Test della simmetria CPT e della meccanica quantistica nel sistema dei mesoni K neutri a KLOE...

Test della simmetria CPT e della meccanica quantistica nel sistema dei mesoni K neutri a KLOE

Antonio Di Domenico

Roma, 23 maggio 2008

2Roma - 23 maggio 2008 A. Di Domenico

CPT: introduction

CPT theorem (Luders, Jost, Pauli, Bell 1955 -1957):Exact CPT invariance holds for any quantum field theory which assumes:(1) Lorentz invariance (2) Locality (3) Unitarity (i.e. conservation of probability).

Testing the validity of the CPT symmetry probes the most fundamental assumptions of our present understanding of particles and their interactions.

Extension of CPT theorem to a theory of quantum gravity far from obvious(e.g. CPT violation appears in some models with space-time foam backgrounds).

No predictive theory incorporating CPT violation => only phenomenological models to be constrained by experiments.

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.


Consequences of CPT symmetry: equality of masses, lifetimes, |q| and || of a particle and its anti-particle.

The neutral kaon system is one of the most intriguing systems in nature; it offers 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:

181000 KKK

mmm

1410 00 BBB

mmm

810 ppp mmm

neutral K system

neutral B system

proton- anti-proton

CPT: introduction


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


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

00 , KK

ttt

i

H

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

The neutral kaon system

Diagonalizing the effective Hamiltonian:

LSLSLS

im ,,, 2

0,,,

LSti

LS KetK LS

1,2,2,1

,

0,

0,

,

,

1

1

1112

1

KK

KKK

LS

LS

LSLS

LS

LS

eigenvalues eigenstates

S ~ 90 ps L ~ 51 ns

2221

1211

2221

1211

22

i

mm

mmiΓMH

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

|K1,2> areCP=±1 states


/im

ΓΓimmHH

LS 2

2

2

1

2112211222211

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

ε LS ,

CPT violation in the mixing:

LSSL

KK

KK

mmm

mmmm

,

,

,

00

00

2211

2211

/im

miHH

LS 2

2

212122112

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

012 (with a phase convention )



dcKTbaKT

dcKTbaKT

00

00

CPT violation in semileptonic decays

a

cx

a

dx

a

by

CPT

viol.

CPT & S=Q viol.

S=Q

Viol.

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

xyeKeK

eKeKA

LSLS

LSLSLS 2222

,,

,,,

Semileptonic charge asymmetry:

00

00

KK

KK

S=Q rule

xAA LS 4

CP T CPT S=Q

a =0 =0

b =0 =0 =0

c =0 =0 =0

d =0 =0 =0 =0


0

0

00

00

0000 200

A

B

KT

KTe

KT

KTe

S

Li

S

Li

CPT violation in decays

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

mSW 2arctan

I

I

iδII

iδII

eBAKTI

eBAKTI

0

0

;

;

0

02211

0

0

2

2

0

200

2Δ2

1

31

2

3

A

B

m

mm-

A

B

A

B

A

A

SW

-2

SW

Im

Re

-

(not to scale)



Study of the time evolution of neutral kaons in semileptonic decays K0

e+

=0 PLB444 (1998) 52

6

0

000 10353

23

1

3

2

A

Bxy

AL

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

AL=( 3322 58 47 ) 10-

6

PRL88,181601(2002)

KL semileptonic charge asymmetry:

Study of regenerator beam two pion decay distribution

+- - SW = 0.61º ±0.62º ± 1.01 º00-+- = 0.39º ± 0.22 º ±0.45 º

PRD67,012005 (2003)

Some results of CPT tests

CPLEAR

KTeV

KTeV


• e+e b W = m = 1019.4 MeV• BR( K0K0) ~ 34%• ~106 neutral kaon pairs per pb-1 produced in an antisymmetric quantum state with JPC = 1

Neutral kaons at a -factory

pKpKpKpK

N

pKpKpKpKi

SLLS

2

2

1 0000

pK = 110 MeV/c S = 6 mm L = 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 -factory, not possible at fixed target experiments)

Production of the vector meson in e+e annihilations:

KL,S

KS,L

e-e+

111122 LSLSN


Day performance: 7-8 pb-1

Best month L dt ~ 200 pb1

Total KLOE L dt ~ 2.5 fb1 (2001 - 05)

~2.5109 KSKL pairs

DANE: the Frascati -factory Integrated luminosity (KLOE)


CalorimeterCalorimeter Drift chamberDrift chamber

E/E 5.7% /E(GeV)

t 54 ps /E(GeV) 50 ps

(relative time between clusters)

~ 2 cm (0 from KL )

p/p 0.4 % (tracks with > 45°)

xhit 150 m (xy), 2 mm (z)

xvertex ~ 1 mm

The KLOE detector at DANE

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

Lead/scintillating fiber4880 PMTs98% coverage of solid angle

Superconducting coil

B = 0.52 T


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

KS momentum resolution: ~ 2 MeV

KKLL “crash”“crash”

= 0.22 (TOF)= 0.22 (TOF)

KKSS ee

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

KKSS

KKLL 2 2

KS and KL Tagging at KLOE


KS e KLOE results

Data sample: 410 pb-1

Emiss-Pmiss

AS = (1.5 9.6 2.9 ) 103

with 2.5 fb1: AS 3 103 2 Re

eKeK

eKeKA

SS

SSS

PLB 636(2006) 173

x = ( 0.8 2.4 0.7) 10

xyA LS 2222,

y = ( 2.4 0.7) 10

xAA LS 4

yAA LS 4

CPT & S=Q viol.

CPT viol.

input from other experiments

If CPT holds, AS=AL =2Re ASAL signals CPT violation in mixing and/or decay with SQ

BR(KS e) = (3.528 0.057 0.027) 104

BR(KS e) = (3.517 0.051 0.029) 104

BR(KS e) = (7.046 0.076 0.050) 104

BR(e) [KLOE ’02, 17 pb1]: (6.91 0.34 0.15) 104

PLB 636(2006) 173


CPT test: the Bell-Steinberger relation

i i

i i

SW

SW

kk

kbk

Nδε

ε

1tan1

tan121111

2

BRKS

00BRK

S

kl3

S

L BR(K

Ll3) (A

S+A

L)/4i Im x

S

L

BRKL

S

L

BRKL

kbkkkN

KBRbk

SW

LLS

12tan11

, 222

SiLii KTfKTf

fLLSS

t

KTfaKTfatKdt

d 2

0

2

LLSS KaKaK

fLS

LSSW

LS

LS KTfKTfii1

1tan 2

Unitarity constraint:

KS KL

observables


Experimental inputs to the Bell-Steinberger relation

Main improvements done with KLOE measurements on KS

semileptonic and 30 decays


Re Im

KLOE result: JHEP12(2006) 011

CPT test: the Bell-Steinberger relation

Combining Re and Im results:

/im

ΓΓimmKKKK

2

2

2

1 0000

Assuming , i.e. no CPT viol. in decay: 000 KK

ΓΓ

GeV 103.6103.5 191900

KK

mm

at 95% c.l.

00 KKΓΓ

00 KKmm

Re

Im


2) Tests of QM and CPT symmetry in the neutral kaon system


Neutral kaon interferometry

2112

2/21

2

2

2

1122211

cos2

,;,

21

2121

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

fi = letc

characteristic interference termat a -factory => interferometry2

21212

2

SSN KTfKTfC

KL,S

KS,L

t1

t2

t=t1- t2 f2

f1

pKpKpKpKN

i SLLS

2


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

21 and 0for

cos2

0;,

122/

21

2

2

2

12112

ttt

tme

eetffI

t

ttC

LS

SL

LS

Neutral kaon interferometry

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

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


Neutral kaon interferometry: main observables

t/S

I(t) (a.u) I(t) (a.u)

I(t) (a.u)

t/S

t/S00 LS KK

LS KK

LS KK


Neutral kaon interferometry: main observables

measured quantity parameters

mode

0;,0;,

0;,0;,0000

0000

tItI

tItItA

00 LS KK

LS KK

0;,0;,

0;,0;,

teeIteeI

teeIteeItACPT

x

x

LS KK

teIteI

teIteItA

;,;,

;,;,

xy

AL 2

tI ;, LS KK

L Sm


LS KK

t/S

I(t

) (a

.u)

Same final state for both kaons: ff

t=|t1-t2|

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

EPR correlation:

t2 t1

0000

2

1KKKKi

t2=t1 t1


tKKtKK

tKKtKKtI N

0000

200

200

2

,,2

,,;,

tKKtKK

tKKtKKtI N

000000

200

200

2

,,21

,,;,

KSKL: test of quantum coherence

edecoherenc total 1

QM 0

00

00

Decoherence parameter:

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

0000

2

1KKKKi


• Analysed data: L=380 pb

• Fit including t resolution and efficiency effects + regeneration• S, L , m fixed from PDG

L=1 fb-1 (2005 data)

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

KLOE result:

6SYSTSTAT00 104.01.20.1

7.04.000

PLB 642(2006) 315

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

057.0029.000

B

6STAT00 102.13.0

KLOE preliminary:

KSKL: test of quantum coherence

Comparison with precision in quantum optics test

as CP viol. O(high sensitivity to

00


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

Decoherence and CPT violation

LHiiHt

QM

extra term inducingdecoherence:pure state => mixed state

Possible decoherence due quantum gravity effects:Black hole information loss paradox => Possible decoherence near a black hole.Hawking [1] suggested that at a microscopic level, in a quantum gravity picture, 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. :

2 , 0,

,,;

LLGeV 102,, 20

2

PLANCK

K

M

MO

[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:

SPACE-TIME FOAM

10-35 m


A

tt

tt

m

tttt

tttt

veKRR

veKRR

RRRR

RRRRA

KRKR

KRKRA

)( )(

)( )(

)()()()(

)()()()()(

)( )(

)( )( )(

)()(0

0)(

)()(0

0)(

00

00

00

00

A Am

datafit 10

CPLEAR

GeV 105.21.1

GeV 103.25.2

GeV 108.25.0

21

19

17

PLB 364, 239 (1999)

at 90% CL

GeV107.3

GeV103.2

GeV100.4

21

19

17

Imposing >0 > 2

Using single kaons

Decoherence and CPT violation induced by QG


KSKL: decoherence & CPTV by QG

KLOE preliminary

GeV 102.14.0

GeV 108.17.3

GeV 10910

218.51.5

199.62.9

174131

SYSTSTAT

SYSTSTAT

SYSTSTAT

The fit with I(t,) gives:

In the complete positivity hypothesis = , = 0 => only one independent parameter: Complete positivity guarantees

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

KLOE preliminary L=1 fb-1

GeV 108.0 215.13.1

STAT

L=380 pb-1

KLOE result

GeV 104.01.1 219.24.2

SYSTSTAT

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


LLSSSLLS KKKKKKKK

KKKKKKKKi

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].

KSKL: CPT violation in correlated K states

at most one expects:35

22

10~10

PLANCKMEO

The maximum sensitivity to is expected for f1=f2=

All CPTV effects induced by QG 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~


KLOE preliminary :

• Analysed data: 1 fb-1 (2005 data)

C.L. 95%at 101.2

106.04.3

109.01.1

3

48.40.5

47.83.5

SYSTSTAT

SYSTSTAT

KSKL: CPT violation in correlated K states

Fit of I(t,):

• Analysed data: 380 pb-1

KLOE result : PLB 642(2006) 315

C.L. 95%at 1098.0

102.2

105.2

3

44.31.3

41.33.2

STAT

STAT

Re x10-2

Im x10-2

0

0

( measured for the first time)


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 (1999) 016002, PRD 64 (2001) 076001]

CPT violation in SME manifests to lowest order only in =>and exhibits a kaon momentum dependence:

maaei KKi

SWSW /sin 0

Possible hidden momentum dependence in other parameters, e.g. , m, , SW , is suppressed w.r.t. .

0 dbBI

cannot be a constant

No CPT viol. in decays

where a are four parameters related to CPT and Lorentz violationa = rq1 aq1 – rq2 aq2 , with aqi CPT and Lorentz violating coupling constants for the two valence quarks in the kaon; rqi factors for quark binding or other normalization effects.aq have mass dimension and are associated to SME lagrangian terms of the form

qqaq


at 6 A.M.

at 6 P.M.

Rotation axis Zcostant vector

a

For a fixed target experiment (fixed momentum direction) depends on sidereal time t since laboratory frame rotates with Earth.

CPT and Lorentz invariance violation (SME)

Earth’s sidereal frequencyangle between the z lab. axis and the Earth’s rotation axis

ta

ta

aam

ei

dtptp

XK

YK

ZKK

iSW

SW

coscossin

sincossin

coscossin

,2

1,,

0

2

0

For a -factory there is an additional dependence on the polar and azimuthal angle of the kaon momentum in the laboratory frame:

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

At DANE K mesons are produced with angular distribution dN/d sin2

KLOE is a kind of telescope, able to explore with a kaon beam almost any direction in space

ze+ e-


xy

eKeK

eKeKA

LSLS

LSLSLS

2222,,

,,,

0

sin4a

m

eiAA K

iSW

LS

SW

a0 from KS and KL semileptonic charge asymmetries

tagged KS and KL

(symmetric polar angle and sidereal time t integration)

ta

ta

aam

eitp

XK

YK

ZKK

iSW

SW

coscossin

sincossin

coscossin

,, 0

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

a

with L=2.5 fb-1 : a0 ~ 7 10-18 GeV

Measurement of a0 at KLOE

(a0 evaluated for the first time)


Measurement of aX,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

Z

Y

X

a

a

a

aX,Y,Z from LS KK +

KS,L

KL,S

cos

cos(analysis vs polar angle and sidereal time t)

I[(cos),(cos<0)t]• at t>>s sensitive to Re()=0• at t~s sensitive to Im()

tp ,,

2/dof=131/117

t/S

0. - 4. sidereal hours

KTeV :aX , aY < 9.2 10-22GeV @ 90% CL

BABAR aBx,y , (aB

0 – 0.30 aBZ ) ~O(10-13 GeV)


4) Future plans


Physics issues:• Neutral kaon interferometry, CPT symmetry & QM tests• Kaon physics, CKM, LFV, rare KS decays• ,’ physics• Light scalars, physics• Hadron cross section at low energy, muon anomaly• (baryon electromagnetic form factors, e+e- pp, nn,

KLOE-2 at upgraded DANE

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

Proposals to upgrade DANE in luminosity (and energy):Crabbed waist scheme at DANE (proposal by P. Raimondi)- increase L by a factor O(5)- requires minor modifications- relatively low cost

- Experimental test at DANE in progress

KLOE-2 Expression of Interest:[ L=50 fb-1 at peak (and s up to 2.5 GeV) ]


Mode Test of Param. Present best published measurement

KLOE-2

L=50 fb-1

KSe CP, CPT AS (1.5 11) 10-3 1 10-3

e CP, CPT AL ( 3322 58 47 ) 10-6 25 10-6

CP Re’ (1.47 0.22) 10-3 0.2 10-3

CP, CPT Im’ (2.3 2.9) 10-3 3 10-3

e e CPT Re()+Re(x-) Re((0.29 0.27) 10-3

Re(x-)(-0.8 2.5) 10-3

0.2 10-3

e e CPT Im()+Im(x+) Im() = (0.4 2.1) 10-5

Im(x+) = (0.8 0.7) 10-2

3 10-3

m (5.288 0.043) 109 s-1 0.03 109 s-1

Perspectives with KLOE-2 at upgraded DANE


Perspectives with KLOE-2 at upgraded DANE

Mode Test of Param. Present best published measurement

KLOE-2

L=50 fb-1

QM 00 (1.0 2.1) 10-6 0.1 10-6

QM SL (1.8 4.1) 10-2 0.2 10-2

CPT & QM (-0.5 2.8) 10-17 GeV 2 10-17 GeV

CPT & QM (2.5 2.3) 10-19 GeV 0.1 10-19 GeV

CPT & QM (1.1 2.5) 10-21 GeV 0.2 10-21 GeV

compl. pos. hyp.

0.1 10-21 GeV

CPT & EPR corr. Re (1.1 7.0) 10-4 2 10-5

CPT & EPR corr. Im (3.4 4.9) 10-4 2 10-5

KS,Le CPT & Lorentz a0 [(0.4 1.8) 10-17 GeV]

2 10-18 GeV

CPT & Lorentz aZ [(2.4 9.7) 10-18 GeV]

7 10-19 GeV

e CPT & Lorentz aX,Y [<10-21 GeV] O(10-19)GeV


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 measured by KLOE, in same cases with a precision reaching the interesting Planck’s scale region;

•All results are consistent with no CPT violation

•The full KLOE data set analysis is almost completed;

•KLOE and DANE are going to be upgraded;•Neutral kaon interferometry, CPT symmetry and QM tests are one of the main issues of the KLOE-2 physics program


http://www.roma1.infn.it/people/didomenico/roadmap/handbook.html

More detailed information can be found in:

Handbook on neutral kaon interferometry

at a -factory G. Amelino-Camelia, M. Arzano, F. Benatti,

J. Bernabeu, R. Bertlmann, A. Bramon, A. Di Domenico, R. Floreanini, A. Go,

B. Hiesmayr, G. Isidori, R. Lehnert, N. Mavromatos J. Ellis, G. Garbarino, A. Marcianò, D. Nanopoulos,

J. Papavassiliou, S. Sarkar

published in Frascati Physics Series, Vol. 43, 2007

also available at:


A. Di Domenico Neutral kaon interferometry at a phi-factory

J. Bernabeu, J. Ellis, N. Mavromatos, D. Nanopoulos, J. Papavassiliou CPT and quantum mechanics tests with kaons

S. Sarkar Methods and models for the study of decoherence

F. Benatti, R. Floreanini Open quantum dynamics: complete positivity and correlated kaons

R. Lehnert CPT and Lorentz symmetry breaking: a review G. Amelino-Camelia, M. Arzano, A. Marciano'

On the quantum gravity phenomenology of multiparticle states G. Isidori

Testing CPT in the neutral kaon system by means of the Bell-Steinberger relation R. Bertlmann, B. Hiesmayr

Strangeness measurements of kaon pairs, CP violation and Bell inequalities A. Bramon, R. Escribano, G. Garbarino

A review of Bell inequality tests with neutral kaons A. Bramon, G. Garbarino, B. Hiesmayr

Kaonic quantum erasers at a phi-factory: "erasing the present, changing the past" A. Go

Kaon interferometry at CPLEAR

http://www.roma1.infn.it/people/didomenico/roadmap/handbook.html


Spare


EFFECTS OF CRAB SEXTUPOLES ON LUMINOSITY

Crab on

Crab off

Transverse beam dimensions at the Synchrotron Light Monitor

LUMINOMETERS

A huge work on machine optimization has been done and is still in progress in term of feedbacks systems tuning, background minimization and tuning of the machine luminosity…

P. Raimondi May 6, 2008


Black hist. : (t)~1S => 6mm (KLOE)

Red hist: (t)~1/4 S => 1.5mm(KLOE + inner tracker)

Blue curve: ideal

Example of interferometry at KLOE-2: KSKL

t/S

I(, ;t) (a.u.)

600 104

t/S

I(, ;t) (a.u.)

000

Possible signal of decoherenceconcentrated at very small t

Theoretical distribution Reconstructed distribution (MC)

Test della simmetria CPT e della meccanica quantistica nel sistema dei mesoni K neutri a KLOE...

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Transcript of Test della simmetria CPT e della meccanica quantistica nel sistema dei mesoni K neutri a KLOE...