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
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.
3Roma - 23 maggio 2008 A. Di Domenico
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
4Roma - 23 maggio 2008 A. Di Domenico
1) “Standard” tests of CPT symmetry in the neutral kaon system
5Roma - 23 maggio 2008 A. Di Domenico
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
6Roma - 23 maggio 2008 A. Di Domenico
/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 )
7Roma - 23 maggio 2008 A. Di Domenico
CPT violation in the neutral kaon system: “standard” picture
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
8Roma - 23 maggio 2008 A. Di Domenico
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)
CPT violation in the neutral kaon system: “standard” picture
9Roma - 23 maggio 2008 A. Di Domenico
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
10Roma - 23 maggio 2008 A. Di Domenico
• 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
11Roma - 23 maggio 2008 A. Di Domenico
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)
12Roma - 23 maggio 2008 A. Di Domenico
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
13Roma - 23 maggio 2008 A. Di Domenico
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
14Roma - 23 maggio 2008 A. Di Domenico
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
15Roma - 23 maggio 2008 A. Di Domenico
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
16Roma - 23 maggio 2008 A. Di Domenico
Experimental inputs to the Bell-Steinberger relation
Main improvements done with KLOE measurements on KS
semileptonic and 30 decays
17Roma - 23 maggio 2008 A. Di Domenico
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
18Roma - 23 maggio 2008 A. Di Domenico
2) Tests of QM and CPT symmetry in the neutral kaon system
19Roma - 23 maggio 2008 A. Di Domenico
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
20Roma - 23 maggio 2008 A. Di Domenico
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
21Roma - 23 maggio 2008 A. Di Domenico
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
22Roma - 23 maggio 2008 A. Di Domenico
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
23Roma - 23 maggio 2008 A. Di Domenico
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
24Roma - 23 maggio 2008 A. Di Domenico
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
25Roma - 23 maggio 2008 A. Di Domenico
• 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
26Roma - 23 maggio 2008 A. Di Domenico
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
27Roma - 23 maggio 2008 A. Di Domenico
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
28Roma - 23 maggio 2008 A. Di Domenico
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
29Roma - 23 maggio 2008 A. Di Domenico
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~
30Roma - 23 maggio 2008 A. Di Domenico
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)
31Roma - 23 maggio 2008 A. Di Domenico
3) Tests of Lorentz invariance and CPT symmetry in the neutral kaon system
32Roma - 23 maggio 2008 A. Di Domenico
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
33Roma - 23 maggio 2008 A. Di Domenico
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-
34Roma - 23 maggio 2008 A. Di Domenico
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)
35Roma - 23 maggio 2008 A. Di Domenico
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)
36Roma - 23 maggio 2008 A. Di Domenico
4) Future plans
37Roma - 23 maggio 2008 A. Di Domenico
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) ]
38Roma - 23 maggio 2008 A. Di Domenico
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
39Roma - 23 maggio 2008 A. Di Domenico
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
40Roma - 23 maggio 2008 A. Di Domenico
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
41Roma - 23 maggio 2008 A. Di Domenico
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:
42Roma - 23 maggio 2008 A. Di Domenico
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
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