CPT symmetry and quantum coherence tests in the neutral kaon

CPT symmetry and quantum coherence tests in the neutral kaon system at KLOE

Antonio Di DomenicoDipartimento di Fisica, Università di Roma “La Sapienza”

and INFN sezione di Roma, Italy

Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies,

April 3rd, 2009, Warsaw, Poland

A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland

CPT: introductionThe 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 (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.

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. :81418 10 ,10 ,10 0000

−−− <−<−<− pppBBBKKK mmmmmmmmm


1) “Standard” tests of CPT symmetry in the neutral kaonsystem


The time evolution of a two-component state vector Ψ in the space is given by (Wigner-Weisskopf approximation):

{ }00 , KK

( ) ( )ttt

i Ψ=Ψ∂∂ H

H is the effective hamiltonian (non-hermitian), decomposed into a HermitianPart (mass matrix M) and an anti-Hermitian part (i/2 decay matrix Γ) :

The neutral kaon system

Diagonalizing the effective Hamiltonian:

LSLSLSim ,,, 2

Γ−=λ

( ) ( )0,,,

LSti

LS KetK LSλ−=( ) ( ) ( )[ ]

( ) [ ]1,2,2,1

,

0,

0,

,

,

1

1

1112

1

KK

KKK

LS

LS

LSLS

LS

LS

εε

εεε

++

=

−±++

=

eigenvalues eigenstates

τS ~ 90 ps τL ~ 51 ns

⎟⎟⎠

⎞⎜⎜⎝

⎛ΓΓΓΓ

−⎟⎟⎠

⎞⎜⎜⎝

⎛=−=

2221

1211

2221

1211

22i

mmmmi ΓMH

small CP impurity ~2 x 10-3mL-mS= 3.5 x 10-15 GeV ~ ΓS / 2

|K1,2> areCP=±1 states


( )( ) ( )( )

/imΓΓimmHH

LS 22

21

2112211222211

ΔΓ+Δ−−−

=−

−=

λλδ

CPT violation in the neutral kaon system: “standard” picture

ε LS δε ±=,

CPT violation in the mixing:

LSSL

KK

KK

mmm

mmmm

Γ−Γ=ΔΓ−=Δ

Γ≡ΓΓ≡Γ

≡≡

,

,

,

00

00

2211

2211

( ) /im

miHH

LS 22

212122112

ΔΓ+ΔΓℑ−ℑ−

=−

−=

λλε

• δ ≠ 0 implies CPT violation • ε ≠ 0 implies T violation• ε ≠ 0 or δ ≠ 0 implies CP violation

012 =Γℑ(with a phase convention )



∗∗+−∗∗−+

−++−

−=−=

+=+=

dcKTbaKT

dcKTbaKT00

00

νπνπ

νπνπ

ll

ll

CPT violation in semileptonic decays

Standard Model prediction of ΔS=ΔQ rule violation is x=c/a ~ O(10-7)

( ) ( )( ) ( ) −−++−

−++−

ℜ±ℜ−ℜ±ℜ=→Γ+→Γ→Γ−→Γ

= xyeKeKeKeK

ALSLS

LSLSLS 2222

,,

,,, δε

νπνπνπνπ

Semileptonic charge asymmetry:

νπνπ

νπνπ+−−+

−++−

→→

→→

ll

ll00

00

KKKK

ΔS=ΔQ rule

( )−ℜ+ℜ=− xAA LS δ4

CP T CPT ΔS=ΔQa ℑ=0 ℑ=0b ℜ=0 ℑ=0 =0c ℑ=0 ℑ=0 =0d ℜ=0 ℑ=0 =0 =0



∗∗+−∗∗−+

−++−

−=−=

+=+=

dcKTbaKT

dcKTbaKT00

00

νπνπ

νπνπ

ll

ll

CPT violation in semileptonic decays

acx

∗

+ =adx

∗

− −=aby −=

CPT viol.

CPT & ΔS=ΔQ viol.

ΔS=ΔQViol.

Standard Model prediction of ΔS=ΔQ rule violation is x=c/a ~ O(10-7)

( ) ( )( ) ( ) −−++−

−++−

ℜ±ℜ−ℜ±ℜ=→Γ+→Γ→Γ−→Γ

= xyeKeKeKeK

ALSLS

LSLSLS 2222

,,

,,, δε

νπνπνπνπ

Semileptonic charge asymmetry:

νπνπ

νπνπ+−−+

−++−

→→

→→

ll

ll00

00

KKKK

ΔS=ΔQ rule



0

0

00

00

0000 200

AB

KT

KTe

KT

KTe

S

Li

S

Li

ℜℜ

−=Δ

′−Δ−===

′+Δ−===−+

−+

−+−+−+

δ

εεππ

ππηη

εεππ

ππηη

φ

φ

CPT violation in ππ decays

AI(BI) CPT conserving (violating) K→ ππ amplitudes for I=0,2(δI strong phase shift for I=0,2)

( )ΔΓΔ= mSW 2arctanφ

( )( ) I

I

iδII

iδII

eBAKTI

eBAKTI∗∗ −=

+=0

0

;

;

ππ

ππ

⎥⎦

⎤⎢⎣

⎡ℜℜ

+−

≈−

⎟⎠⎞

⎜⎝⎛ ′

ℑ−≈⎟⎟⎠

⎞⎜⎜⎝

⎛ℜℜ

−ℜℜ

ℜℜ

≈−

−+−+

−+−+

0

02211

0

0

2

2

0

200

2Δ21

312

3

AB

mmm-

AB

AB

AA

SW ηφφ

εε

ηφφ

η00η+−

ε

ε′-2ε′

φ00φ+−

φSW

Im

Re

-Δ

(not to scale)



Neutral kaons at CPLEAR (CERN)

( )( )( ) 00

0

0

KKpp

KKpp

KKpp

REST

REST

REST

+→+

++→+

++→+−+

+−

π

π

Pure initial are produced from antiprotonannihilation at rest with a hydrogen target

00 , KK

PK ~500 MeV

The detection of a charged kaon tags the strangeness of the accompanying neutral kaon


CPLEAR results

Test of CPT in the time evolution of neutral kaons using the semileptonicasymmetry

ℜδ = (0.30 ± 0.33 ± 0.06) × 10−3

PLB444 (1998) 52

( )( )

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

ℜ+=

→=

→=

+−

++−

=

=−++−

=+−

=+−−+

=−+

+−

+−

−+

−+

L

tt

tt

veKRR

veKRR

RRRR

RRRRA

εα

πτ

πτ

ταττατ

τατταττ

τ

τ

δ

41

)( )(

)( )(

)()()()(

)()()()()(

)()(0

0)(

)()(0

0)(

δττδ ℜ=>> 8)( SA

K0 e+

π−

ντ=0 τ


KTeV (Fermilab) results

PK ~50-150 GeVRegenerator beam decay distribution allowsCPT tests based on φ+- , φ00-φ+-

)cos(2

);( )(

2 2

−+Γ+Γ−

−+

Γ−−+

Γ−−+

−+Δ+

+∝

φφηρ

ηρππ

ρmte

eetRt

tt

LS

LS

φ+- - φSW = 0.61º ±0.62º ± 1.01 ºφ00-φ+- = 0.39º ± 0.22 º ±0.45 º

PRD67,012005 (2003)

SLL KKK ρ+→



PK ~50-150 GeVRegenerator beam decay distribution allowsCPT tests based on φ+- , φ00-φ+-

)cos(2

);( )(

2 2

−+Γ+Γ−

−+

Γ−−+

Γ−−+

−+Δ+

+∝

φφηρ

ηρππ

ρmte

eetRt

tt

LS

LS

SLL KKK ρ+→

Presented atMoriond08, HQL08

φε - φSW = 0.40º ±0.56ºφ00-φ+- = 0.30º ± 0.35º


( ) 6

0

000 10353

231

32 −

−−+ ×±−=⎟⎟⎠

⎞⎜⎜⎝

⎛ℜℜ

++ℜ=−⎟⎠⎞

⎜⎝⎛ +ℜ

ABxyALηη

Constraints on CPT violation in ππ and semileptonic decays obtained combining KTeV and PDG results:


AL=( 3322 ± 58 ± 47 ) × 10-6

PRL88,181601(2002)

KL semileptonic charge asymmetry:


• e+e− → φ σφ∼3 μbW = mφ = 1019.4 MeV

• BR(φ → K0K0) ~ 34%• ~106 neutral kaon pairs per pb-1 produced in an antisymmetric quantum state with JPC = 1−− :

Neutral kaons at a φ-factory

( ) ( ) ( ) ( )[ ]( ) ( ) ( ) ( )[ ]pKpKpKpKN

pKpKpKpKi

SLLSrrrr

rrrr

−−−=

−−−=

2

21 0000

pK = 110 MeV/c λS = 6 mm λL = 3.5 m

The detection of a kaon at large (small) times tags a KS (KL)⇒ possibility to select a pure KS beam (unique at a φ-factory, not possible at fixed target experiments)

Production of the vector meson φin e+e− annihilations:

KL,S

KS,Le-e+

φ

( )( ) ( ) 1111 22 ≅−++= LSLSN εεεε


Day performance: 7-8 pb-1

Best month ∫L dt ~ 200 pb−1

Total KLOE ∫L dt ~ 2.5 fb−1

(2001 - 05)→ ~2.5×109 KSKL pairs

DAΦNE: the Frascati φ-factoryIntegrated luminosity (KLOE)

Max L ~ 1.4 cm-2s-1


CalorimeterCalorimeter Drift chamberDrift chamber

σE/E ≅ 5.7% /√E(GeV)σt ≅ 54 ps /√E(GeV) ⊕ 50 ps

(relative time between clusters)

σγγ ~ 2 cm (π0 from KL → π+π−π0)

σp/p ≅ 0.4 % (tracks with θ > 45°)

σxhit ≅ 150 μm (xy), 2 mm (z)

σxvertex ~ 1 mm

4 m diameter × 3.3 m length90% helium, 10% isobutane12582/52140 sense/total wiresAll-stereo geometry

Lead/scintillating fiber4880 PMTs98% coverage of solid angle

The KLOE detector at DAΦNE

Superconducting coil B = 0.52 T


KS tagged by KL interaction in EmCEfficiency ~ 30% (largely geometrical)KS angular resolution: ~ 1° (0.3° in φ)KS momentum resolution: ~ 2 MeV

KKLL ““crashcrash””ββ= 0.22 (TOF)= 0.22 (TOF)

KKSS →→ ππ−−ee++νν

KL tagged by KS → π+π− vertex at IPEfficiency ~ 70% (mainly geometrical)KL angular resolution: ~ 1°KL momentum resolution: ~ 2 MeV

KKSS →→ ππ++ππ−−

KKLL →→ 22ππ00

KS and KL Tagging at KLOE


KS→ πeν: KLOE results

Data sample: 410 pb-1

Emiss-Pmiss

BR(KS → π−e+ν) = (3.528 ± 0.057 ± 0.027) × 10−4

BR(KS → π+e−ν) = (3.517 ± 0.051 ± 0.029) × 10−4

BR(KS → πeν) = (7.046 ± 0.076 ± 0.050) × 10−4

BR(πeν) [KLOE ’02, 17 pb−1]: (6.91 ± 0.34 ± 0.15) × 10−4

PLB 636(2006) 173


KS→ πeν: KLOE results

Data sample: 410 pb-1

Emiss-Pmiss

BR(KS → π−e+ν) = (3.528 ± 0.057 ± 0.027) × 10−4

BR(KS → π+e−ν) = (3.517 ± 0.051 ± 0.029) × 10−4

BR(KS → πeν) = (7.046 ± 0.076 ± 0.050) × 10−4

BR(πeν) [KLOE ’02, 17 pb−1]: (6.91 ± 0.34 ± 0.15) × 10−4

PLB 636(2006) 173

AS = ( 1.5 ± 9.6 ± 2.9 ) × 10−3 with 2.5 fb−1: δAS ∼ 3 × 10−3 ∼ 2Re ε

( ) ( )( ) ( )νπνπ

νπνπ−++−

−++−

→Γ+→Γ→Γ−→Γ

=eKeKeKeKA

SS

SSS

ℜx− = ( −0.8 ± 2.4 ± 0.7) × 10−3

ℜy = ( 0.4 ± 2.4 ± 0.7) × 10−3


( )yAA LS ℜ−ℜ=+ ε4

CPT & ΔS=ΔQ viol.

CPT viol.

input from other experiments


CPT test: the Bell-Steinberger relation

( ) ( )( ) ( ) ⎟

⎟⎠

⎞⎜⎜⎝

⎛ℑℜ

⎟⎟⎠

⎞⎜⎜⎝

⎛+−−

−−+=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

ℑ+

ℜ

∑∑

i i

i i

SW

SW

kkkbk

Nδεε

αα

φφ

1tan1tan12111

1 2

α+−= η+− BR(KS→π+π−)

α00= η00 BR(KS→π0π0)

αkl3 = 2τS/τL BR(KLl3) [(AS+AL)/4− i Im x+]

α+−0= τS/τL η+− 0∗ BR(KL→π+π−π0)

α000= τS/τL η 000∗ BR(KL→π0π0π0)

( )( ) ( ) ( )kbkkkN

KBRbk

SW

LLS

+−−++=

→==

12tan11

, 222 φ

νπττ lSiLii KTfKTf=η

( ) ∑ +=⎟⎠⎞

⎜⎝⎛−

= fLLSS

t

KTfaKTfatKdtd 2

0

2

LLSS KaKaK +=

∑ ∗

Γ−Γ=

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ℑ−

+

ℜ⎟⎟⎠

⎞⎜⎜⎝

⎛+

Γ−ΓΓ+Γ

fLS

LSSW

LS

LS KTfKTfii 11

tan 2 δεεφ

Unitarity constraint:

KS KLobservables


Experimental inputs to the Bell-Steinberger relation

Main improvements done with KLOE measurements on KS semileptonic and 3π0 decays


Re ε = (159.6 ± 1.3) ×10−5 Im δ =(0.4 ± 2.1) × 10−5

KLOE result: JHEP12(2006) 011

��

�

��

-10 0 10

�M ��

GeV

�� CL

�� CL��

GeV

Combining Reδ and Imδ results:

( ) ( )( )

/imΓΓimm KKKK

22

21 0000

ΔΓ+Δ

−−−=δ

Assuming , i.e. no CPT viol. in decay:( ) 000 =− KK ΓΓ

GeV 103.6103.5 191900

−− ×<−<×−KK

mmat 95% c.l.

( )00 KKΓΓ −

( )00 KKmm −

Reδ

Imδ


ℜδ = (0.30 ± 0.33 ± 0.06) × 10−3

CPLEAR: study of the time evolution of neutral kaons in semileptonic decays

PLB444 (1998) 52


Combining Reδ and Imδ results:

( ) ( )( )

/imΓΓimm KKKK

22

21 0000

ΔΓ+Δ

−−−=δ

Assuming , i.e. no CPT viol. in decay:( ) 000 =− KK ΓΓ

( )00 KKΓΓ −

( )00 KKmm −

Reδ

Imδ

( using new KTeV results on φππ :Moriond EW 08, HQL08)


Re ε = (161.2 ± 0.6) ×10−5 Im δ =(−0.1 ± 1.4) × 10−5

M. Palutan, presented at FLAVIANET Kaon ws 08 (prelim.):

ℜδ = (0.30 ± 0.33 ± 0.06) × 10−3

CPLEAR: study of the time evolution of neutral kaons in semileptonic decays

PLB444 (1998) 52

C.L. 95%at GeV 100.4 1900

−×<−KK

mm


2) Search for decoherence and CPT violation in the neutral kaon system


Neutral kaon interferometry

( ) {( )( ) ( )[ ]}2112

2/21

22

21122211

cos2

,;,21

2121

φφηη

ηη

−+−Δ−

+=+Γ+Γ−

Γ−Γ−Γ−Γ−

ttme

eeCtftfItt

tttt

LS

LSSL

Double differential time distribution:

where t1(t2) is the proper time of one (the other) kaon decay into f1 (f2) final state and:

SiLii

ii KTfKTfe i == φηη

fi = π+π−, π0π0, πlν, π+π−π0, 3π0, π+π−γ ..etc

characteristic interference termat a φ-factory => interferometry2

21212

2

SSN KTfKTfC =

KL,S

KS,L

t1

t2

Δt=t1- t2 f2

f1

φ( ) ( ) ( ) ( )[ ]pKpKpKpKNi SLLSrrrr

−−−=2


Integrating in (t1+t2) we get the time difference (Δt=t1-t2) distribution (1-dim plot simpler to manipulate than 2-dim plot):

( ) {( ) ( )}

21 and 0for

cos2

0;,

122/

21

22

2121

12

↔Δ→Δ<Δ

−+ΔΔ−

+=≥ΔΔΓ+Γ−

ΔΓ−ΔΓ−Γ+Γ

ttt

tme

eetffIt

ttC

LS

SL

LS

φφηη

ηη

From these distributions for various final states fi one can measure the following quantities:

Neutral kaon interferometry

( )iiLS m ηφη arg , , , , i ≡ΔΓΓPhases (difference of) from the interference term => interferometry


Neutral kaon interferometry: main observables

νπ +−l

νπ −+l

Δt/τS

I(Δt) (a.u) I(Δt) (a.u)

I(Δt) (a.u)

Δt/τS

Δt/τS00 ππππφ −+→→ LS KK

νπνπφ +−−+→→ ll LSKK

νπππφ l →→ LS KK

⎟⎠⎞

⎜⎝⎛ ′

ℜεε

⎟⎠⎞

⎜⎝⎛ ′

ℑεε

−ℜ+ℜ xδ

+ℑ+ℑ xδ

−ℜ−ℜ−ℜ−ℜ=

xyAL δε2

ππφ


−+−+→→ ππππφ LS KK

Δt/τS

I(Δ

t)(a

.u)

Same final state for both kaons: f1 = f2 = π+π−

Δt=|t1-t2|

[ ]0000

21 KKKKi −=

φ ππ

ππ t2 t1


−+−+→→ ππππφ LS KK

Δt/τS

I(Δ

t)(a

.u)

Same final state for both kaons: f1 = f2 = π+π−

Δt=|t1-t2|

no simultaneous decays (Δt=0) in the samefinal state due to thedestructive quantum interference

EPR correlation:

[ ]0000

21 KKKKi −=

φ ππ

ππ t2=t1 t1

φ ππ

ππ t2 t1


( ) ( ) ( )

( ) ( ) ⎥⎦⎤⎟

⎠⎞⎜

⎝⎛ ΔΔℜ−

⎢⎣⎡ Δ+Δ=Δ

∗−+−+−+−+

−+−+−+−+−+−+

tKKtKK

tKKtKKtI N

0000

2002002

,,2

,,;,

ππππππππ

ππππππππππππ

φ →KSKL→π+π− π+π− : test of quantum coherence

[ ]0000

21 KKKKi −=

Feynman described the phenomenon of interference as containing “the only mistery” of quantum mechanics


( ) ( ) ( )

( ) ( ) ( ) ⎥⎦⎤⎟

⎠⎞⎜

⎝⎛ ΔΔℜ⋅−−

⎢⎣⎡ Δ+Δ=Δ

∗−+−+−+−+

−+−+−+−+−+−+

tKKtKK

tKKtKKtI N

000000

2002002

,,21

,,;,

ππππππππζ



[ ]0000

21 KKKKi −=



( ) ( ) ( )

( ) ( ) ( ) ⎥⎦⎤⎟

⎠⎞⎜

⎝⎛ ΔΔℜ⋅−−

⎢⎣⎡ Δ+Δ=Δ

∗−+−+−+−+

−+−+−+−+−+−+

tKKtKK

tKKtKKtI N

000000

2002002

,,21

,,;,

ππππππππζ



[ ]0000

21 KKKKi −=

edecoherenc total 1QM 0

00

00

→=

→=

ζζDecoherence parameter:

(also known as Furry's hypothesis or spontaneous factorization) [W.Furry, PR 49 (1936) 393]



t/ s

Data

KLKS+ - + -

KL inc. regeneration

e+e- + - + -

0

50

100

150

200

250

300

350

400

450

500

0 5 10 15 20 25 30 35

• Analysed data: L=380 pb−1

• Fit including Δt resolution and efficiency effects + regeneration• ΓS, ΓL , Δm fixed from PDG

From CPLEAR data, Bertlmann et al. (PR D60 (1999) 114032) obtain:

KLOE result:

( ) 6SYSTSTAT00 104.01.20.1 −×±±=ζ

7.04.000 ±=ζ

PLB 642(2006) 315

In the B-meson system, BELLE coll.(PRL 99 (2007) 131802) obtains:

057.0029.000

±=Bζ

as CP viol. O(|η+−|2) ∼ 10−6

=> high sensitivity to


00ζ


KLOE FINAL:

• Analysed data:• Fit including Δt resolution and efficiency effects + regeneration• ΓS, ΓL , Δm fixed from PDG

L=1.5 fb-1 (2004-05 data)


7.04.000 ±=ζIn the B-meson system, BELLE coll.(PRL 99 (2007) 131802) obtains:

057.0029.000

±=Bζ


as CP viol. O(|η+−|2) ∼ 10−6

=> high sensitivity to 00ζ

( ) 7SYSTSTAT00 108.35.94.1 −×±±=ζ


KLOE FINAL:

• Analysed data:• Fit including Δt resolution and efficiency effects + regeneration• ΓS, ΓL , Δm fixed from PDG

L=1.5 fb-1 (2004-05 data)


7.04.000 ±=ζIn the B-meson system, BELLE coll.(PRL 99 (2007) 131802) obtains:

057.0029.000

±=Bζ


as CP viol. O(|η+−|2) ∼ 10−6

=> high sensitivity to 00ζ

( ) 7SYSTSTAT00 108.35.94.1 −×±±=ζ

Comparison with quantum optics test precisions


Modified Liouville – von Neumann equation for the density matrix of the kaon system:

Decoherence and CPT violation

( ) ( )ρρρρ LHiiHt ++−= +

44 344 21&

QM

extra term inducingdecoherence:pure state => mixed state





44 344 21&

QM


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, non-trivial 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:

( ) ( )2 , 0,

,,;βαγγα

γβαρρ

>>

= LLGeV 102,, 20

2−×≈⎟⎟

⎠

⎞⎜⎜⎝

⎛=

PLANCK

K

MMOγβα

[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]

At most:





44 344 21&

QM



( ) ( )2 , 0,

,,;βαγγα

γβαρρ

>>

= LLGeV 102,, 20

2−×≈⎟⎟

⎠

⎞⎜⎜⎝

⎛=

PLANCK

K

MMOγβα


At most:

SPACE-TIME FOAM

10-35 m

J.A. Wheeler





44 344 21&

QM



( ) ( )2 , 0,

,,;βαγγα

γβαρρ

>>

= LLGeV 102,, 20

2−×≈⎟⎟

⎠

⎞⎜⎜⎝

⎛=

PLANCK

K

MMOγβα


At most:


φ →KSKL→π+π− π+π− : decoherence & CPTV by QG

The fit with I(π+π−,π+π−;Δt,γ) gives:

t/ s

Data

KLKS+ - + -

KL inc. regeneration

e+e- + - + -

0

50

100

150

200

250

300

350

400

450

500

0 5 10 15 20 25 30 35

In the complete positivity hypothesis α = γ , β = 0 => only one independent parameter: γ

Complete positivity guarantees the positivity of the eigenvalues of density matrices describing states of correlated kaons.

KLOE result

( ) GeV 104.01.1 219.24.2

−+− ×±= SYSTSTATγ

PLB 642(2006) 315L=380 pb-1

CPLEAR( )( )( ) GeV 105.21.1

GeV 103.25.2GeV 108.25.0

21

19

17

−

−

−

×±=

×±=

×±−=

γ

β

α

PLB 364, 239 (1999)

Study of time evolution of single kaonsdecaying in π+π− and semileptonic final state


φ →KSKL→π+π− π+π− : decoherence & CPTV by QG

The fit with I(π+π−,π+π−;Δt,γ) gives:

In the complete positivity hypothesis α = γ , β = 0 => only one independent parameter: γ

CPLEAR( )( )( ) GeV 105.21.1

GeV 103.25.2GeV 108.25.0

21

19

17

−

−

−

×±=

×±=

×±−=

γ

β

α

PLB 364, 239 (1999)

Study of time evolution of single kaonsdecaying in π+π− and semileptonic final state

KLOE FINAL L=1.5 fb-1

Complete positivity guarantees the positivity of the eigenvalues of density matrices describing states of correlated kaons.

( ) GeV 103.02.17.0 21−×±±= SYSTSTATγ


( ) ( )( ) ( )LLSSSLLS KKKKKKKK

KKKKKKKKi−+−∝

++−∝

ωω 00000000

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].

φ →KSKL→π+π− π+π− : CPT violation in correlated K states

at most one expects:35

22 10~10 −− ⇒≈⎟⎟

⎠

⎞⎜⎜⎝

⎛ΔΓ

= ωω PLANCKMEO

The maximum sensitivity to ω is expected for f1=f2=π+π−

All CPTV effects induced by QG (α,β,γ,ω) could be simultaneously disentangled.

In some microscopic models of space-time foam arising from non-critical string theory: [Bernabeu, Mavromatos, Sarkar PRD 74 (2006) 045014] 54 1010~ −− ÷ω


( )( )

C.L. 95%at 101.2

106.04.3

109.01.1

3

48.40.5

47.83.5

−

−+−

−+−

×<

×±=ℑ

×±=ℜ

ω

ω

ω

SYSTSTAT

SYSTSTAT


Fit of I(π+π−,π+π−;Δt,ω):

PLB 642(2006) 315

• Analysed data: 380 pb-1

KLOE result :

Re

Im

68% CL

95% CL

-0.1

-0.05

0

0.05

0.1

0.15

0.2

x 10-2

-0.1 -0.05 0 0.05 0.1 0.15 0.2x 10

-2

Re ω x10-2

Im ω x10-2

0

0

In the B system [Alvarez, Bernabeu, Nebot JHEP 0611, 087]:

C.L. 95%at 0100.00084.0 ≤ℜ≤− ω


KLOE FINAL :


Fit of I(π+π−,π+π−;Δt,ω):

Re ω x10-2

Im ω x10-2

0

0

In the B system [Alvarez, Bernabeu, Nebot JHEP 0611, 087]:

C.L. 95%at 0100.00084.0 ≤ℜ≤− ω

• Analysed data: 1.5 fb-1 (2004-05 data)

( )( )

C.L. 95%at 100.1

102.17.1

104.06.1

3

43.30.3

40.31.2

−

−+−

−+−

×<

×±−=ℑ

×±−=ℜ

ω

ω

ω

SYSTSTAT

SYSTSTAT


3) Tests of Lorentz invariance and CPT symmetry in the neutral kaon system


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]

( ) maaei KKi

SWSW ΔΔ⋅−Δ= /sin 0

rrβγφδ φ

where Δaμ are four parameters associated to SME lagrangian terms and related to CPT and Lorentz violation.

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)

ε LS δε ±=,


at 6 A.M.

at 6 P.M.

Rotation axis Z costantvector

arΔ


Ω: Earth’s sidereal frequencyχ : angle between the z lab. axis and the Earth’s rotation axis

( ) ( )

[

]tata

aam

ei

dtptp

XK

YK

ZKK

iSW

SW

ΩΔ+ΩΔ+

Δ+ΔΔ

=

= ∫

coscossinsincossin

coscossin

,21,,

0

2

0

θχβθχβ

θχβγφ

φδπ

θδ

φ

πrr

δ depends on sidereal time t since laboratory frame rotates with Earth (fixed beam). For a φ-factory there is an additional dependence on the polar and azimuthalangle θ, φ of the kaon momentum in the laboratory frame:

( ) maaei KKi


rrβγφδ φ




( ) ( )

[

]tata

aam

ei

dtptp

XK

YK

ZKK

iSW

SW

ΩΔ+ΩΔ+

Δ+ΔΔ

=

= ∫

coscossinsincossin

coscossin

,21,,

0

2

0

θχβθχβ

θχβγφ

φδπ

θδ

φ

πrr


(in general z lab. axis is non-normal to Earth’s surface)

( ) maaei KKi


rrβγφδ φ




( ) ( )

[

]tata

aam

ei

dtptp

XK

YK

ZKK

iSW

SW

ΩΔ+ΩΔ+

Δ+ΔΔ

=

= ∫

coscossinsincossin

coscossin

,21,,

0

2

0

θχβθχβ

θχβγφ

φδπ

θδ

φ

πrr


( ) maaei KKi


rrβγφδ φ

At DAΦNE K mesons are produced with angular distribution dN/dΩ ∝ sin2θ

ze+ e-


( ) ( )( ) ( )

−

−++−

−++−

ℜ±ℜ−ℜ±ℜ=

→Γ+→Γ→Γ−→Γ

=

xyeKeKeKeK

ALSLS

LSLSLS

2222,,

,,,

δενπνπνπνπ ( )

0sin4 a

meiAA K

iSW

LS

SW

ΔΔ

ℜ≅−

γφ φ

Δa0 from KS and KL semileptonic charge asymmetries

tagged KS and KL(symmetric polar angle θ and sidereal time t integration)

( ) [

]tata

aam

eitp

XK

YK

ZKK

iSW

SW

ΩΔ+ΩΔ+

Δ+ΔΔ

=

coscossinsincossin

coscossin,, 0

θχβθχβ

θχβγφθδφr

with L=400 pb-1 (preliminary): ( ) GeV 108.14.0 170

−×±=Δa

with L=2.5 fb-1 : σ(Δa0) ~ 7 × 10-18 GeV

Measurement of Δa0 at KLOE

(Δa0 evaluated for the first time)


Measurement of ΔaX,Y,Z at KLOE

With L=1 fb-1 (preliminary):

( )( )( ) GeV 107.94.2

GeV 109.58.2

GeV 100.63.6

18

18

18

−

−

−

×±=Δ

×±=Δ

×±−=Δ

Z

Y

X

a

a

a

ΔaX,Y,Z from −+−+→→ ππππφ LS KK π+

π−

KS,Lπ−

π+

KL,S

θ

cosθ>0

cosθ<0(analysis vs polar angle θ and sidereal time t)

I[π+π−(cosθ>0),π+π− (cosθ<0);Δt]• at Δt>>τs sensitive to Re(δ/ε)=0• at Δt~τs sensitive to Im(δ/ε)

( )tp ,,θδεη −=−+

Δt/τS

0. - 4. sidereal hours

KTeV :ΔaX , ΔaY < 9.2 × 10-22GeV @ 90% CLBABAR ΔaB

x,y , (ΔaB0 – 0.30 ΔaB

Z ) ~O(10-13 GeV) [PRL 100 (2008) 131802]


4) Future plans


Physics issues:• Neutral kaon interferometry, CPT symmetry & QM tests• Kaon physics, CKM, LFV, rare KSdecays• η,η’ physics• Light scalars, γγ physics• Hadron cross section at low energy, muon anomaly

KLOE-2 at upgraded DAΦNE

Detector upgrade issues:• Inner tracker R&D• γγ tagging system • Calorimeter, increase of granularity • FEE maintenance and upgrade• Computing and networking update• etc.. (Trigger, software, …)

Upgrade of DAΦNE in luminosity:Crabbed waist scheme at DAΦNE (proposal by P. Raimondi)- increase L by a factor O(5)- requires minor modifications- relatively low cost

- Successful experimental test at DAΦNE

KLOE-2 Plan:- phase 0: KLOE restart taking data end 2009 with a

minimal upgrade (L~5 fb-1)- phase 1: full KLOE upgrade (KLOE-2) > 2011 (L>20 fb-1){


DAΦNE Luminosity versus colliding currents

original collision scheme}

NEW COLLISION SCHEME:Large Piwinski angleCrab-Waist compensation SXTs}

from P. Raimondi’s talk


DAΦNE Luminosity versus colliding currents


Black hist. : σ(Δt)~1τS => 6mm (KLOE)

Red hist: σ(Δt)~1/4 τS => 1.5mm(KLOE + inner tracker)

Blue curve: ideal

Δt/τS

I(π+π−, π+π−;Δt) (a.u.)

Interferometry at KLOE-2: φ →KSKL→π+π− π+π−

600 104 −×=ζ

Δt/τS

I(π+π−, π+π−;Δt) (a.u.)

000 =ζ

Possible signal of decoherenceconcentrated at very small Δt

Theoretical distribution Reconstructed distribution (MC)


5 independent tracking layers for a fine vertex reconstruction of KS and η

200 µm σrφ and 500 µm σZ spatial resolutions with XV readout

700 mm active length

from 150 to 250 mm radii

1.8% X0 total radiation length in the active region

Realized with Cylindrical-GEM detectors

Inner tracker at KLOE


Mode Test of Param. Present best published measurement

KLOE-2L=50 fb-1

KS→πeν CP, CPT AS (1.5 ± 11) × 10-3 ± 1 × 10-3

π+π− πeν CP, CPT AL ( 3322 ± 58 ± 47 ) × 10-6 ± 25 × 10-6

π+π− π0π0 CP Re(ε’/ε) (1.65 ± 0.26) × 10-3 (*) ± 0.2 × 10-3

π+π− π0π0 CP, CPT Im(ε’/ε) (-1.2 ± 2.3) × 10-3 (*) ± 3 × 10-3

πeν πeν CPT Re(δ)+Re(x-) Re(δ) = (0.25 ± 0.23) × 10-3 (*)Re(x-) = (-4.2 ± 1.7) × 10-3 (*)

± 0.2 × 10-3

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

± 3 × 10-3

π+π− π+π− Δm (5.288 ± 0.043) × 109 s-1 ± 0.03 × 109 s-1

Perspectives with KLOE-2 at upgraded DAΦNE

(*) = PDG 2008 fit


Perspectives with KLOE-2 at upgraded DAΦNE

Mode Test of Param. Present best published measurement

KLOE-2L=50 fb-1

π+π− π+π− QM ζ00 (1.0 ± 2.1) × 10-6 ± 0.1 × 10-6

π+π− π+π− QM ζSL (1.8 ± 4.1) × 10-2 ± 0.2 × 10-2

π+π− π+π− CPT & QM α (-0.5 ± 2.8) × 10-17 GeV ± 2 × 10-17 GeVπ+π− π+π− CPT & QM β (2.5 ± 2.3) × 10-19 GeV ± 0.1 × 10-19 GeVπ+π− π+π− CPT & QM γ (1.1 ± 2.5) × 10-21 GeV ± 0.2 × 10-21 GeV

compl. pos. hyp.± 0.1 × 10-21 GeV

π+π− π+π− CPT & EPR corr. Re(ω) (1.1 ± 7.0) × 10-4 ± 2 × 10-5

π+π− π+π− CPT & EPR corr. Im(ω) (3.4 ± 4.9) × 10-4 ± 2 × 10-5

KS,L→πeν CPT & Lorentz Δa0 [(0.4 ± 1.8) × 10-17 GeV] ± 2 × 10-18 GeV

π+π− π+π− CPT & Lorentz ΔaZ [(2.4 ± 9.7) × 10-18 GeV] ± 7 × 10-19 GeV

π+π− πeν CPT & Lorentz ΔaX,Y [<10-21 GeV] ± 4 × 10-19 GeV

[….] = preliminary


Conclusions•The neutral kaon system is an excellent laboratory for the study of CPT symmetry and the basic principles of Quantum Mechanics;

•Several parameters related to possible •CPT violation (within QM)•CPT violation and decoherence•CPT violation and Lorentz symmetry breaking

have been recently measured at KLOE, 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 KLOE data sample is completed (apart the analysis of CPTV and LV);

•KLOE and DAΦNE are going to be upgraded•KLOE (KLOE-2) will restart taking data at the end of this year•Neutral kaon interferometry, CPT symmetry and QM tests are one of the main issues of the KLOE-2 physics program

•Other interesting QM tests possible, e.g. quantum eraser.

CPT symmetry and quantum coherence tests in the neutral kaon

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