± t/ s eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

34 Analysed data: 38 fb - pb(5 data) Fit including Δt resolution and efficiency effects regeneration Γ Γ Δm fixed from PDG OE preliminary: ζ φ : test of quantum coherence From CPEAR data Bertlmann et al. (PR D6 (999) 43) obtain: ζ.4 ±.7 In the B-meson system BEE coll. (PR 99 (7) 38) obtains: ζ B 6 (.3 ±. ) TAT as CP viol. O( η ) 6 > high sensitivity to ζ.9 ±.57 eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

35 Analysed data: 38 fb - pb(5 data) Fit including Δt resolution and efficiency effects regeneration Γ Γ Δm fixed from PDG OE preliminary: ζ φ : test of quantum coherence From CPEAR data Bertlmann et al. (PR D6 (999) 43) obtain: ζ.4 ±.7 In the B-meson system BEE coll. (PR 99 (7) 38) obtains: ζ B 6 (.3 ±. ) TAT as CP viol. O( η ) 6 > high sensitivity to ζ.9 ±.57 Comparison with quantum optics test precisions eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

36 Decoherence and CPT violation Modified iouville von Neumann equation for the density matrix of the kaon system: & ρ () t ih ρ iρ H ( ρ ) QM extra term inducing decoherence: pure state > mixed state eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

37 Decoherence and CPT violation Modified iouville von Neumann equation for the density matrix of the kaon system: & ρ () t ih ρ iρ H ( ρ ) QM 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 [] 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 []. J. Ellis et al.[3-6] > model of decoherence for neutral kaons > 3 new CPTV param. αβγ: ( ρ ) ( ρ; α β γ ) α γ > αγ > β At most: α β γ O M M PANC GeV [] Hawking Comm.Math.Phys.87 (98) 395; [] Wald PR D (98) 74;[3] Ellis et. al NP B4 (984) 38; PRD53 (996)3846 [4] Huet Peskin NP B434 (995) 3; [5] Benatti Floreanini NPB5 (998) 55 [6] Bernabeu Ellis Mavromatos Nanopoulos Papavassiliou: Handbook on kaon interferometry [hep-ph/673] eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

38 Decoherence and CPT violation Modified iouville von Neumann equation for the density matrix of the kaon system: & ρ () t ih ρ iρ H ( ρ ) QM extra term inducing decoherence: pure state > mixed state Possible decoherence due quantum gravity effects: Black hole information J.A. loss paradox Wheeler > Possible PACE-TIME decoherence FOAM near a black hole. Hawking [] 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 []. J. Ellis et al.[3-6] > model of decoherence for neutral kaons > 3 new CPTV param. αβγ: ( ρ ) ( ρ; α β γ ) α γ > αγ > β At most: α β γ O -35 m M M PANC GeV [] Hawking Comm.Math.Phys.87 (98) 395; [] Wald PR D (98) 74;[3] Ellis et. al NP B4 (984) 38; PRD53 (996)3846 [4] Huet Peskin NP B434 (995) 3; [5] Benatti Floreanini NPB5 (998) 55 [6] Bernabeu Ellis Mavromatos Nanopoulos Papavassiliou: Handbook on kaon interferometry [hep-ph/673] eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

39 Decoherence and CPT violation Modified iouville von Neumann equation for the density matrix of the kaon system: & ρ () t ih ρ iρ H ( ρ ) QM 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 [] 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 []. J. Ellis et al.[3-6] > model of decoherence for neutral kaons > 3 new CPTV param. αβγ: ( ρ ) ( ρ; α β γ ) α γ > αγ > β At most: α β γ O M M PANC GeV [] Hawking Comm.Math.Phys.87 (98) 395; [] Wald PR D (98) 74;[3] Ellis et. al NP B4 (984) 38; PRD53 (996)3846 [4] Huet Peskin NP B434 (995) 3; [5] Benatti Floreanini NPB5 (998) 55 [6] Bernabeu Ellis Mavromatos Nanopoulos Papavassiliou: Handbook on kaon interferometry [hep-ph/673] eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

40 φ : decoherence & CPTV by QG tudy of time evolution of single kaons decaying in and semileptonic final state CPEAR α β γ PB (999) 7 (.5 ±.8) 9 (.5 ±.3) (.±.5) GeV GeV GeV In the complete positivity hypothesis α γ β > only one independent parameter: γ The fit with I( ;Δtγ) gives: OE result 38 pb - PB 64(6) 35 Complete positivity guarantees the positivity of the eigenvalues of density matrices describing states of correlated kaons Data - - inc. regeneration e e γ (.9..4 ) ± GeV.4 YT TAT t/ s eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

41 φ : decoherence & CPTV by QG tudy of time evolution of single kaons decaying in and semileptonic final state CPEAR α β γ PB (999) 7 (.5 ±.8) 9 (.5 ±.3) (.±.5) GeV GeV GeV Complete positivity guarantees the positivity of the eigenvalues of density matrices describing states of correlated kaons. In the complete positivity hypothesis α γ β > only one independent parameter: γ The fit with I( ;Δtγ) gives: OE preliminary fb - γ (.5.8 ) GeV.3 TAT eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

42 φ : CPT violation in correlated 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. PR 9 (4) 36 NPB744 (6) 8]. i ( ) ( ω ) ( ) ω( ) at most one expects: ω E O M ΔΓ PANC 5 ω ~ 3 In some microscopic models of space-time foam arising from non-critical string theory: [Bernabeu Mavromatos arkar PRD 74 (6) 454] 4 5 ω ~ The maximum sensitivity to ω is expected for f f All CPTV effects induced by QG (αβγω) could be simultaneously disentangled. eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

43 φ : CPT violation in correlated states Fit of I( ;Δtω): Analysed data: 38 pb - Im ω x - x Im % C 68% C OE result : Rω Iω ( 8.7. ) 5.3 ±.9 TAT YT ( ±.6 ) ω <. 5. TAT 3 PB 64(6) 35 YT at 95% C.. (ω measured for the first time) x Re ω x - Re eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

44 φ : CPT violation in correlated states Im ω x - Fit of I( ;Δtω): Analysed data: fb - (5 data) OE preliminary : Rω ( 3..5 ).3TAT 4 Iω ( 3.4. ) 3. TAT 4 ω <.98 3 at 95% C.. (ω measured for the first time) Re ω x - eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

45 3) Tests of orentz invariance and CPT symmetry in the neutral kaon system eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

46 CPT and orentz invariance violation (ME) ostelecky et al. developed a phenomenological effective model providing a framework for CPT and orentz violations based on spontaneous breaking of CPT and orentz symmetry which might happen in quantum gravity (e.g. in some models of string theory) tandard Model Extension (ME) [ostelecky PRD6 6 PRD64 76] CPT violation in neutral kaons according to ME: CPTV only in mixing not in decay at first order (i.e. B I y x - ) δ cannot be a constant (momentum dependence) ε ε ± δ r iφ r W δ i sinφwe γ / ( Δa β Δa) Δm where Δa μ are four parameters associated to ME lagrangian terms and related to CPT and orentz violation. eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

47 CPT and orentz invariance violation (ME) ( r i e a a) iφ r W δ sinφw γ Δ β Δ / 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: δ r ( p θ t) δ ( p t) iφw i sinφwe γ [ Δa β Δa Δm β Δa sin χ cosθ sin Ωt β Δa Y X r dφ sin χ cosθ cosω t] Z cos χ cosθ (in general z lab. axis is non-normal to Earth s surface) Ω: Earth s sidereal frequency χ : angle between the z lab. axis and the Earth s rotation axis eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

48 CPT and orentz invariance violation (ME) ( r i e a a) iφ r W δ sinφw γ Δ β Δ / 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: δ r ( p θ t) δ ( p t) iφw i sinφwe γ [ Δa β Δa Δm β Δa sin χ cosθ sin Ωt β Δa Y X r dφ sin χ cosθ cosω t] Z cos χ cosθ At DAΦNE mesons are produced with angular distribution dn/dω sin θ ẑ e e - Ω: Earth s sidereal frequency χ : angle between the z lab. axis and the Earth s rotation axis eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

49 Measurement of Δa μ at OE Δa from semileptonic asymmetries A (with symmetric polar angle θ and sidereal time t integration) with 4 pb - (preliminary): A A 4R Δa ( iφ isin e ) W φ W Δm γ Δa ( ) 7.4 ±.8 GeV η Δa XYZ from with.5 fb - : σ(δa ) ~ 7-8 GeV ε δ cosθ< φ ( p θt) θ cosθ> (analysis vs polar angle θ and sidereal time t) Fit to: I[ (cosθ>) (cosθ<);δt] at Δt~τ s sensitive to Im(δ/ε) Δa Δa Δa With fb - ( 6.3 ± 6.) (.8 ± 5.9) eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland (Δa evaluated for the first time) X Y Z (preliminary): 8 8 GeV GeV ( ) 8.4 ± 9.7 GeV TeV :Δa X Δa Y < % C BABAR Δa B xy (ΔaB.3 ΔaB Z )~O(-3 GeV) [PR (8) 38]

50 Measurement of Δa μ at OE Δa from semileptonic asymmetries A (with symmetric polar angle θ and sidereal time t integration) with 4 pb - (preliminary): A A 4R Δa ( iφ isin e ) W φ W Δm γ Δa ( ) 7.4 ±.8 GeV η Δa XYZ from with.5 fb - : σ(δa ) ~ 7-8 GeV ε δ cosθ< φ ( p θt) θ Δt/τcosθ> (analysis vs polar angle θ and sidereal time t) Fit to:. I[ - 4. sidereal (cosθ>) hours (cosθ<);δt] at Δt~τ s sensitive to Im(δ/ε) Δa Δa Δa With fb - ( 6.3 ± 6.) (.8 ± 5.9) eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland (Δa evaluated for the first time) X Y Z (preliminary): 8 8 GeV GeV ( ) 8.4 ± 9.7 GeV TeV :Δa X Δa Y < % C BABAR Δa B xy (ΔaB.3 ΔaB Z )~O(-3 GeV) [PR (8) 38]

51 4) Future plans eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

52 OE- at upgraded DAΦNE Proposals to upgrade DAΦNE in luminosity (and energy): Crabbed waist scheme at DAΦNE (proposal by P. Raimondi) - increase by a factor O(5) - Experimental test at DAΦNE in progress - requires minor modifications - relatively low cost OE- Proposal: Physics issues: Neutral kaon interferometry CPT symmetry & QM tests aon physics CM FV rare decays ηη physics ight scalars γγ physics Hadron cross section at low energy muon anomaly (baryon electromagnetic form factors e e - pp nn ΛΛ) - phase : OE should restart taking data mid 9 with a minimal upgrade - phase : full OE upgrade (OE-) (?) Detector upgrade issues: Inner tracker R&D γγ tagging system Calorimeter increase of granularity FEE maintenance and upgrade Computing and networking update etc.. (Triggersoftware ) eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

53 Perspectives with OE- at upgraded DAΦNE Mode Test of Param. Present best published measurement OE- 5 fb - e CP CPT A (.5 ± ) -3 ± -3 e CP CPT A ( 33 ± 58 ± 47 ) -6 ± 5-6 CP Re(ε /ε) (.65 ±.6) -3 (*) ±. -3 CP CPT Im(ε /ε) (-. ±.3) -3 (*) ± 3-3 e e CPT Re(δ)Re(x - ) Re(δ) (.5 ±.3) -3 (*) Re(x - ) (-4. ±.7) -3 (*) e e CPT Im(δ)Im(x ) Im(δ) (-.6 ±.9) -5 (*) Im(x ) (. ±.) -3 (*) ±. -3 ± 3-3 Δm (5.88 ±.43) 9 s - ±.3 9 s - (*) PDG 8 fit eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

54 Perspectives with OE- at upgraded DAΦNE Mode Test of Param. Present best published measurement OE- 5 fb - QM ζ (. ±.) -6 ±. -6 QM ζ (.8 ± 4.) - ±. - CPT & QM α (-.5 ±.8) -7 GeV ± -7 GeV CPT & QM β (.5 ±.3) -9 GeV ±. -9 GeV CPT & QM γ (. ±.5) - GeV ±. - GeV compl. pos. hyp. ±. - GeV CPT & EPR corr. Re(ω) (. ± 7.) -4 ± -5 CPT & EPR corr. Im(ω) (3.4 ± 4.9) -4 ± -5 e CPT & orentz Δa [(.4 ±.8) -7 GeV] ± -8 GeV CPT & orentz Δa Z [(.4 ± 9.7) -8 GeV] ± 7-9 GeV e CPT & orentz Δa XY [< - GeV] ± 4-9 GeV [.] preliminary eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland

55 Conclusions The neutral kaon system is an excellent laboratory for the study of CPT symmetry and the basic principles of Quantum Mechanics; everal parameters related to possible CPT violation (within QM) CPT violation and decoherence CPT violation and orentz symmetry breaking have been measured at OE in same cases with a precision reaching the interesting Planck s scale region; All results are consistent with no CPT violation The analysis of the full OE data sample (.5 fb - ) is in being completed; OE and DAΦNE are going to be upgraded; Neutral kaon interferometry CPT symmetry and QM tests are one of the main issues of the OE- physics program eminar at Institute of Physics Jagiellonian University - October 8th 8 Cracow Poland