the neutral kaon systemecole-de-gif.in2p3.fr/gif2003/gautier2.pdf · kaon decay modes 69% 31% 21%...

The Neutral Kaon System

G. Hamel de Monchenault – Experimental Aspects of CP Violation

Characteristics of the Kaon System

In the neutral kaon system, the two physical states,

differ significantly in their lifetimesand the K-longthe K-short ,

The is the heavier state

A striking numerical “coincidence”

The “super-weak” phase


More Phases write

with

where we have introduced (convention-dependent) phases and

define

the effective Hamiltonian

CP violation in mixing is small if either or is small,

or if is close to or

in the kaon system


Indirect CP ViolationThe decay of neutral kaon is dominated by a single CP final state

and are almost antiparallel

andTherefore, to first order in

almost a pure phase

In the limit of CP conservation ( )


Specific Kaon Notations

anddefine

do not depend

on phase conventions

or, equivalently

link with previous notations

using

alternate definitions


Specific Kaon NotationsPhysical states, as a function of flavor states

T conservation

CPT conservation

CP conservation… and as a function of the CP eigenstates

with

Note: Always more K0 than K0!


The Bell-Steinberger Relation

If CP is violated, the physical states are not orthogonal

Conservation of the probability (general unitarity)

,Taken at t=0, this leads to

connects indirect CPT violation with

CP-violating decays

Bell-Steinberger, 1966with


Kaon Decay Modes

69%

31%

21%

13%

27%

39%

0.2%

0.1%

Physical states Flavor eigenstates

decays are dominated by three-pion and semileptonic

The two-pion final states, common to both , are dominantand

The two-pion decays of theare CP-violating

CP violation

lifetimesplitting:pure KLbeam

KS-KLinterference

region


The ππ Final Statesangular momentum

Consider the decay

The two-pion final states are common to both and

Note: when CP is conserved

and

the CP-odd eigenstate

cannot decay into two pions

(identified to physical state)

Define the CP-violating observables

,

all three types of CP violation can lead to non-zero andNote:


Experimental Methodson purpose,

only last generationexperiments

Measurements of ( and )

Pure and (almost pure) beamsNA48

& KTeV

sensitive to and double ratio

Regeneration of in a beam

sensitive tois the regeneration amplitude

Incoherent production of and (close target)NA48/2

sensitive to

“Strangeness” tagging, and “beams”CPLEAR

sensitive to

Coherent production of and at the KLOE

Where It All Started…

V.L.Fitch R.Turlay J.W.Cronin J.H.Christenson

Phys. Rev. Lett. 83 (1964) 138.

A very active field in the seventies!


E832 (KTeV) at FNALDouble KL beams (<p>=70 GeV/c)Regenerator for KSPure CsI calorimeterTagging by event positionMC acceptance correctionMaximize statistics

regenerator beam

neutral pionreconstruction

in CsI Calorimeter


KTeV: Acceptance Issues

vacuum

regenerateddifferent average

acceptance

different momentum spectra

Need an analysis technique

to put the two beams on equal footing


KTeV: Detector Simulation

KTeV analysis relies on a verydetailed Monte-Carlo simulationto predict the acceptance of each beam

Counting experiment: large Monte-Carlo acceptance corrections –

but mostly geometric (90%)

check of acceptance using vacuum beam

use large statistics control samplesto cross-check Monte-Carlo performance

correct residual bias due to different vertex distributions in vac/reg beams

Other difficulty: the regenerator beam


KteV: the Regenerator Beam

The regenerator beam is a NOT a pure beamIt is a coherent superpositionof and

Two-pion time-dependent decay rate

Quantum coherenceover 30m !

With the regenerator beam, KTeV can measure not only decay rates, but also phases (and other kaon parameters, including and )

(assuming CPT)


NA48 at CERN

Simultaneous near/far targetsConverging beams (<p>=100 GeV/c )Liquid Kr calorimeterTagging by time-of-flightLifetime weighting to minimize acceptance correction

separate and decays in time

analyse andwith the same effective proper time

relative acceptancecancels ☺

NA48 technique:


Neutral Kaon Beam at NA48

The NA48 Detector

π0π0 detection ( →4 γ)LKr calorimeterσ(E)/E=0.032/√E⊕0.09/E⊕0.0042

< 1% for E=25 GeV

π+π- detectionmagnetic spectrometerσ(p)/p = 0.5%⊕0.9%∗(p/100 GeV)


CP Violation in Semileptonic Decays

semileptonicasymmetries

only non-zero semileptonic amplitudes

rule semileptonic decays can be used to monitor the

content of the stateand

Experimentally, use a pure KL beam

Assuming CPT( )

CP and Tviolation or CP and CPTviolation?

measurement of CP violation

in mixing


KL Semileptonic Asymmetries

KTeV KTeV 2001 data events

Pπ (GeV/c)

δ · 10-3

χ2/n.d.f=0.90 (n.d.f.=9)1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

10 20 30 40 50 60 70 80 90 100 110

NA48 preliminary

eventsNA48 2001 data


Check of Initial Statement

semileptonic decayshave slightly more positively-charged

than negatively-charged leptonsdue to a slight excess of over

to second order in

CP violation in mixing is smallbecause the relative phase

between andis close to zero

CPLEAR at CERN

intense beam of slow antiprotons


The CPLEAR DetectorCP physics at a Low Energy Antiproton Ring

Technique: stop 200 MeV/c antiprotons in a gaseous pressurized hydrogen target

strangeness tagging

detection of low energy particles within 4π solid angle

kaon tagging, tracking, calorimetrypresence of large backgrounds

Experimental challenge


CPLEAR, Event Displays

Semileptonic eventTwo-neutral pionsTwo-charged pions


charged kaon

primary pion

neutral kaon

track fit

9-C fitCPLEAR, Analysis

Resonant structure of the reaction

9-C Constrained kinematic fitimproves considerably the momentum (and decay-time) resolution


KLOE at Frascati

• Ebeam=510 MeV• 2 separate rings for e+ and e- to

minimize beam-beam• high current (20 mA per bunch)• up to 120 bunches• crossing angle at 12.5 mrad

DAΦNE factory


KLOE, Analysis Technique

in a state

factoryat a

coherent production

constrained kinematics


KLOE Data Sample

1999 run : 2.5 pb-1

machine and detector studies

2000 run : 25 pb-1

7.5 x 107 φpublished results

2001 run: 190 pb-1

5.7 x 108 φ analysis in progress

2002 run: 300 pb-1

9.0 x 108 φ analysis in progress


The KLOE Detector

Pb-SciFi Calorimeter( barrel + endcap,15 X0 depth, 98%solid angle coverage)

0.52 T magnetic field

Big volume Drift Chamber(13K cells, He gas mixt.)

Interaction region:Instrumented quadrupoles,Al-Be spherical beam pipe


K-Long “Beam”

KS tagtwo opposite charge tracks

from Interaction Point,with loose cuts on mass

and momentum Good determination of the KL

direction and momentum (~2MeV)

efficiency ~ 85%


K-Short “Beam”

KL-crashclean KS tags by

time of flight identification of KL interactions in the calorimeter

efficiency ~ 30%

Total sample:1.5 108 tagged KS


Quantum Coherence

KLOE preliminary310 pb-1 (2001+2002)

First observation of quantum interference in relative decay-time

distribution of KL,KS

KLOE preliminary

in principle such distributionscontain all the CP-violating informationbut two order of magnitude more datais needed to compete with NA48 & kTeV

An interesting prelim. result from KLOEfrom decays


Isospin Amplitudes

To separate from CP violation effects, one introduces

due to Bose statisticsonly and

states are allowed

isospinstates

, , withisospinamplitudes

Watson’s theorem: FSI of states

is only elastic

only two scattering phasesand

no direct CP violation in

the amplitude is dominantrule

from measured decay rates

one gets


The Phase of Γ12

rulesemileptonicfinal states

are not common

The evaluation of involves the decay final states

andthat are common to

Significant common final states

almost saturates

define

expect up to tiny corrections


The ε0 Parameterdominates the and two-pion decays

define with

phase-invariant parameters

because we consider only one amplitude

CP violation in mixing

CP violation in interferencemixing/decay

The parameter receives

the contribution of two types of CP violation

what about direct CPV?


The ε′ Parameter

define

then, to first order in and,

alternate definition


Double Ratios

eliminate mixing by forming the ratio

manifestation of direct CP violation in the decays

implies and/or

contribution of two amplitudes andwith different weak phases and strong phases

a different type of direct CP violation! direct CP because no mixing involved

due to phase difference between the decays to two different final states

Experimentally: the double ratio R


CP Parameters in ππ Decays

= phase vs

= phase vs

not to scale!


The ππ Asymmetry

neglecting direct CP violation

one has

and


The ππ Asymmetry

one checks that, at , before mixing starts

The asymmetry is an interplay between two types of CP violation

CP violation in mixing

CP violation in the interference mixing.decay

non zero

Unique to the K system: dominance of one common channel

Note: the two phases are strongly related

If direct CP violation is not neglected,


CPLEAR: ππ Decay RatesMeasured decay rates (after acceptance corrections)

as expected, not a pure exponential

background

andafter acceptance correction and background subtraction


The CPLEAR Asymmetry

CPLEAR ππ asymmetrydefined so that

CPLEAR 99The relative reconstruction efficiency

is corrected event by event

From the fit to the distribution

in agreement with the superweak phase

(in the limit of low backgrounds)

The Quest for Direct CPViolation


Indirect CP Violation in the SM

In the Standard Model (refer to Guido’s lecture 1)

box diagrams with internal u,c,t exchange including short-distance QCD

—0.4x10—3 1.1x10—3 2.1

~dominateshyperbolic constraintin the ρ−η plane


Direct CP Violation in the SM Tree diagrams QCD and electroweak penguin diagrams

Gluonic penguin undergo transitionsonly contribute to

Eletroweak penguins contribute to both and(with opposite signs!)

gluonic electroweak ~1

relativeweak phase

main theoreticaluncertainties fromthe hadronic matrixelements


Experimental MeasurementsNew generation of experiments after measurements in the early 90’s


Data Taking Periods

ε’/ε

ε’/εRare Rare

Rareε’/ε

1996Total: 5.3M KL→π0π0

NA48: ε’/ε

ε’/ε

ε’/ε

ε’/ε low intensity

KS

KS

KS

NA48/1: KS

KL

no spectrometer

NA48/2: K±

1997

1998

1999

2000 FNAL-KTeV2001

2002

2003

Total: 7.1M KL→π0π0

= ε’/ε resultsCERN-NA48


NA48: Acceptance Weighting

Residual correction (beam geometry)∆(R) = (21.9±3.5±4.0) 10-4

does not rely on detailed detector simulation

weight KL events to equalizedecay vertex distribution andmake detector acceptance the same


NA48: Control of SystematicsExample: determine KS ToF tagging inefficiencies and accidental KL tagging from the data

Check result as a function of kaon momentum(different acceptance corrections)

χ2/ ndof = 32/19

analysis is performed in kaon energy bins:less sensitive to

differences between KLand KS spectra

Control of tagging efficiency

History of a Measurement


World Average

After 5 (2) years of data taking by NA48 and KTeV

This implies direct CP violation in decays

… really a small effect!

it translates into a tiny CP-violating phase difference

Theoretical Pre(post)dictions

The ball is on the theory side


Also the Imaginary Part?

Measurements of Im e’/eare not quite as precise yet

Current data is consistent with CPT conservation

different fermilab experiments have various regenerator lengths

KTeV


T-odd Asymmetry in KL →π+π−e+e−

decay dominated by two amplitudes:−+−+ππ→ eeKL

CP-violating inner bremstrahlung CP-conserving direct emission

INTERFERENCEgives rise to indirect CP-violating circular photon polarization

large asymmetry (~14%) between (e+e-) and (π+π-) planes predicted

BR = (3.63 ± 0.18) × 10-7very rare decay


KTeV: KL

NA48: KL,KS

1.5K eventsKTeV: BR = (3.63 ± 0.18) × 10-7

No asymmetry:AΦ = (−1.1 ± 4.1)%

NA48: BR = (3.08 ± 0.2) × 10-7

KTeV:AΦ = (13.3 ± 1.7)%

NA48:AΦ = (14.2 ± 3.6)%

NA48: BR = (4.69 ± 0.30) × 10-5

compatible with indirect CP violation only, no evidence of direct CP violation

subtleties in interpretation as a T-odd effect: controversy in literature

Nice cross-check, no asymmetry in KS decays

KTeV

NA48

−+−+ππ→ eeKL

−+−+ππ→ eeKL

Tests of CPT from Kaon Physics


KS Semileptonic Asymmetry

Possible test of CPT

assuming CPT in SL decay amplitudes

KTeV

KLOE preliminary

KLOE preliminary

first timemeasurement


T-odd AsymmetryIs the indirect CP violation observed in KL decays accompanied with T violation?

compare and

CPLEAR T-odd asymmetry

assumerule

at times larger than

in agreement with

direct observation of T violation

CPLEAR


CPT-odd Asymmetry

Is the indirect CP violation observed in KL decays accompanied with CPT violation?

compare and

assumerule

CPLEAR CPT-odd asymmetry

No evidence for CPT violation


CPLEAR: KS → 3π0

CP-violating parameter

Fitted asymmetry

CPLEAR 1999


NA48/1: KS → 3π0

Time-distribution of events from near target

NA48 2000 run (without tracking chambers)

near-target data, 3.5M 3π0 eventsnormalize to far-target data,

155M eventscorrection of residual acceptance

difference from Monte Carlo

cible


NA48/1: KS → 3π0

NA48 2003, preliminary

fixing to

NA48

pre

limin

ary

example of momentum bin fit


Test of CPT with η000

recallBell-Steinberger

Previous contributions:

With NA48/1 preliminary result:

assuming

the neutral kaon systemecole-de-gif.in2p3.fr/gif2003/gautier2.pdf · kaon decay modes 69% 31% 21%...

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