Post on 03-Feb-2022
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
1) “Standard” tests of CPT symmetry in the neutral kaonsystem
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
( )( ) ( )( )
/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 )
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
CPT violation in the neutral kaon system: “standard” picture
∗∗+−∗∗−+
−++−
−=−=
+=+=
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
CPT violation in the neutral kaon system: “standard” picture
∗∗+−∗∗−+
−++−
−=−=
+=+=
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
( )−ℜ+ℜ=− xAA LS δ4
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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)
CPT violation in the neutral kaon system: “standard” picture
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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+→
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
SLL KKK ρ+→
Presented atMoriond08, HQL08
φε - φSW = 0.40º ±0.56ºφ00-φ+- = 0.30º ± 0.35º
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
( ) 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:
KTeV (Fermilab) results
AL=( 3322 ± 58 ± 47 ) × 10-6
PRL88,181601(2002)
KL semileptonic charge asymmetry:
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
• 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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
( )−ℜ+ℜ=− xAA LS δ4
( )yAA LS ℜ−ℜ=+ ε4
CPT & ΔS=ΔQ viol.
CPT viol.
input from other experiments
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
Experimental inputs to the Bell-Steinberger relation
Main improvements done with KLOE measurements on KS semileptonic and 3π0 decays
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
CPT test: the Bell-Steinberger relation
ℜδ = (0.30 ± 0.33 ± 0.06) × 10−3
CPLEAR: study of the time evolution of neutral kaons in semileptonic decays
PLB444 (1998) 52
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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)
CPT test: the Bell-Steinberger relation
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
2) Search for decoherence and CPT violation in the neutral kaon system
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
−+−+→→ 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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
−+−+→→ 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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
−+−+→→ 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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
( ) ( ) ( )
( ) ( ) ⎥⎦⎤⎟
⎠⎞⎜
⎝⎛ 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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
( ) ( ) ( )
( ) ( ) ( ) ⎥⎦⎤⎟
⎠⎞⎜
⎝⎛ ΔΔℜ⋅−−
⎢⎣⎡ Δ+Δ=Δ
∗−+−+−+−+
−+−+−+−+−+−+
tKKtKK
tKKtKKtI N
000000
2002002
,,21
,,;,
ππππππππζ
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
( ) ( ) ( )
( ) ( ) ( ) ⎥⎦⎤⎟
⎠⎞⎜
⎝⎛ ΔΔℜ⋅−−
⎢⎣⎡ Δ+Δ=Δ
∗−+−+−+−+
−+−+−+−+−+−+
tKKtKK
tKKtKKtI N
000000
2002002
,,21
,,;,
ππππππππζ
ππππππππππππ
φ →KSKL→π+π− π+π− : test of quantum coherence
[ ]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]
Feynman described the phenomenon of interference as containing “the only mistery” of quantum mechanics
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
φ →KSKL→π+π− π+π− : test of quantum coherence
00ζ
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
φ →KSKL→π+π− π+π− : test of quantum coherence
00ζ
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
φ →KSKL→π+π− π+π− : test of quantum coherence
00ζ
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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)
From CPLEAR data, Bertlmann et al. (PR D60 (1999) 114032) obtain:
7.04.000 ±=ζIn the B-meson system, BELLE coll.(PRL 99 (2007) 131802) obtains:
057.0029.000
±=Bζ
φ →KSKL→π+π− π+π− : test of quantum coherence
as CP viol. O(|η+−|2) ∼ 10−6
=> high sensitivity to 00ζ
( ) 7SYSTSTAT00 108.35.94.1 −×±±=ζ
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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)
From CPLEAR data, Bertlmann et al. (PR D60 (1999) 114032) obtain:
7.04.000 ±=ζIn the B-meson system, BELLE coll.(PRL 99 (2007) 131802) obtains:
057.0029.000
±=Bζ
φ →KSKL→π+π− π+π− : test of quantum coherence
as CP viol. O(|η+−|2) ∼ 10−6
=> high sensitivity to 00ζ
( ) 7SYSTSTAT00 108.35.94.1 −×±±=ζ
Comparison with quantum optics test precisions
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
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:
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
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:
SPACE-TIME FOAM
10-35 m
J.A. Wheeler
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
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:
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
( ) ( )( ) ( )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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
( )( )
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
φ →KSKL→π+π− π+π− : CPT violation in correlated K states
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
KLOE FINAL :
φ →KSKL→π+π− π+π− : CPT violation in correlated K states
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
3) Tests of Lorentz invariance and CPT symmetry in the neutral kaon system
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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 ±=,
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
at 6 A.M.
at 6 P.M.
Rotation axis Z costantvector
arΔ
CPT and Lorentz invariance violation (SME)
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
SWSW ΔΔ⋅−Δ= /sin 0
rrβγφδ φ
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
CPT and Lorentz invariance violation (SME)
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:
(in general z lab. axis is non-normal to Earth’s surface)
( ) maaei KKi
SWSW ΔΔ⋅−Δ= /sin 0
rrβγφδ φ
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
CPT and Lorentz invariance violation (SME)
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
SWSW ΔΔ⋅−Δ= /sin 0
rrβγφδ φ
At DAΦNE K mesons are produced with angular distribution dN/dΩ ∝ sin2θ
ze+ e-
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
( ) ( )( ) ( )
−
−++−
−++−
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)
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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]
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
4) Future plans
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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){
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
DAΦNE Luminosity versus colliding currents
original collision scheme}
NEW COLLISION SCHEME:Large Piwinski angleCrab-Waist compensation SXTs}
from P. Raimondi’s talk
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
DAΦNE Luminosity versus colliding currents
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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)
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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
A. Di Domenico Seminar at Physics Department, Warsaw University and A. Soltan Institute for Nuclear Studies – April 3rd, 2009, Warsaw, Poland
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.