Testing discrete symmetries with kaons: status and perspectives

Antonio Di Domenico Dipartimento di Fisica, Sapienza Università di Roma and INFN sezione di Roma, Italy

DISCRETE2012 - Third Symposium on Prospects in the Physics of Discrete Symmetries, 3–7 December, 2012 CFTP, IST - Lisboa, Portugal Kaon experiments at hadron machines Fixed-target high-energy hadron beams: KTeV and NA48

Physics with K in the 90s driven by ε’/ε experiments Their legacy: The first confirmation of the CKM picture of CPV A 12% measurement of ε’/ε

(and much more: εK, CPT…) Innovative detection and analysis techniques Two state-of-the-art EM 100 physicists calorimeters 130 physicists 12 USA/Japan institutions 16 European institutions 1997-1999 Much more physics: 1998-2003 50 papers each and counting…

M. Sozzi DISCRETE2010 ± ± ± ± RK=Γ(K → e ν)/Γ(K → µ ν) : theory

0.4%

see S. Balev’s talk in the parallel session

Rare KS decays at LHCb

1 fb-1 pp at sqrt(S)=7 TeV

Yasmine Amhis LHCC open session Sep. 2012 Future kaon experiments at hadron machines The K→ πνν decays in the Standard Model

(CPV) The K→ πνν decays beyond the Standard Model Rare K decays: the full picture Switch to quantitative test of the SM; Flavour sector probing extremely high energy scales: precision frontier complementary to LHC energy frontier Some (tiny!) BRs can be computed to very high (few percent) precision

C. Smith K+→ π+νν decay at NA62

P. Cenci BEACH 2012 NA62: guiding principles K+→ π+νν decay at NA62 S. Balev’s talk yesterday in the parallel session

Commissioning run 2012 Present status: - The technical run started during this summer has been successfully completed on 3rd December - Other technical runs foreseen during 2013 while completing the installation of detectors - Installation will continue in 2013 and 2014 - First physics run at the end of 2014 (after CERN machines shutdown) On schedule to get a 10% measurement by 2015-2016 (~ 3 SM events) H. Nanjio CKM 2012 J-PARC Hadron Hall

56m

KL beam line (KL decay in flight)

K1.1BR beam line (K+ decay at rest)

60m 30GeV Slow Extraction T1 target H. Nanjio CKM 2012 MB CV

CsI (from KTeV)

Present status - After the major Earthquake in Japan on 11 March 2011 (no damages to beam line and KOTO detector) JPARC started re-commissioning on Dec.2011 and resumed operations on Jan.2012. - Construction of the CsI calorimeter, the charged-particle veto counters (CV) in front of it, and the main-barrel photon veto counters (MB) which surrounds the decay volume in the vacuum vessel finished. - Front-end photon counters soon ready - Commissioning and engineering runs scheduled during beam times Dec’12-Jan’13 and Mar’13 - First physics run expected for May – June ’13 to break the Grossman-Nir bound. - After the long shutdown of the J-PARC accelerators from August 2013 to January 2014 expected to start a series of long physics runs. T. Komatsubara stopped K as in E787/949

E. Worcester BEACH2012

waiting for DOE approval of missions First data: end 2016 Evolution of the existing Fermilab accelerator complex to provide MW class beam power to a wide range of experimental programs

TREK experiment Transverse µ+ polarization in K+→π0µ+υ decay Search for T reversal violation KEK E246 experiment (final 2006):

J-PARC experiment Goal:

3HDM, LQ, SUSY w. RPB in 1 year

E36/TREK on K1.1BR beam. The JPARC E36/TREK experiment aims to measure RK and reduce the error by x2. Physics run of E36 expected in 2014-15. Approval going on. Protvino project

SPHINX+GAMS+ISTRA → OKA at Protvino: 65-70 GeV 1013 ppp at U-70 (38% DC) 12.5 GeV RF-separated K+ beam 5·106 Kpp (K/π ≈ 4) Commissioning beam and detector with runs started 2009 10-100x improvement on ISTRA Kaon program + spectroscopy e+e- collider Status of DAΦNE and KLOE/KLOE-2 KLOE-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

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 Detector upgrade: (see EPJC 68 (2010) 619-681) • γγ tagging system • Neutral kaon interferometry, CPT • inner tracker symmetry & QM tests • small angle and quad calorimeters • Kaon physics, CKM, LFV, rare K decays S • FEE maintenance and upgrade • η,η’ physics • Computing and networking update • Light scalars, γγ physics • etc.. (Trigger, software, …) • Hadron cross section at low energy, aµ • Dark forces: search for light U boson Improve precision on QM, CPT observables by approximately an order of magnitude Prospects for KLOE-2 at upgraded DAΦNE

Param. Present best published KLOE-2 KLOE-2 KLOE-2 measurement L=5 fb-1 L=10 fb-1 L=20 fb-1 -3 -3 -3 -3 AS (1.5 ± 11) × 10 ± 2.7 × 10 ± 1.9 × 10 ± 1.4 × 10 -5 -5 -5 -5 AL ( 332.2 ± 5.8 ± 4.7 ) × 10 ± 8.9 × 10 ± 6.3 × 10 ± 4.5 × 10

Re(ε’/ε) (1.65 ± 0.26) × 10-3 (*) ± 0.72 × 10-3 ± 0.51 × 10-3 ± 0.36 × 10-3

Im(ε’/ε) (-1.2 ± 2.3) × 10-3 (*) ± 9.4 × 10-3 ± 6.7 × 10-3 ± 4.7 × 10-3

-3 -3 -3 -3 Re(δ)+Re(x-) Re(δ) = (0.25 ± 0.23) × 10 (*) ± 0.7 × 10 ± 0.5 × 10 ± 0.4 × 10 -3 Re(x-) = (-4.2 ± 1.7) × 10 (*)

-5 -3 -3 -3 Im(δ)+Im(x+) Im(δ) = (-0.6 ± 1.9) × 10 (*) ± 9 × 10 ± 7 × 10 ± 5 × 10 -3 Im(x+) = (0.2 ± 2.2) × 10 (*)

Δm (5.288 ± 0.043) × 109 s-1 ± 0.096 × 109 s-1 ± 0.068 × 109 s-1 ± 0.048 × 109 s-1

(*) = PDG 2010 fit Prospects for KLOE-2 at upgraded DAΦNE

Para Present best published KLOE-2 (IT) KLOE-2 (IT) KLOE-2 (IT) m. measurement L=5 fb-1 L=10 fb-1 L=20 fb-1 -6 -6 -6 -6 ζ00 (0.1 ± 1.0) × 10 ± 0.26 × 10 ± 0.18 × 10 ± 0.13 × 10 -2 -2 -2 -2 ζSL (0.3 ± 1.9) × 10 ± 0.49 × 10 ± 0.35 × 10 ± 0.25 × 10 α (-0.5 ± 2.8) × 10-17 GeV ± 5.0 × 10-17 GeV ± 3.5 × 10-17 GeV ± 2.5 × 10-17 GeV β (2.5 ± 2.3) × 10-19 GeV ± 0.50 × 10-19 GeV ± 0.35 × 10-19 GeV ± 0.25 × 10-19 GeV γ (1.1 ± 2.5) × 10-21 GeV ± 0.75 × 10-21 GeV ± 0.53 × 10-21 GeV ± 0.38 × 10-21 GeV compl. pos. hyp. compl. pos. hyp. compl. pos. hyp. compl. pos. hyp. (0.7 ± 1.2) × 10-21 GeV ± 0.33 × 10-21 GeV ± 0.23 × 10-21 GeV ± 0.16 × 10-21 GeV

-4 -4 -4 -4 Re(ω) (-1.6 ± 2.6) × 10 ± 0.70 × 10 ± 0.49 × 10 ± 0.35 × 10 -4 -4 -4 -4 Im(ω) (-1.7 ± 3.4) × 10 ± 0.86 × 10 ± 0.61 × 10 ± 0.43 × 10 -17 -17 -17 -17 Δa0 [(0.4 ± 1.8) × 10 GeV] ± 0.52 × 10 GeV ± 0.36 × 10 GeV ± 0.26 × 10 GeV -18 -18 -18 -18 ΔaZ [(2.4 ± 9.7) × 10 GeV] ± 2.2 × 10 GeV ± 1.5 × 10 GeV ± 1.1 × 10 GeV -21 -18 -18 -18 ΔaX,Y [<10 GeV] ± 1.3 × 10 GeV ± 0.95 × 10 GeV ± 0.67 × 10 GeV

[….] = preliminary DAΦNE luminosity upgrade

Crabbed waist scheme at DAΦNE

NEW COLLISION SCHEME: Large Piwinski angle Crab-Waist compensation SXTs

Old collision scheme

-1 -1 max. expected at KLOE-2 : Lint ~ 20 pb /day x 200 dd/year = 4 fb /year DAΦNE luminosity upgrade

Crabbed waist scheme at DAΦNE

NEW COLLISION SCHEME: Large Piwinski angle Crab-Waist compensation SXTs Present commissioning phase New coll. scheme + KLOE det.

Old collision scheme

-1 -1 max. expected at KLOE-2 : Lint ~ 20 pb /day x 200 dd/year = 4 fb /year DAΦNE luminosity upgrade

Crabbed waist scheme at DAΦNE

Dec. 2012 NEW COLLISION SCHEME: Large Piwinski angle Crab-Waist compensation SXTs Present commissioning phase New coll. scheme + KLOE det.

Old collision scheme

-1 -1 max. expected at KLOE-2 : Lint ~ 20 pb /day x 200 dd/year = 4 fb /year From KLOE to KLOE-2: γγ taggers

LET: Ee ~ 160-230 MeV Ø Inside KLOE detector Ø LYSO+SiPM

Ø σE<10% for E>150 MeV

HET: Ee > 400 MeV Ø 11 m from IP Ø Scintillator hodoscopes

Ø σE ~ 2.5 MeV

Ø σT ~ 200 ps KLOE γγ taggers are installed and ready for the KLOE-2 run

From KLOE to KLOE-2: IP detectors Major detector upgrades ready in fall 2012, start install. end 2012:

INNER TRACKER

Ø 4 layers of cylindrical triple GEM Ø Better vertex reconstruction near IP

Ø Larger acceptance for low pt tracks

QCALT Ø W + scintillator tiles + SiPM/WLS

Ø Low-beta quadrupoles: coverage for KL decays CCALT Ø LYSO + SiPM Ø Increase acceptance for γ’s from IP (21°→10°) From KLOE to KLOE-2: IP detectors Major detector upgrades ready in fall 2012, start install. end 2012:

INNER TRACKER

Ø 4 layers of cylindrical triple GEM Ø Better vertex reconstruction near IP

Ø Larger acceptance for low pt tracks

QCALT Ø W + scintillator tiles + SiPM/WLS

Ø Low-beta quadrupoles: coverage for KL decays CCALT Ø LYSO + SiPM Ø Increase acceptance for γ’s from IP (21°→10°) Search for CP violation in KS decay 0 0 0 KS→ π π π : a pure CP violating decay

∂ i $ m11 m12 ' i $ #11 #12 ' Ψ = a(t) K 0 + b(t) K 0 i Ψ = H Ψ H = M " # = & ) " & ) ∂t 2 % m21 m22 ( 2% #21 #22 ( 1 1 KS = [ K1 +εS K2 ] KL = [ K2 +εL K1 ] € (1+ εS ) (1+ εL ) € ! εS = ε +δ εL = ε −δ

0 0 (δ: CPT viol.) 3π is a pure CP=-1 state; observation of KS → 3π is an € unambiguous sign of CP violation in mixing and/or in decay. € 0 0 0 € π π π T K to lowest order in χPT: η = S = ε +ε 000 0 0 0 ʹ000 ε = −2ε π π π T KL ʹ000 ʹ [Li, Wolfenstein PRD21,178 (1980)]

BR K 3 0 τ L ( S → π ) Standard Model prediction: η = 000 0 BR(K → 3π0) = 1.9 ∙ 10-9 τ S BR(KL →3π ) S € €

€ 0 0 0 KS→ π π π : search for a CP violating decay

0 0 KS → 3π → 6γ KS → 2π + accidental/splitted clusters + - - KL → 3π, KS → π π ( „fake KL crash” ) 0 0 0 KS→ π π π : search for a CP violating decay

39§ The analysis has been updated §N obs =0 evts. in data - improving clustering procedure to reduce split clusters * §N exp=0 evts. in MC - hardening the β (KL) cut for tagging the Ks decays 7 §0.12 evts expected in SM - processing the entire data set (~8x10 tagged KSKL pairs)

• DATA • DATA § signal box • MC background • MC background

§ Rmin > 65 cm

§ ε3π = 0.23(1)

§ N3π0 ≤ 2.33/ε3π0 at 90% C.L.

§ Normalized to 8 N2π0/ε2π0=(1.14130±0.00011)×10 New KLOE result 2012 0 -8 BR(KS→3π )< 2.6 × 10 @ 90% CL |η000|< 0.0088 @ 90% CL improvement of factor ~ 5 see M. Silarski’s talk in the parallel session This result points to the feasibility of the first observation at KLOE-2 39 Entanglement (i)

CPT and Lorentz invariance test in neutral kaons CPT and Lorentz invariance violation (SME)

Kostelecky et al. developed a phenomenological effective model providing a framework for CPT and Lorentz violations, based on spontaneous breaking of CPT and Lorentz symmetry, which might happen in quantum gravity (e.g. in some models of string theory) Standard Model Extension (SME) [Kostelecky PRD61, 016002, PRD64, 076001]

CPT violation in neutral kaons according to SME:

• CPTV only in mixing, not in decay, at first order (i.e. BI = y = x- = 0) • δ cannot be a constant (momentum dependence)   δ = isinφ eiφ SW γ Δa − β ⋅ Δa /Δm SW K ( 0 K )

where Δaµ are four parameters associated to SME lagrangian terms and related to CPT and Lorentz violation. € CPT and Lorentz invariance violation (SME)   δ = isinφ eiφ SW γ Δa − β ⋅ Δa /Δm SW K ( 0 K ) 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:

iφ SW  isinφSW e δ(p, t) = γ K {Δa0 Δm (in general z lab. axis is non-normal to Earth’s surface) +βK ΔaZ (cosθ cos χ − sinθ sinφ sin χ)

+βK [−ΔaX sinθ sinφ + ΔaY (cosθ sin χ + sinθ cosφ cos χ)]sinΩt

+βK +ΔaY sinθ sinφ + ΔaX (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 eiφ SW γ Δa − β ⋅ Δa /Δm SW K ( 0 K ) At DAΦNE K mesons are produced with angular δ depends on sidereal time t since laboratory distribution dN/dΩ ∝ sin2θ 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: e+ e- iφ SW  isinφSW e δ(p, t) = γ K {Δa0 Δm

+βK ΔaZ (cosθ cos χ − sinθ sinφ sin χ)

+βK [−ΔaX sinθ sinφ + ΔaY (cosθ sin χ + sinθ cosφ cos χ)]sinΩt

+βK +ΔaY sinθ sinφ + ΔaX (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

€ Exploiting neutral kaon interferometry

1 0 0 0 0 i = K K " K K iφ i 2 [ ] ηi = ηi e = f i T KL fi T KS

2 2 −Γ Δt −Γ Δt −(ΓS +ΓL )Δt / 2 I f , f ;Δt ∝ η e L + η e S − 2η η e cos ΔmΔt + φ − φ ( 1 2 ) { 1 2 1 2 ( 2 1)} ! f φ € I(Δt) (a.u) 1 f2 Δt=t1-t2 t1 t2 €

an example with nearly equal final states

Δt/τS Exploiting neutral kaon interferometry

1 0 0 0 0 i = K K " K K iφ i 2 [ ] ηi = ηi e = f i T KL fi T KS

2 2 −Γ Δt −Γ Δt −(ΓS +ΓL )Δt / 2 I f , f ;Δt ∝ η e L + η e S − 2η η e cos ΔmΔt + φ − φ ( 1 2 ) { 1 2 1 2 ( 2 1)} ! f φ € I(Δt) (a.u) 1 f2 Δt=t1-t2 t1 t2 €

η2 η1 from the asymmetry at small t Δ an example with nearly equal final € states

Δt/τS Exploiting neutral kaon interferometry

1 0 0 0 0 i = K K " K K iφ i 2 [ ] ηi = ηi e = f i T KL fi T KS

2 2 −Γ Δt −Γ Δt −(ΓS +ΓL )Δt / 2 I f , f ;Δt ∝ η e L + η e S − 2η η e cos ΔmΔt + φ − φ ( 1 2 ) { 1 2 1 2 ( 2 1)} ! f φ € I(Δt) (a.u) 1 f2 Δt=t1-t2 t1 t2 €

η2 η1 from the asymmetry at small t Δ an example with nearly equal final € 2 states η2 η1 Δt/τS from the asymmetry at large Δt

€ Exploiting neutral kaon interferometry

1 0 0 0 0 i = K K " K K iφ i 2 [ ] ηi = ηi e = f i T KL fi T KS

2 2 −Γ Δt −Γ Δt −(ΓS +ΓL )Δt / 2 I f , f ;Δt ∝ η e L + η e S − 2η η e cos ΔmΔt + φ − φ ( 1 2 ) { 1 2 1 2 ( 2 1)} ! π+ φ €π0 - Δt=t -t I(Δt) (a.u) π 0 1 2 t1 t2 π € As an example η+− = ε(1+ε ʹ ε) 0 0 f1=π+π- f2=π π η00 = ε(1− 2ε ʹ ε) ℑ(ε ʹ ε) , ℜ(ε ʹ ε) from the asymmetry at small Δt

€ ℜ(ε ʹ ε) Δt/τS € from the asymmetry at large Δt

€ Exploiting neutral kaon interferometry

1 0 0 0 0 i = K K " K K iφ i 2 [ ] ηi = ηi e = f i T KL fi T KS

2 2 −Γ Δt −Γ Δt −(ΓS +ΓL )Δt / 2 I f , f ;Δt ∝ η e L + η e S − 2η η e cos ΔmΔt + φ − φ ( 1 2 ) { 1 2 1 2 ( 2 1)} ! π+ φ €π0 - Δt=t -t I(Δt) (a.u) π 0 1 2 t1 t2 π € As an example η+− = ε(1+ε ʹ ε) 0 0 f1=π+π- f2=π π η00 = ε(1− 2ε ʹ ε) ℑ(ε ʹ ε) , ℜ(ε ʹ ε) from the asymmetry at small Δt

€ ℜ(ε ʹ ε) Δt/τS € from the asymmetry at large Δt

€ Exploiting neutral kaon interferometry

1 0 0 0 0 i = K K " K K iφ i 2 [ ] ηi = ηi e = f i T KL fi T KS

2 2 −Γ Δt −Γ Δt −(ΓS +ΓL )Δt / 2 I f , f ;Δt ∝ η e L + η e S − 2η η e cos ΔmΔt + φ − φ ( 1 2 ) { 1 2 1 2 ( 2 1)} ! π+ φ €π+ - I(Δt) (a.u) π - t1 t2 π

€ (1)  η+− = ε(1−δ(+p, t) ε)  η(2) = ε 1−δ −p, t ε +− ( ( ) )

€ Δt/τS Exploiting neutral kaon interferometry

1 0 0 0 0 i = K K " K K iφ i 2 [ ] ηi = ηi e = f i T KL fi T KS

2 2 −Γ Δt −Γ Δt −(ΓS +ΓL )Δt / 2 I f , f ;Δt ∝ η e L + η e S − 2η η e cos ΔmΔt + φ − φ ( 1 2 ) { 1 2 1 2 ( 2 1)} ! π+ φ €π+ - I(Δt) (a.u) π - t1 t2 π

€ (1)  η+− = ε(1−δ(+p, t) ε)  η(2) = ε 1−δ −p, t ε +− ( ( ) )

€ Δt/τS Exploiting neutral kaon interferometry

1 0 0 0 0 i = K K " K K iφ i 2 [ ] ηi = ηi e = f i T KL fi T KS

2 2 −Γ Δt −Γ Δt −(ΓS +ΓL )Δt / 2 I f , f ;Δt ∝ η e L + η e S − 2η η e cos ΔmΔt + φ − φ ( 1 2 ) { 1 2 1 2 ( 2 1)} ! π+ φ €π+ - I(Δt) (a.u) π - t1 t2 π

€ (1)  η+− = ε(1−δ(+p, t) ε)  η(2) = ε 1−δ −p, t ε +− ( ( ) ) ℑ(Δδ ε) from the asymmetry at small Δt € ℜ(Δδ ε) ≈ 0 because Δδ⊥ε Δt/τ from€ the asymmetry at large Δt S

€ Measurement of Δaµ at KLOE

The analysis is performed in Example: 4 bins of sidereal time 1 bin sidereal time x 2 bins for the φ quadrant of (0-4 hours) the forward kaon for quadrant x 30 bins of Δt = 240 bins (cosθ>0 cosφ>0). Data: black points Fit result: green band (stat. err. only)

Δt/τS with L=1.7 fb-1 new KLOE result (2012) −18 Δa0 = (−6.2 ± 8.2STAT ± 3.3SYST ) ×10 GeV see A. De Santis’s talk −18 in the parallel session ΔaX = (3.3 ±1.6STAT ±1.5SYST ) ×10 GeV An improvement in the precision −18 ΔaY = (−0.7 ±1.3STAT ±1.5SYST ) ×10 GeV of a factor ~ 3 wrt old KLOE preliminary results. −18 ΔaZ = (−0.7 ±1.0STAT ± 0.3SYST ) ×10 GeV -22 KTeV preliminary :ΔaX , ΔaY < 9.2 × 10 GeV @ 90% CL

€ Entanglement (ii)

Test of Time reversal symmetry in the neutral kaon system Direct test of Time Reversal symmetry with neutral kaons • A direct evidence for T violation would mean an experiment that, considered by itself, clearly shows T violation INDEPENDENT and unconnected to the results for CP violation and CPT invariance

• Only one evidence of T violation: Kabir asymmetry, comparing a process with its T-conjugated one, i.e. K 0 K ¯ 0 vs K¯0 K0 performed by the CPLEAR experiment → →

0 0 P(K →K 0) − P(K 0 →K ) A T = 0 0 P(K →K 0) + P(K 0 →K )

-3 〈AT〉 = (6.6 ± 1.3) · 10 PLB444(1998)43 € • Criticism: K 0 K ¯ 0 is a CPT-even transition, so CP T in this case ! we cannot→ distinguish between CP or T tests (not≡ independent) Direct test of Time Reversal symmetry with neutral kaons

• EPR correlations at a φ-factory can be exploited to study other transitions involving also “CP states” K+ and K- 1 i>= K0 K¯ 0 K¯ 0 K0 | √2 | ￿| ￿−| ￿| ￿ 1 ￿ ￿ = [ K+ K K K+ ] √2 | ￿| −￿−| −￿| ￿

φ 0 K+ K- K ππ π-l+ν e.g.

t1 t1 Δt=t2-t1

I(ππ,l+; ∆t)=C(ππ,l+) P [K (0) K0(∆t)] × − →

In general with fX decayng before fY, i.e. Δt>0 :

with Direct test of Time Reversal symmetry with neutral kaons T symmetry test

One can define the following ratios of probabilities:

Any deviation from Ri=1 constitutes a violation of T-symmetry

Bernabeu, Di Domenico, Villanueva: NPB 868 (2013) 102 Direct test of CP and CPT symmetry with neutral kaons CP symmetry test

CPT symmetry test

T, CP and CPT tests are all experimentally independent Direct test of Time Reversal symmetry with neutral kaons

Any deviation from Ri=1 constitutes a direct evidence of T-symmetry violation

Ri(Δt=0)=1 R1 R2

R2(Δt>>τS)=1-4Re(ε) R4(Δt>>τS)=1+4Re(ε)

R3 R4 Direct test of Time Reversal symmetry with neutral kaons

In practice two measurable ratios with Δt <0 or >0 Direct test of Time Reversal symmetry with neutral kaons toy MC with L=10 fb-1 Direct test of Time Reversal symmetry with neutral kaons toy MC with L=10 fb-1 Direct test of Time Reversal symmetry with neutral kaons toy MC with L=10 fb-1 Direct test of Time Reversal symmetry with neutral kaons toy MC with L=10 fb-1 Direct test of Time Reversal symmetry with neutral kaons toy MC with L=10 fb-1

T conserved

0.7% violation

0.7% violation

T conserved

R2(Δt>>τS)=1-4Re(ε) ∼ 0.993 R4(Δt>>τS)=1+4Re(ε) ∼ 1.007 Direct test of Time Reversal symmetry with neutral kaons

Integrating in a Δt region between 0 and 300 τS => stat. significance of 4.4, 6.2, 8.8 σ with L=5, 10, 20 fb-1 (full efficiency)

But, in the “plateau” region one needs to measure the absolute value of Ri

It is needed to measure the constant D with at least 0.1% precision,

i.e. BRs and KS, KL lifetimes

T test could be feasible at KLOE-2 with L=O(10 fb-1) Direct test of Time Reversal symmetry with neutral kaons

φ 0 K+ K- K ππ π-l+ν e.g.

t1 t1 Δt=t2-t1 Direct test of Time Reversal symmetry with neutral kaons

~ φ 0 K+ K- K ππ π-l+ν e.g.

t1 t1 Δt=t2-t1

0 state orthogonal to K+ cannot decay in ππ state orthogonal to K- cannot decay in 3π

need to assume => not valid if direct CP violation is present Direct test of Time Reversal symmetry with neutral kaons

direct CP violation effects have to be evaluated, they could spoil the significance of the T test: Conclusion: they can be neglected Entanglement (iii) decoherence and ω-effect + - + - φ →KSKL→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) 131601, NPB744 (2006) 180]. I(π+π-, π+π-;Δt) (a.u.) i ∝ ( K 0 K 0 − K 0 K 0 ) +ω( K 0 K 0 + K 0 K 0 ) ∝ K K − K K +ω K K − K K ( S L L S ) ( S S L L ) ω = 3 ×10−3 φ = 0 at most one ω expects: Δt/τ € S In some microscopic models of ℜω = −1.6+3.0 €± 0.4 ×10−4 space-time foam arising from KLOE result ( −2.1STAT SYST ) non-critical string theory: +3.3 −4 -4 -5 ℑω = −1.7 ±1.2 ×10 ω~ 10 ÷ 10 PLB 642(2006) 315 ( −3.0STAT SYST ) [Bernabeu, Mavromatos, Sarkar Found. Phys. 40 (2010) 852 −3 PRD 74 (2006) 045014] ω <1.0 ×10 at 95% C.L.

€ + - + - φ →KSKL→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: I(π+π-, π+π-;Δt) (a.u.) [Bernabeu, et al. PRL 92 (2004) 131601, NPB744 (2006) 180]. i ∝ ( K 0 K 0 − K 0 K 0 ) +ω( K 0 K 0 + K 0 K 0 )

∝ ( KS KL − KL KS ) +ω( KS KS − KL KL )

at most one expects: € In some microscopic models of ℜω = −1.6+3.0 ± 0.4 ×10−4 space-time foam arising from KLOE result ( −2.1STAT SYST ) non-critical string theory: +3.3 −4 -4 -5 ℑω = −1.7 ±1.2 ×10 ω~ 10 ÷ 10 PLB 642(2006) 315 ( −3.0STAT SYST ) [Bernabeu, Mavromatos, Sarkar Found. Phys. 40 (2010) 852 −3 PRD 74 (2006) 045014] ω <1.0 ×10 at 95% C.L.

€ Entanglement (iv)

Bell’s inequality for kaons and discrete symmetries New formulation of Bell’s inequality for kaons

min S t1,t2,t3,t4 ρsep ≤ S t1,t2,t3,t4 ≤ max S t1,t2,t3,t4 ρsep all ρ sep ( )[ ] ( ) all ρ sep ( )[ ] where: Hiesmayr, A.D.D. et al. EPJC (2012) 72:1856

S(t1,t2,t3,t4 ) = E(t1,t2) − E(t1,t3 ) + E(t4 ,t2) + E(t4,t3 ) € 0 0 0 0 E(t1,t2) =1+ 4P(K ,t1;K ,t2) − 2P(K ,t1;*) − 2P(*;K ,t2)

€ φ €

In this example: t1, t2, t3, t4 ~ 5 τS

CP violation plays a crucial role in Bell’s inequality violation Conclusions • In a couple of years the next generation of experiments at hadron machines (NA62 and KOTO) will be operational, allowing us to definitely enter the very rare kaon decay era.

• Ultra high sensitivity and precision will be essential and crucial as a probe of New Physics beyond the SM, and complementary to LHC.

• The good performance of the experiments will be crucial for the continuation and extension of the physics program.

• The connection of entanglement with discrete symmetries of neutral kaons is still surprising and will continue to be one of the key issues at KLOE-2.