Transcript kektc5 - Istituto Nazionale di Fisica Nucleare

Test della simmetria CPT e della meccanica
quantistica nel sistema dei mesoni K neutri a KLOE
Antonio Di Domenico
Roma, 23 maggio 2008
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 (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.
A. Di Domenico
Roma - 23 maggio 2008
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CPT: introduction
Consequences of CPT symmetry: equality of masses, lifetimes, |q| and |m|
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:
neutral K system
mK 0  mK 0 mK  10 18
neutral B system
mB 0  mB 0 mB  10 14
proton- anti-proton
m p  m p m p  10 8
A. Di Domenico
Roma - 23 maggio 2008
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1) “Standard” tests of CPT symmetry in the neutral kaon
system
A. Di Domenico
Roma - 23 maggio 2008
4
The neutral kaon system

The time evolution of a two-component state vector Y in the K 0 , K
given by (Wigner-Weisskopf approximation):

i
t
0
 space is
Y t   HY t 
H is the effective hamiltonian (non-hermitian), decomposed into a Hermitian
Part (mass matrix M) and an anti-Hermitian part (i/2 decay matrix G) :
 m11 m12  i  G11 G12 
i
  

H  M  Γ  
2
 m21 m22  2  G21 G22 
Diagonalizing the effective Hamiltonian:
eigenvalues
i
S , L  mS , L  GS , L
2
 i t
K S , L t   e S ,L K S , L 0 
eigenstates
K S ,L 
tS ~ 90 ps tL ~ 51 ns
mL-mS= 3.5 x 10-15 GeV ~ GS / 2
A. Di Domenico


1
2 1   S ,L
1
1   
S ,L
Roma - 23 maggio 2008
1    K  1    K 

K
0
0
S ,L
1, 2
  S , L K 2,1
S ,L

|K1,2> are
CP=±1 states
small CP impurity ~2 x 10-3
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CPT violation in the neutral kaon system: “standard” picture
CPT violation in the mixing:
εS , L    
H12  H 21  im12  G12 2


2S  L 
m  iG/ 2
H11  H 22 1 m22  m11   i 2 Γ 22  Γ11 


2S  L  2
m  iG/ 2
m11  mK 0 , m22  mK 0
•  ≠ 0 implies CPT violation
•  ≠ 0 implies T violation
•  ≠ 0 or  ≠ 0 implies CP violation
G11  GK 0 , G22  GK 0
m  m L  m S ,
G  GS  GL
(with a phase convention G12  0 )
A. Di Domenico
Roma - 23 maggio 2008
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CPT violation in the neutral kaon system: “standard” picture
CPT violation in semileptonic decays
S=Q rule
   T K 0  a  b
    T K 0  c  d
K 0     
K 0     
    T K 0  a  b
   T K 0  c  d 
K 0     
K 0     
CP
CPT
=0
viol.
=0
a
b
c
d
b
y  =0
a
=0
T
CPT
S=Q
CPT &
S=Q
=0 viol.
S=Q
Viol.
=0
=0 

d
x =0

a
=0
x 
=0
c
a
=0
=0
Semileptonic charge asymmetry:
AS , L


GK
 
e    GK
Standard Model prediction of S=Q
rule violation is x=c/a ~ O(10-7)
  2  2  2y  2x
e
G K S , L    e   G K S , L    e 
S ,L
 

S ,L
 


AS  AL  4  x 
A. Di Domenico
Roma - 23 maggio 2008
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CPT violation in the neutral kaon system: “standard” picture
CPT violation in  decays
 ; I T K
0
 ; I T K
0
  AI  BI e


I

I

iδI
       ei 

 A B e
AI(BI) CPT conserving (violating)
K  amplitudes for I=0,2
iδI
I strong phase shift for I=0,2)
Im

-
00   

00


00
A. Di Domenico

00
S

 0 0 T K L
  T KS
0
3 1 A2

2    A0
   SW 
W
  T KS

B0
  
A0
(not to scale)
-2
00  00 ei 
   T K L
0
    
     2 
SW  arctan2m G
 B2 B0 


  3 

 
 A2 A0 
-1  m11  m22 B0 



2Δ
m

A
2  
0 
Re
Roma - 23 maggio 2008
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Some results of CPT tests
CPLEAR
Study of the time evolution of
neutral kaons in semileptonic decays
  0.30  0.33  0.06  103
KTeV
Study of regenerator beam
two pion decay distribution
t=0
KTeV
+- - SW = 0.61º ±0.62º ± 1.01 º
00-+- = 0.39º ± 0.22 º ±0.45 º


PRL88,
181601(2002)
AL=( 3322  58  47 )  10-6
Constraints on CPT violation in  and semileptonic decays obtained
combining KTeV and PDG results:

B0 
1  AL
2
   3  35106
     00  
  y  x 
3  2
A0 
3

A. Di Domenico
t
PLB444 (1998) 52
KL semileptonic charge asymmetry:
e+
K0
Roma - 23 maggio 2008
PRD67,012005 (2003)
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Neutral kaons at a -factory
Production of the vector meson 
KS,L
in e+e annihilations:
+
e
e

• e+e  
s~3 mb
W = m = 1019.4 MeV
KL,S
• BR(  K0K0) ~ 34%
• ~106 neutral kaon pairs per




1
i 
K 0  p  K 0  p   K 0  p  K 0  p 
pb-1 produced in an
2
antisymmetric quantum state




N
with JPC = 1 :
 K S  p  K L  p   K L  p  K S  p  

2
pK = 110 MeV/c
2
2
S = 6 mm L = 3.5 m
N  1   S 1   L  1   S  L   1

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)
A. Di Domenico
Roma - 23 maggio 2008
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
DANE: the Frascati -factory
Integrated luminosity (KLOE)
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
A. Di Domenico
Roma - 23 maggio 2008
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The KLOE detector at DANE
Superconducting coil
B = 0.52 T
Drift chamber
Calorimeter
4 m diameter × 3.3 m length
90% helium, 10% isobutane
12582/52140 sense/total wires
All-stereo geometry
Lead/scintillating fiber
4880 PMTs
98% coverage of solid angle
sE/E  5.7% /E(GeV)
st
 54 ps /E(GeV)  50 ps
(relative time between clusters)
sgg
~ 2 cm (0 from
A. Di Domenico
KL  0)
sp/p  0.4 % (tracks with q > 45°)
sxhit  150 mm (xy), 2 mm (z)
sxvertex ~ 1 mm
Roma - 23 maggio 2008
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KS and KL Tagging at KLOE
KL “crash”
b= 0.22 (TOF)
KS  
KS  e
KS tagged by KL interaction in EmC
Efficiency ~ 30% (largely geometrical)
KS angular resolution: ~ 1° (0.3 in )
KS momentum resolution: ~ 2 MeV
A. Di Domenico
KL  20
KL tagged by KS   vertex at IP
Efficiency ~ 70% (mainly geometrical)
KL angular resolution: ~ 1°
KL momentum resolution: ~ 2 MeV
Roma - 23 maggio 2008
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KS e: KLOE results
Data sample: 410 pb-1


 
 


PLB 636(2006) 173
G KS   e  G K S    e
AS 
  e ) = (3.528
BR(K
 0.057  0.027)
 104
 
 
G KS   e   G KS   e 
BR(KS  e) = (3.517  0.051  0.029)  104
AS = ( 1.5  9.6  2.9 )  103
BR(KS  e) = (7.046  0.076  0.050)  104
with 2.5 fb1: AS ~ 3  103 ~ 2 Re 
BR(e) [KLOE ’02, 17 pb1]: (6.91  0.34  0.15)  104
AS ,L  2  2  2y  2x
Emiss-Pmiss
If CPT holds, AS=AL =2Re  ASAL
signals CPT violation in mixing
and/or decay with SQ
AS  AL  4  x 
x = ( 0.8  2.4  0.7)  103 CPT & S=Q viol.
AS  AL  4  y 
y = ( 0.4  2.4  0.7)  103
CPT viol.
input from other experiments
A. Di Domenico
Roma - 23 maggio 2008
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CPT test: the Bell-Steinberger relation
K  aS KS  aL KL
Unitarity constraint:
 d
K t 

 dt
2

   aS f T K S  a L f T K L
t 0
f

 GS  GL
 
 1

 i tanSW 

i


2

 GS  GL
G

G
1


L
 S


 ε 

1  1  k 1  2b 
2 
 1  ε    1  k  tan
SW
 δ  N 



2

f T KS
f T KL
f
1  k  tanSW  i  i 

 1  k   i  i 
KS KL
observables
  BRKS
0 tS/tL  0 BRKL0
00 00 BRKS00
000 tS/tL  000 BRKL000
kl3  2tS/tL BR(KLl3) (AS+AL)/4 i Im x
i  fi T KL
A. Di Domenico
f i T KS
k tS tL
b  BRK L   
,
N  1  k   1  k  tan2 SW  2bk1  k 
2
Roma - 23 maggio 2008
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15
Experimental inputs to the Bell-Steinberger relation
Main improvements done with
KLOE measurements on KS
semileptonic and 30 decays
A. Di Domenico
Roma - 23 maggio 2008
16
CPT test: the Bell-Steinberger relation
KLOE result:
Re   159.6  1.3 105
Im  0.4  2.1  105
Combining Re and Im results:
1 mK 0  mK 0   i 2Γ K 0  Γ K 0 

2
m  iG/ 2
Assuming
Γ
K0
Γ
K0
 Γ K 0   0 , i.e. no CPT viol. in decay:
 5.31019  mK 0  mK 0  6.31019 GeV
 ΓK 0 
Im
m
K0
 mK 0 
Re
at 95% c.l.
A. Di Domenico
Roma - 23 maggio 2008
17
2) Tests of QM and CPT symmetry in the neutral kaon system
A. Di Domenico
Roma - 23 maggio 2008
18
Neutral kaon interferometry
f1




N
 K S  p  K L  p   K L  p  K S  p  
i 
2
Double differential time distribution:

I  f1 , t1; f 2 , t2   C12 1 e
2
GL t1 GS t 2
t1
KS,L 
t=t1- t2
t2
KL,S
  2 e GS t1 GLt2
f2
2

 21  2 e GS GL t1 t2 / 2 cosmt2  t1   1  2 
where t1(t2) is the proper time of one (the other) kaon decay into f1 (f2)
final state and:
ii
i  i e  fi T KL
C12 
N
2
2
f1 T K S
fi T KS characteristic interference term
2
at a -factory => interferometry
f2 T KS
fi = , 00, l, 0, 30, g ..etc
A. Di Domenico
Roma - 23 maggio 2008
19
Neutral kaon interferometry
Integrating in (t1+t2) we get the time difference (t=t1-t2)
distribution (1-dim plot simpler to manipulate than 2-dim plot):
I  f1 , f 2 ; t  0  
C12
GS  GL

2
1
e
 GL t
 2 e
2
 GS t

 2 1  2 e GS  GL t / 2 cosmt  2  1 
for t  0
t  t and 1  2
From these distributions for various final states fi one can measure the
following quantities:
Phases (difference of) from the
term =>
GS , GL , m , i , i  arg i interference
interferometry
 
A. Di Domenico
Roma - 23 maggio 2008
20
Neutral kaon interferometry: main observables
I(t) (a.u)
I(t) (a.u)
  KS KL     
I(t) (a.u)
   
   
t/tS
  KS KL      0 0
t/tS
  K S K L   
t/tS
A. Di Domenico
Roma - 23 maggio 2008
21
Neutral kaon interferometry: main observables
mode
parameters
measured quantity
  KS KL      0 0
At  


 
 
I   ,   ; t  0  I   ,   ; t  0
I    ,  0 0 ; t  0  I    ,  0 0 ; t  0
  KS KL     


0
0




0
0
 
 
 
   
   


I  e ,   e ; t  0  I  e ,   e ; t  0
ACPT t      
I  e  ,  e  ; t  0  I  e ,   e ; t  0
  K S K L   


 
 
A. Di Domenico

I    ,    ; t
Roma - 23 maggio 2008


  x
AL  2  
I    ,  e  ; t  I    ,   e  ; t
At  
I    ,  e  ; t  I    ,   e  ; t
  KS KL       
  x


 
m
 y  x
GS
GL
22
  K S K L       

t=|t1-t2|




t1
t2

Same final state for both kaons: f1  f2  
I(t) (a.u)

1
i 
K0 K 0  K 0 K0
2
EPR correlation:
no simultaneous decays
(t=0) in the same
final state due to the
destructive
quantum interference


A. Di Domenico


t1
t2=t1
t/tS

Roma - 23 maggio 2008
23
 KSKL  : test of quantum coherence

1
i 
K0 K 0  K 0 K0
2
 

 
2
2
2




0
0




0
0





0
0




0
0

I  I ,  ,  ; t ;t  N2  ,  ,  K KK K
t t   ,  ,  K KK K
t t 
 

    

N
2
2


        0 0 0 0
       0  0 0 0  







 1  2

2



,


K
K

t


,


K
K

t








,


K
K

t


,


K
K

t
 
00 


 
Decoherence parameter:
 00  0  QM
 00  1  totaldecoherence
(also known as Furry's hypothesis
or spontaneous factorization)
[W.Furry, PR 49 (1936) 393]
A. Di Domenico
Roma - 23 maggio 2008
24
 KSKL  : test of quantum coherence
1
• Analysed data: L=1
L=380
fb-1pb(2005
data)
• Fit including t resolution and
efficiency effects + regeneration
• GS, GL , m fixed from PDG
KLOE preliminary:
result:
6
106
.4SYST
 00  10.03  12.21STAT 010
as CP viol. O(||2 ~ 106
 high sensitivity to  00
From CPLEAR data, Bertlmann et al.
(PR D60 (1999) 114032) obtain:
 00  0.4  0.7
In the B-meson system, BELLE coll.
(PRL 99 (2007) 131802) obtains:
 B  0.029 0.057
Comparison with precision in quantum optics test
00
A. Di Domenico
Roma - 23 maggio 2008
25
Decoherence and CPT violation
Modified Liouville – von Neumann equation for the density matrix of the kaon system:
SPACE-TIME
FOAM
extra
term inducing



 t   
iH


i

H

L




QM
decoherence:
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, nontrivial 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. ,b,g:
L   L ; , b , g 
 , g  0 , g  b 2
 MK2 
  2 10 20 GeV
At most:  , b , g  O
 M10-35 m

 PLANCK 
[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]
A. Di Domenico
Roma - 23 maggio 2008
26
Decoherence and CPT violation induced by QG






R K 0 t 0  (   ) t t  R K 0 t 0  (   ) t t
A  (t ) 
R K 0 t 0  (   ) t t  R K 0 t 0  (   ) t t
Am (t ) 
R (t )  R (t ) R (t )  R (t )
R (t )  R (t ) R (t )  R (t )









(t )  R K
R (  ) (t )  R K
0
R(  )
0
t 0
t 0

(  )

( )
 (e
( )
 (e
(  )
v) t t
v) t t


Using single kaons
CPLEAR
   0.5  2.81017 GeV
b  2.5  2.31019 GeV
g  1.1  2.510 21 GeV
Amt
At


data
fit
, b, g  10
A
PLB 364, 239 (1999)
Imposing , g >0  g > b2
at 90% CL
  4.0  1017 GeV
b  2.3  1019 GeV
g  3.7  10 21 GeV
A. Di Domenico
Roma - 23 maggio 2008
27
 KSKL  : decoherence & CPTV by QG
The fit with I(,;t,,b,g) gives:
KLOE preliminary
L=380 pb-1
17

   1041

9

10
GeV
31 STAT
SYST
b  3.7 96..29 STAT  1.8SYST 1019 GeV
g   0.455..18 STAT  1.2 SYST 1021 GeV
In the complete positivity hypothesis
=g , b=0
=> only one independent parameter: g
preliminary
L=1 fb-1
KLOE result
L=380 pb-1
21
21

g  10.182211....9435STAT

10
GeV


0
.
4

10
GeV
STAT
SYST
A. Di Domenico
Roma - 23 maggio 2008
Complete positivity guarantees
the positivity of the eigenvalues of
density matrices describing states
of correlated kaons.
28
 KSKL  : CPT violation in correlated 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  K 0K 0  K 0K 0   K 0K 0  K 0K 0

 K S K L  K L K S     K S K S  K L K L 
 E 2 M PLANCK
at most one expects:   O
G

2

  105   ~ 103

In some microscopic models of space-time foam arising from non-critical string theory:
[Bernabeu, Mavromatos, Sarkar PRD 74 (2006) 045014]
 ~ 104 105
The maximum sensitivity to  is expected for f1=f2=
All CPTV effects induced by QG ,b,g, could be simultaneously disentangled.
A. Di Domenico
Roma - 23 maggio 2008
29
 KSKL  : CPT violation in correlated K states
Im  x10-2
Fit of I(,;t,):
-1
• Analysed data: 1380
fb-1pb(2005
data)
0
result :
KLOE preliminary
:
3.1
4
4


  1.12.855..73STAT

0

.
9
10

10
2.3 STAT
SYST
0
.4
4
4


  3.24.254..0833STAT

0

.
6
10

10
.1 STAT
SYST
33
  02.98
1
10
10
atat95%
95%
C.L.
C.L.
( measured for the first time)
A. Di Domenico
Roma - 23 maggio 2008
Re  x10-2
30
3) Tests of Lorentz invariance and CPT symmetry
in the neutral kaon system
A. Di Domenico
Roma - 23 maggio 2008
31
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]
No CPT viol. in decays
BI  b  d  0
CPT violation in SME manifests to lowest order only in  =>
and exhibits a kaon momentum dependence:
 cannot be a constant
iS W
  i sin SW e




g K a0  bK  a / m
where am are four parameters related to CPT and Lorentz violation
am = rq1 amq1 – rq2 amq2 , with amqi CPT and Lorentz violating coupling constants for the
two valence quarks in the kaon; rqi factors for quark binding or other normalization effects.
amq have mass dimension and are associated to SME lagrangian terms of the form  amq q g m q
Possible hidden momentum dependence in other parameters, e.g. , m, G, SW ,
is suppressed w.r.t. .
A. Di Domenico
Roma - 23 maggio 2008
32
CPT and Lorentz invariance violation (SME)
For a fixed target experiment (fixed
momentum direction)  depends on
sidereal time t since laboratory frame
rotates with Earth.
For a -factory there is an additional
dependence on the polar and azimuthal
angle q,  of the kaon momentum in the
laboratory frame:
  p ,q , t  

1
2
2
At DANE K mesons are producedcostant
with
Rotation
Z
2q
angularaxis
distribution
dN/d  sinvector

KLOE is a kind of telescope,
a
able to explore with a kaon
beam almost any
direction in space
at 6 A.M.
zˆ

   p, t d
(in general
z axis is non-normal
+
e surface)
to Earth’s
at 6 P.M.
0
i sin SW e iSW

g K a0  b K aZ cos c cosq
m
 b K aY sin c cosq sin t
: Earth’s sidereal frequency
 b K a X sin c cosq cost 
A. Di Domenico
Roma - 23 maggio 2008
c : angle between the z lab. axis and
the Earth’s rotation axis
33
e-
Measurement of a0 at KLOE
a0 from KS and KL semileptonic charge asymmetries

i sin SW ei
  p ,q , t  
g K a0  b K aZ cos c cosq
SW
m
 b K aY sin c cosq sin t
tagged KS and KL
(symmetric polar angle q and
sidereal time t integration)
AS , L


GK
 
  e    GK

 e  
G K S , L    e   G K S , L    e 
 
S ,L
 
S ,L
 2  2  2y  2x
with L=400 pb-1 (preliminary):
 b K a X sin c cosq cost 


4 i sin SW eiSW g K
AS  AL 
a0
m
a0  0.4 1.81017 GeV
(a0 evaluated for the first time)
with L=2.5 fb-1 :
A. Di Domenico
sa0 ~ 7  10-18 GeV
Roma - 23 maggio 2008
34
Measurement of aX,Y,Z at KLOE
aX,Y,Z from   KS KL       
(analysis vs polar angle q and sidereal time t)
      p,q , t 
cosq0

q
I[(cosq0), (cosq<0);t]
• at t>>ts sensitive to Re(/)=0
• at t~ts sensitive to Im(/)
With L=1 fb-1 (preliminary):
KL,S
+


KS,L
cosq0
0. - 4. sidereal hours
c2/dof=131/117
a X   6.3  6.01018 GeV
aY  2.8  5.91018 GeV
aZ  2.4  9.7 1018 GeV
KTeV :aX , aY < 9.2  10-22GeV @ 90% CL
t/tS
BABAR aBx,y , (aB0 – 0.30 aBZ ) ~O(10-13 GeV)
A. Di Domenico
Roma - 23 maggio 2008
35
4) Future plans
A. Di Domenico
Roma - 23 maggio 2008
36
KLOE-2 at upgraded DANE
Proposals to upgrade DANE in luminosity (and energy):
Crabbed waist scheme at DANE (proposal by P. Raimondi)
- Experimental test at DANE in progress
- increase L by a factor O(5)
- requires minor modifications
- relatively low cost
KLOE-2 Expression of Interest:
[ L=50 fb-1 at  peak (and s up to 2.5 GeV) ]
Physics issues:
• Neutral kaon interferometry, CPT
symmetry & QM tests
• Kaon physics, CKM, LFV, rare KS
decays
• ,’ physics
• Light scalars, gg physics
• Hadron cross section at low energy,
muon anomaly
• (baryon electromagnetic form factors,
e+e-  pp, nn, 
A. Di Domenico
Detector upgrade issues:
• Inner tracker R&D
• gg tagging system
• Calorimeter, increase of granularity
• FEE maintenance and upgrade
• Computing and networking update
• etc.. (Trigger,software, …)
Roma - 23 maggio 2008
37
Perspectives with KLOE-2 at upgraded DANE
Mode
Test of
Param.
Present best published
measurement
KLOE-2
L=50 fb-1
KSe
CP, CPT
AS
(1.5  11)  10-3
 1  10-3
 e
CP, CPT
AL
( 3322  58  47 )  10-6
 25  10-6
 00
CP
Re’/
(1.47  0.22)  10-3
 0.2  10-3
 00
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
 
A. Di Domenico
Roma - 23 maggio 2008
38
Perspectives with KLOE-2 at upgraded DANE
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
b
(2.5  2.3)  10-19 GeV
 0.1  10-19 GeV
 
CPT & QM
g
(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,Le
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
A. Di Domenico
Roma - 23 maggio 2008
39
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 DANE 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
A. Di Domenico
Roma - 23 maggio 2008
40
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:
http://www.roma1.infn.it/people/didomenico/roadmap/handbook.html
A. Di Domenico
Roma - 23 maggio 2008
41
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
A. Di Domenico
Roma - 23 maggio 2008
42
Spare
A. Di Domenico
Roma - 23 maggio 2008
43
EFFECTS OF CRAB SEXTUPOLES ON
LUMINOSITY
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…
Crab off
Transverse beam dimensions at
the Synchrotron Light Monitor
Crab on
P. Raimondi May 6, 2008
A. Di Domenico
Roma - 23 maggio 2008
44
Example of interferometry at KLOE-2:  KSKL 
Possible signal of decoherence
concentrated at very small t
I(, ;t) (a.u.)
I(, ;t) (a.u.)
Black hist. :
s(t)~1tS => 6mm
(KLOE)
Red hist:
s(t)~1/4 tS => 1.5mm
(KLOE + inner tracker)
 00  4 10
6
 00  0
Blue curve: ideal
t/tS
Theoretical distribution
A. Di Domenico
t/tS
Reconstructed distribution (MC)
Roma - 23 maggio 2008
45