CP Violation in the Decay

KL→ π+π-e+e-Katsumi Senyo
Osaka UniversityContents
Physics Motivations

Recent results

KTeV Detector

Event Selection

Form Factor Measurement

CP Asymmetry Measurement

Branching Ratio Measurement

Conclusion

CP Violating Process inK L → π+ π-e+e-

CP Violating

CP Conserving

CP violating effect comes frominterference between IB and DE amplitudes.

Critical Angles in KL → π+π-e+e-

Angular Asymmetry in ΦdΓ= Γ1 cos2 φ + Γ2 sin 2 φ + Γ3 sin φ cosφdφp+ + p−  ⋅ (nee ⋅ nππ )
|pp|++− sin φ cos φ = nee × nππ ⋅ nee ( nππ ) : Normal to e+ e- (π + π − ) planep+ ( p− ) : Momentum of π + (π − ) in Kaon CM frame
πdΓdΓd−φ∫0 dφ∫π / 2 dφ dφ
A = π /2
≈ 14%πdΓdΓ
∫0 dφ dφ + ∫π / 2 dφ dφ
π /2

Sehgal and Wanninger
Phys. Rev. D46, 1035(1992);ibid D46,5209(E)(1992)

Angular Dist.(MC)M1 Form factor
gM 1 → gM 1⋅ Fa1
F=+ a222*( M ρ − M K ) + 2M K EγM ρ : mass of ρ meson
M K : mass of K meson
Eγ* = E e + E e : Virtual photon Energy in Kaon CM frame+a)With form factor−b)Without formfactor

E.J.Ramberg et al., Phys. Rev. Lett. 70, 2525(1993)

Recent Experimental Status
Recent Publication:Branching Ratio(3.2 × 0.6(stat.)× 0.4(syst.))× 10-7
Based on 46 events(one day of data) by KTeV
J.Adams et al., Phys. Rev. Lett. 80, 4123(1998)

Our analysis shown here based on whole(90 days) dataset.

KTeV Detector (plane view)

Spectrometer(Magnet + Drift Chambers)
Measure the momentum of a charged particle

Electromagnetic Calorimeter
Measure the energy of a photon
Particle identification

Spectrometer(Magnet + Drift Chamber)
Purpose: charged track trajectory reconstruction
vertex reconstruction
Measure the momentum of a charged particle

4 Drift Chambers(DC1 - DC4)
Spatial resolution : 100µ m

Analysis Magnet (between DC3 and 4)
Transverse momentum kick: 205 MeV/c

Momentum Resolution:σpp= 0.016% × p (GeV/c) ⊕ 0.38%

Electromagnetic Calorimeter
Measure the energy of a photon
Particle identification
3100 CsI crystals(27 rad. lengths)
Energy Resolution:

σE=E0.6%
× ⊕0.6%E (GeV)KL→π +π-e+e- Signal Selection

Strategy・4 charged tracks sharing a common vertex.
・Identified 2 pions and 2 electrons
including charge consistency

・Invariant mass forms KL mass
・Total momentum consistent with
KL flight direction

・Constraint from other kinematics relations

CsI calorimeter
Signal: K L→π +π-e+e-π+e+e-π−

CsI calorimeter
BG: KL →π + π- π D0π+γe+e-π−Background sources

K L → π +π −π D0 (π 0 → e + e −γ )0
K L → π +π −π DD(π 0 → e+ e − e+ e− )K L → π +π −π 0 (π 0 → γγ )γ conversion at material(γ→e+e-)

K L → π +π −γγ conversion at material(γ→e+e-)

Ξ → Λ(→ pπ − )π D0 (→ e + e −γ )( K L → π + e −ν ) + ( K L → π − e +ν )

Background distribution

Total Momentum(ππee) CutTotal Momentum Cut:
Data and Background MC Overlay

Vertex χ2(quality) Cut:
Data and Background MC Overlay

Mee CutMee Cut:
Data and Background MC Overlay

pt2 Cutpt2 Cut:
Data and Background MC Overlay

Pp0kine Cut・Assuming KL→π+π−π0 kinematics
・Reject physically allowed region of
KL→π+π−π0Pp0kine Cut

Pp0kine Cut:
Data and Background MC Overlay

Data after all the cuts

1173± 34.2 events in the signal region

Background Estimation
Background

Efficiency

K L → π +π −π D0 (π 0 → e +e −γ )#Background2.4 x 10-8

9.0 ± 3.00
K L → π +π −π DD(π 0 → e + e − e + e − )2.7 x 10-7

0.3 ± 0.2K L → π +π −π 0 (π 0 → γγ )< 1.2 x 10-11<0.8(90%CL)

K L → π +π −γ< 3.0 x 10-8<0.7(90%CL)Ξ → Λ (→ pπ − )π D0 (→ e + e −γ )( K L → π + e −ν ) + ( K L → π −e +ν)<0.7(90%CL)
2.0 ± 1.4
11.3 ± 3.5

Normalization with

K L → π +π −π D0Dataset#events

K L flux

Winter1301650

1.421 x 1011

Summer8142270.922 x 1011

Total

2115877(2.343 ± 0.002(stat.)± 0.085(syst.)) x 1011

Form Factor MeasurementgM 1 → gM 1 ⋅ F
F=a1+ a2
( M ρ2 − M K2 ) + 2 M K Eγ*a1 / a2 , a1

Extracted from 5 parameter
Maximum likelihood method.

Mππ , M ee , φ , cos θπ + , cosθ e + In Kaon CM frameForm Factor Fit Result

a1 / a2 = −0.684+−00..031043
a1 = 1.05 ± 0.14

Mππ Comparison
Form Factor

Constant gM1

CP violating Angular Asymmetry

π dΓdΓ
∫0 dφ dφ − ∫π / 2 dφ dφ
A = π /2
≈ 14%π dΓdΓ
∫0 dφ dφ + ∫π / 2 dφ dφπ /2Sehgal and Wanninger
Phys. Rev. D46, 1035(1992);ibid D46,5209(E)(1992)

Angular Distributions

The Raw Asymmetry

N sin φ cosφ>0 = 719
N sin φ cosφ>0 = 454
Asym =Nsin φ cosφ >0 − N sin φ cosφ <0N sin φ cosφ > 0 + N sin φ cosφ <0= 0.237 ± 0.029( stat.)

MC study
MC with input asymmetry of 0.147 gave
the raw asymmetry of 0.258.

Acceptance correction should be applied to
the raw asymmetry.

Before proceeding to
the acceptance correction...

Raw Asymmetry = -0.00015 ± 0.00051
Consistent with zero asymmetryInput-Raw asymmetry relation
with Monte Carlo Simulation

Raw Asym. = 1.75 × Input Asym.

Raw asymmetry in different Mass region

No obvious asymmetry found in outside region.

MC study on the relation
between input and raw asymmetries

Distribution in acceptable region has larger asymmetry.

Raw Asymmetry...
Measured raw asymmetry of data is 0.237± 0.029(stat.)while the MC with input parameter of 0.147 gave
the raw asymmetry of 0.258.

The detector or analysis did not induce the raw asymmetry.
This is also supported by the signal MC with zero input
asymmetry.

The input and raw asymmetry have the simple linear relation
which suggests the asymmetry enhancement.

The KTeV detector only accepted events with high momentum
electrons. Those events showed the large asymmetry.

Singal Acceptance in φAcceptance Corrected Data and MC

Acceptance Corrected Asymmetry
0.127 ± 0.029

Detector Smearing

Detector Smearing; continue

X track swapping causes the dilution.

Track in sin φ cos φ region → − sin φ cos φ region

Detector Smearing; continue

Systematic Uncertainty

Detector resolution

8.7%(0.011)

M1 form factor

2.4%(0.003)

Physics Input parameter 6.9%(0.007)
Vertex quality

0.8%(0.001)

DC ineff.

<0.1%(0.000)

Background subtraction 0.9%(0.001)
Analysis dependency

4.7%(0.005)

Total

12.4%(0.016)

Asymmetry: Result
Asym. = 0.127 ± 0.029(stat.)± 0.016(syst.)

Theoretical Prediction
Asym. ~ 14%
Sehgal and Wanninger
Phys. Rev. D46, 1035(1992);ibid D46,5209(E)(1992)

Branching Ratio Measurement

Recent Publication:(3.2 × 0.6(stat.)× 0.4(syst.))× 10-7
Based on 46 events(one day of data) by KTeV

J.Adams et al., Phys. Rev. Lett. 80, 4123(1998)

Data Selection

Relax pt2 cut and Pp0kine cut to increase
acceptance.
Pt2 cut : <0.00006 GeV2/c2 → <0.00010 GeV2/c2
Pp0kine cut : <-0.0025 GeV2/c2 → N/A#events in the signal region
1173 events → 1731 events

Mass distribution after final cutsPt2 Sideband
0.00010 GeV2 /c2 <pt2 <0.00020 GeV2/c2

Background Estimation
Background#BackgroundK L → π +π −π D0 (π 0 → e + e −γ )169.2 ± 13.00
K L → π +π −π DD(π 0 → e + e − e + e − )32.2 ± 3.2

K L → π +π −π 0 (π 0 → γγ )46.7 ± 2.0

K L → π +π −γ

3.3 ± 0.6

Ξ → Λ(→ pπ − )π D0 (→ e + e −γ )0.99± 0.14

( K L → π + e −ν ) + ( K L → π − e +ν )3.0 ± 1.7

255.4 ± 13.7

Signal peak after background subtraction#signal after background subtraction:
1475.6 events

Statistical/Systematic Uncertainty(BR)Statistical Error3.13%

BR ( K L → π +π −π D0 )3.14%

Physics Input parameter 2.60%
Normalization

0.33%

Chamber inefficiency

0.17%

Vertex quality

0.87%

MC statistics

0.25%

Background subtraction 1.6%
Analysis dependency

0.7%

Total (3.13( stat.) ⊕ 2.00( syst .internal ) ⊕ 4.08( syst .external ))%Branching Ratio: Result(3.55 ± 0.11(stat.)± 0.07(syst.internal )± 0.14 (syst.external))× 10-7
Based on 1475.6 events

Good agreement with recent experimental result;(3.2 × 0.6(stat.) × 0.4(syst.))× 10-7J.Adams et al., Phys. Rev. Lett. 80, 4123(1998)

And theoretical prediction;~3 × 10-7

Sehgal and Wanninger
Phys. Rev. D46, 1035(1992);ibid D46,5209(E)(1992)

Discussion: Asymmetry Measurement
Origin of the asymmetry

Final State Interaction:

negligible.
(M.J.Savage,1999)

T Violation:(strictly speaking,)rejected.

CPT Violation:

unnatural, but not yet rejected.
(J. Ellis and N.E. Mavromatos, 1999)(I.I.Bigi and A.I.Sanda, 1999)

CP Violation/CPT Conservation:
Most probable interpretation.
(L.M.Sehgal and M.Wanninger, 1992)

ConclusionCP Violating Angular Asymmetry

Asym. = 0.127 ± 0.029(stat.)± 0.016(syst.)

Form Factor Measurement:

a1 / a2 = −0.684+−00..031
043
a1 = 1.05 ± 0.14

Branching Ratio(3.55 ± 0.11(stat.)± 0.07(syst.internal )± 0.14 (syst.external))× 10-7
Based on 1475.6 events