The Final Measurement of ε´/ε from KTeVEd Blucher
University of Chicago•••••

Introduction to ε´/εThe KTeV Experiment
Overview of Analysis
Measurements of ε´/ε and other K0 parameters
Summary

KTeV Collaboration: Arizona, Chicago, Colorado, Elmhurst, Fermilab,Osaka, Rice, Sao Paolo, UCLA, Virginia, Wisconsin
9 June 2009

KAON 091

Kaons and the CKM Matrix• 1964 observation of KL→π+π− demonstrated CP violation andpresented problem for the electroweak theory with 2 generations• Kobayashi and Maskawa recognized that 3 generation theory
allowed CP violation, with a single CP-violating quantity• For decades, however, there was only one measured CP0violating
parameter, ε, describing an asymmetry between K 0 → K and0K → K 0 mixing − “indirect” CP violation• Search for “direct” CP violation (ε´) motivated many of the kaon
experiments done during the 40 years following discovery of CPV23

ε´/ε : Indirect vs. Direct CP Violation

KL~ Kodd + εKeven“Direct”
in decayprocessε´ππ“Indirect” fromasymmetricmixingTo distinguish between direct and indirectCP violation, compare KL,S→π+π−, π0π0:(() () ())+ −+ −⎤1 ⎡ Γ KL → π π / Γ Ks → π πRe ( ε ′ / ε ) ≈ ⎢− 1⎥
0 00 06 ⎢⎣ Γ K L → π π / Γ K s → π π⎥⎦Re(ε´/ε) ≠ 0

direct CP violation

Γ(K 0 → π +π − ) ≠ Γ(K 0 → π +π − )4“Recent” Measurements of Re(ε´/ε)halfKTeV 2003 result (based on half of KTeV data sample):Re(ε′/ε) = (20.7 ± 1.5(stat) ± 2.4(syst)) ×10-4= (20.7 ± 2.8) ×10-4

Improvement in systematics needed to take advantage of increase instatistics.
Re(ε′/ε) Systematics (2003)

2008 analysis of full data sample includes many improvements incharged and neutral event reconstruction and simulation.

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The KTeV Detector

6• Charged particle momentum
resolution < 1% for p>8 GeV/c;
Momentum scale known to0.01% from K→π+π−• CsI energy resolution < 1% forEγ > 3 GeV; energy scale known
to 0.05% from K→πeν.

KLFor EK ~ 70 GeV,KL + ρKS

KS: γβcτ ~ 3.5m
KL: γβcτ~ 2.2 km

7CsI Calorimeter Performance
Full calibration sample includes 1.5 billion electrons
from K→πeν.

KTeV Data Samples• 2003 result included ~3 million KL →π0π0 decays from 1996 and 1997
– σstat = 1.5 × 10-4
• 1999 dataset contains ~3 million KL → π0π0 decays– σ stat = 1.5 × 10-4
• Today: results from full data sample: σ stat = 1.1 × 10-48KS→π+π−910KL→π0π0abzabrab

11Invariant Mass Plots

KL→π+π−“KS→π+π−”KL→π0π0Mass resolution is ~1.5 MeV/c2for both decay modes.
“KS→π0π0”Backgrounds and event yields
Main classes of background:• Misidentified kaon decays– For K→π+π−: KL→πeν, KL→πµν– For K→π0π0: KL→π0π0π0• Scattered K→ππ events– From regenerator and final collimator• Backgrounds are simulated with MC, normalized to data sidebands,
and subtracted• Background level is ~0.1% for charged mode and ~1% for neutral
mode.

After background subtraction:

K→π+π−
K→π0π0KL
Vacuum Beam
25,107,242
5,968,198“KS”
Reg. Beam
43,674,208
10,180,175

12Reconstructed Vertex z Distributions

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Reconstructed Vertex z Distributions

0.1% shift in E scale: ~3 cm shift in vertex; ~1×10−4 shift in ε´/ε14

Acceptance Correction

15• A detailed Monte Carlo simulation based on measured detector
geometry and response is used to calculate acceptance as afunction of p,z, and beam (reg or vac).
• Includes effects of accidental activity.
Many improvements compared to 2003 analysis:
More complete treatment of particle interactions with matter:• Ionization energy loss
• Improved Bremsstrahlung• Improved delta rays
• Hadronic interactions in drift chambers
Improved electromagnetic shower simulation:• Shower library binned in incident particle angle• Simulate effects of dead material (wrapping and shims) in CsI
calorimeter

Monte Carlo Improvements: Simulation of photon angles
Fraction of energy in 49 crystals forelectron shower

2003 data / MCcurrent data / MC

20-30 mrad incident angles used16

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Improved Modeling of Energy Nonlinearities
Mass vs. Energy
2003
MCDataMass vs. Photon Angle
2003

Current
MCDataCurrent
MCDataMCData18

Systematic Uncertainties in Re(ε′/ ε)Reducedfrom 1.47

19Uncertainty from Energy Non-linearity• Use MK vs EK plot to determine
distortion that provides best dataMC match• 0.1%/100 GeV nonlinearity
applied to data for 1997 and 1999
• 0.3%/100 GeV nonlinearity for
1996• Change in Re(e′/e)– 1996: -0.1 × 10-4
– 1997: -0.1 × 10-4
– 1999: +0.2 × 10-4
• Systematic error: ±0.15 × 10-4

DistorteddataNominaldataMC

Calorimeter Energy Scale•Calorimeter calibrated with momentum-analyzed
electrons from K→πeν•Final energy scale adjustment based on K0→π0π0 atregenerator edge

Before E scalecorrection

After E scalecorrection

1999:z shift = 2.7 cm
energy scale
adjustment = 0.05%

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Improvement in Energy Scale Correction

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Energy scale fixed at regenerator
edge  check scale at vacuum
window.
Uncertainty in Re(ε´/ε):±0.65 × 10-4~×2 improvementcompared to previousanalysis.

Data – MC comparisons of z vertex distributions

Difference
between mean zvertex in reg andvac beams isabout 6 m⇒
δRe(ε´/ε)≈ data/mc slopedataMC2324Calculating Re(ε´/ε)Naively,but regenerator beam is not purely KS.

KL - KS Interference Downstream of Regenerator

2N ( p, z) ∝ η e− Γ Lt

2+ρ e− ΓS t+2η ρ e−(Γ S + Γ L )t / 2cos(Δmt + Φ ρ − Φη )25

Fit to Extract Re(ε´/ε)•Acceptance applied to prediction function in 2 m z bins and 10GeV/c momentum bins
•Data are fit in 10 GeV/c momentum bins and a single z bin foreach beam•KL fluxes are floated in 10 GeV/c p bins separately for charged
and neutral mode
•Regenerator beam attenuation measured directly from data using
KL→π+π−π0 decays (special trigger in 99 gave 9-fold increase insample):

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KTeV Result: Re(ε´/ε) = [19.2 ± 1.1(stat) ± 1.8(syst)] × 10−4
= (19.2 ± 2.1) × 10−4

World average:Re(ε´/ε) = (16.8 ± 1.4) × 10−4
(confidence level = 13%)

(KTeV 2003: Re(ε′/ ε) = [20.7 ± 1.5(stat) ± 2.4 (syst)] × 10−4)

Re(ε´/ε) Cross checks
Momentum Bins

Run Ranges28

Fit Strategy for z-binned Fits29• In contrast with Re(ε´/ε) fit, in which a single ~50 m z bin isconsidered, we now fit the regenerator beam data in 2 m z bins.
• Float Δm=mL−mS, τS, ϕε, Re(ε′/ε), Im(ε′/ε) with no CPT assumption.
• CPT constraint (ϕε=ϕSW and Im(ε′/ε)=0) then applied a posteriori
to find best values τs, Δm.

z-binned Fit Results
ϕε = (43.86 ± 0.63)°
ϕε−ϕSW = (0.40 ± 0.56)°
Im(ε´/ε)=(−17.2 ± 20.2)×10−4 ⇒ Δϕ = (0.30 ± 0.35)°
NA48+KTeVAll results consistent with CPT symmetry30

ϕ+− and Δϕ31

KTeV 2008: Δϕ = (0.30 ± 0.35)°
KTeV 2008: ϕ+−= (43.8 ± 0.6)°(KTeV 2003: ϕ+−= (44.1 ± 1.4)°)

Improvement: better treatment of reg.
transmission, screening(KTeV 2003: Δϕ = (0.39 ± 0.50)°)

Improvement: neutral energy scalez-binned Fit Results (cont)No CPT constraint:

Δm = (5279.7 ± 19.5) × 106 ħs-1
τS = (89.589 ± 0.070) × 10-12 s

CPT constraint applied:Δm = (5269.9 ± 12.3) × 106 ħs-1
τS = (89.623 ± 0.047) × 10-12 s

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Δm and τS

KTeV 2008: Δm = (5270 ± 12) × 106 ħs-1

KTeV 2008: τS = (89.62 ± 0.05) × 10-12 s(KTeV 2003: Δm = (5261 ± 13) × 106 ħs-1)(KTeV 2003: τS = (89.65 ± 0.07) × 10-12 s)

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Summary
KTeV Results:• Re(ε′/ ε) = (19.2 ± 2.1) × 10-4
Assuming CPT• Δm = (5269.9 ± 12.3) × 106 ħs-1
• τS = (89.623 ± 0.047) × 10-12 s• ϕε = (43.86 ± 0.63)°
No CPT assumption• ϕε− ϕSW = (0.40 ± 0.56)°• Δϕ = (0.30 ± 0.35)°•Direct CP violation measured precisely:•Future lattice calculations may make these precise experimental
measurements equally precise tests of the Standard Model.
•All measurements are consistent with CPT symmetry.

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35EXTRA

Screening Corrections•Determine regeneration amplitude in 10 GeV kaon momentum bins. Agrees
with screening correction calculations for low P.
•Calculate phase at each P using Derivative Analyticity Relation using the 12
amplitudes•Compare variation of the phase vs P from DAR to direct fit to data – goodagreement.

36KL→π0π0 Distributions

Vac (KL)Reg (KS)37