kektc5 - PowerPoint PPT Presentation

Title: kektc5


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Test della simmetria CPT e della meccanica
quantistica nel sistema dei mesoni K neutri a KLOE
Antonio Di Domenico
Roma, 23 maggio 2008
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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
• 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
gt only phenomenological models to be constrained
by experiments.
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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
neutral B system
proton- anti-proton
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1. Standard tests of CPT symmetry in the neutral
   kaon system

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The neutral kaon system
The time evolution of a two-component state
vector Y in the space is given by
(Wigner-Weisskopf approximation)
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)
Diagonalizing the effective Hamiltonian
eigenvalues
eigenstates
K1,2gt are CP1 states
tS 90 ps
tL 51 ns
mL-mS 3.5 x 10-15 GeV GS / 2
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

• d ? 0 implies CPT violation
• e ? 0 implies T violation
• e ? 0 or d ? 0 implies CP violation

(with a phase convention )
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CPT violation in the neutral kaon system
standard picture
CPT violation in semileptonic decays
DSDQ rule
CP T CPT DSDQ
a ?0 ?0
b ?0 ?0 0
c ?0 ?0 0
d ?0 ?0 0 0
Standard Model prediction of DSDQ rule violation
is xc/a O(10-7)
CPT viol. CPT DSDQ viol. DSDQ Viol.

Semileptonic charge asymmetry
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CPT violation in the neutral kaon system
standard picture
CPT violation in pp decays
AI(BI) CPT conserving (violating) K? pp
amplitudes for I0,2 (dI strong phase shift for
I0,2)
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Some results of CPT tests
CPLEAR
Study of the time evolution of neutral kaons in
semileptonic decays
?d (0.30 ? 0.33 ? 0.06) ? 10-3
PLB444 (1998) 52
KTeV
f- - fSW 0.61º 0.62º 1.01 º f00-f-
0.39º 0.22 º 0.45 º
PRL88, 181601(2002)
Study of regenerator beam two pion decay
distribution
AL( 3322 ? 58 ? 47 ) ? 10-6
KL semileptonic charge asymmetry
Constraints on CPT violation in pp and
semileptonic decays obtained combining KTeV and
PDG results
KTeV
PRD67,012005 (2003)
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Neutral kaons at a f-factory
Production of the vector meson f in ee?
annihilations

• ee? ? f sf3 mb
• W mf 1019.4 MeV
• BR(f ? K0K0) 34
• 106 neutral kaon pairs per pb-1 produced in an
  antisymmetric quantum state with JPC 1??

pK 110 MeV/c lS 6 mm lL 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 f-factory, not possible at fixed target
  experiments)

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DA?NE the Frascati f-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
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The KLOE detector at DAFNE
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
(p0 from KL ? pp-p0)
sp/p ? 0.4 (tracks with q gt 45) sxhit ? 150
mm (xy), 2 mm (z) sxvertex 1 mm
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KS and KL Tagging at KLOE
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KS? pen KLOE results
Data sample 410 pb-1
Emiss-Pmiss
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CPT test the Bell-Steinberger relation
Unitarity constraint
KS KL observables
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Experimental inputs to the Bell-Steinberger
relation
Main improvements done with KLOE measurements on
KS semileptonic and 3p0 decays
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CPT test the Bell-Steinberger relation
KLOE result
JHEP12(2006) 011
Re ? (159.6 ? 1.3) ?10-5? Im ? (0.4 ? 2.1) ?
10-5
Combining Red and Imd results
Imd
Assuming , i.e. no
CPT viol. in decay
Red
at 95 c.l.
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2) Tests of QM and CPT symmetry in the neutral
kaon system
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Neutral kaon interferometry
Double differential time distribution
where t1(t2) is the proper time of one (the
other) kaon decay into f1 (f2) final state and
characteristic interference term at a f-factory
gt interferometry
fi pp-, p0p0, pln, pp-p0, 3p0, pp-g ..etc
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Neutral kaon interferometry
Integrating in (t1t2) we get the time difference
(Dtt1-t2) distribution (1-dim plot simpler to
manipulate than 2-dim plot)
From these distributions for various final states
fi one can measure the following quantities
Phases (difference of) from the interference term
gt interferometry
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Neutral kaon interferometry main observables
I(Dt) (a.u)
I(Dt) (a.u)
I(Dt) (a.u)
Dt/tS
Dt/tS
Dt/tS
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Neutral kaon interferometry main observables
parameters
measured quantity
mode
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Same final state for both kaons f1 f2 pp-
Dtt1-t2
I(Dt) (a.u)
Dt/tS
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f ?KSKL?pp- pp- test of quantum coherence
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f ?KSKL?pp- pp- test of quantum coherence

• Analysed data L380 pb-1
• Fit including Dt resolution and efficiency
  effects regeneration
• GS, GL , Dm fixed from PDG

L1 fb-1 (2005 data)
KLOE result
KLOE preliminary
PLB 642(2006) 315
as CP viol. O(h-2) 10-6 gt high sensitivity
to
From CPLEAR data, Bertlmann et al. (PR D60
(1999) 114032) obtain
In the B-meson system, BELLE coll. (PRL 99 (2007)
131802) obtains
Comparison with precision in quantum optics test
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Decoherence and CPT violation
Modified Liouville von Neumann equation for the
density matrix of the kaon system
extra term inducing decoherence pure state gt
mixed state
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Decoherence and CPT violation induced by QG
Using single kaons
CPLEAR
PLB 364, 239 (1999)
ADm(t)
A-(t)
data fit a, b, g ? 10
Imposing a, g gt0 a g gt b2
at 90 CL
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f ?KSKL?pp- pp- decoherence CPTV by QG
The fit with I(pp-,pp-Dt,a,b,g) gives
KLOE preliminary
L380 pb-1

In the complete positivity hypothesis a g
, b 0 gt only one independent
parameter g
Complete positivity guarantees the positivity of
the eigenvalues of density matrices describing
states of correlated kaons.
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f ?KSKL?pp- pp- 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.
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f ?KSKL?pp- pp- CPT violation in correlated K
states
Im w x10-2
Fit of I(pp-,pp-Dt,w)

• Analysed data 1 fb-1 (2005 data)

• Analysed data 380 pb-1

0
KLOE preliminary
KLOE result
PLB 642(2006) 315
0
Re w x10-2
(w measured for the first time)
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3) Tests of Lorentz invariance and CPT symmetry
in the neutral kaon system
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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 d gt and exhibits a kaon
momentum dependence
No CPT viol. in decays
d cannot be a constant
where Dam are four parameters related to CPT and
Lorentz violation Dam 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
Possible hidden momentum dependence in other
parameters, e.g. e, Dm, DG, fSW , is suppressed
w.r.t. d.
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CPT and Lorentz invariance violation (SME)
For a fixed target experiment (fixed momentum
direction) d depends on sidereal time t since
laboratory frame rotates with Earth.
For a f-factory there is an additional dependence
on the polar and azimuthal angle q, f of the kaon
momentum in the laboratory frame

• Earths sidereal frequency
• c angle between the z lab. axis and the Earths
  rotation axis

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Measurement of Da0 at KLOE
Da0 from KS and KL semileptonic charge
asymmetries
tagged KS and KL (symmetric polar angle q and
sidereal time t integration)
with L400 pb-1 (preliminary)
(Da0 evaluated for the first time)
with L2.5 fb-1 s(Da0) 7 ? 10-18
GeV
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Measurement of DaX,Y,Z at KLOE
DaX,Y,Z from
(analysis vs polar angle q and sidereal time t)

• Ipp-(cosqgt0),pp- (cosqlt0)Dt
• at Dtgtgtts sensitive to Re(d/e)0
• at Dtts sensitive to Im(d/e)

0. - 4. sidereal hours
With L1 fb-1 (preliminary)
c2/dof131/117
Dt/tS
KTeV DaX , DaY lt 9.2 ? 10-22GeV _at_ 90 CL
BABAR DaBx,y , (DaB0 0.30 DaBZ ) O(10-13 GeV)
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4) Future plans
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KLOE-2 at upgraded DAFNE
Proposals to upgrade DAFNE in luminosity (and
energy)

• Crabbed waist scheme at DAFNE (proposal by P.
  Raimondi)
• - increase L by a factor O(5)
• requires minor modifications
• relatively low cost

• Experimental test at DAFNE in progress

KLOE-2 Expression of Interest L50 fb-1 at f
peak (and ?s up to 2.5 GeV)

• Physics issues
• Neutral kaon interferometry, CPT symmetry QM
  tests
• Kaon physics, CKM, LFV, rare KS decays
• h,h physics
• Light scalars, gg physics
• Hadron cross section at low energy, muon anomaly
• (baryon electromagnetic form factors, ee- ??pp,
  nn, ??)

• Detector upgrade issues
• Inner tracker RD
• gg tagging system
• Calorimeter, increase of granularity
• FEE maintenance and upgrade
• Computing and networking update
• etc.. (Trigger,software, )

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Perspectives with KLOE-2 at upgraded DAFNE
Mode Test of Param. Present best published measurement KLOE-2 L50 fb-1
KS?pen CP, CPT AS (1.5 ? 11) ? 10-3 ? 1 ? 10-3
pp- pen CP, CPT AL ( 3322 ? 58 ? 47 ) ? 10-6 ? 25 ? 10-6
pp- p0p0 CP Re(e/e) (1.47 ? 0.22) ? 10-3 ? 0.2 ? 10-3
pp- p0p0 CP, CPT Im(e/e) (2.3 ? 2.9) ? 10-3 ? 3 ? 10-3
pen pen CPT Re(d)Re(x-) Re(d) (0.29 ? 0.27) ? 10-3 Re(x-) (-0.8 ? 2.5) ? 10-3 ? 0.2 ? 10-3
pen pen CPT Im(d)Im(x) Im(d) (0.4 ? 2.1) ? 10-5 Im(x) (0.8 ? 0.7) ? 10-2 ? 3 ? 10-3
pp- pp- Dm (5.288 ? 0.043) ? 109 s-1 ? 0.03 ? 109 s-1
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Perspectives with KLOE-2 at upgraded DAFNE
Mode Test of Param. Present best published measurement KLOE-2 L50 fb-1
pp- pp- QM z00 (1.0 ? 2.1) ? 10-6 ? 0.1 ? 10-6
pp- pp- QM zSL (1.8 ? 4.1) ? 10-2 ? 0.2 ? 10-2
pp- pp- CPT QM a (-0.5 ? 2.8) ? 10-17 GeV ? 2 ? 10-17 GeV
pp- pp- CPT QM b (2.5 ? 2.3) ? 10-19 GeV ? 0.1 ? 10-19 GeV
pp- pp- CPT QM g (1.1 ? 2.5) ? 10-21 GeV ? 0.2 ? 10-21 GeV compl. pos. hyp. ? 0.1 ? 10-21 GeV
pp- pp- CPT EPR corr. Re(w) (1.1 ? 7.0) ? 10-4 ? 2 ? 10-5
pp- pp- CPT EPR corr. Im(w) (3.4 ? 4.9) ? 10-4 ? 2 ? 10-5
KS,L?pen CPT Lorentz Da0 (0.4 ? 1.8) ? 10-17 GeV ? 2 ? 10-18 GeV
pp- pp- CPT Lorentz DaZ (2.4 ? 9.7) ? 10-18 GeV ? 7 ? 10-19 GeV
pp- pen CPT Lorentz DaX,Y lt10-21 GeV O(10-19)GeV
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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 Plancks scale
  region
• All results are consistent with no CPT violation
• The full KLOE data set analysis is almost
  completed
• KLOE and DAFNE 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

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More detailed information can be found in
Handbook on neutral kaon interferometry at a
f-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
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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
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Spare
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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
Crab on
Transverse beam dimensions at the Synchrotron
Light Monitor
P. Raimondi May 6, 2008
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Example of interferometry at KLOE-2 f ?KSKL?pp-
pp-
I(pp-, pp-Dt) (a.u.)
Possible signal of decoherence concentrated at
very small Dt
I(pp-, pp-Dt) (a.u.)
Black hist. s(Dt)1tS gt 6mm (KLOE) Red
hist s(Dt)1/4 tS gt 1.5mm (KLOE inner
tracker) Blue curve ideal
Dt/tS
Dt/tS
Theoretical distribution
Reconstructed distribution (MC)