1. A New Measurement of Re(e’/e) from KTeV at Fermilab
Introduction to CP Violation in the Kaon System
The KTeV Experiment at Fermilab
Analysis of Re(e’/e)
New 1997 Result, and Re-analysis of 1996 Result
P. Shanahan – FNAL SLAC - July 26, 2001

2. The Neutral Kaon System
are quark flavor eigenstates
Mixing via ElectroWeak interaction:
In CP conserving limit, mass eigenstates=CP eigenstates:
Expect K1 to be much shorted lived than K2,
since MK-3Mp0<< MK-2Mp0
P. Shanahan – FNAL SLAC - July 26, 2001

3. P. Shanahan – FNAL SLAC - July 26, 2001
CP Violation in Kaons
1st Observation of CP Violation was KLpp (1964):
Bulk of effect is from mixing asymmetry:
Smallness of CP violation.
Mass Eigenstates:
KSK1+eK2, KLeK1+K2
tL580 tS, Dm1/2tS
P. Shanahan – FNAL SLAC - July 26, 2001

4. CP Violation in the Standard Model
CP Violation is accommodated in imaginary part of quark mixing parameters:
P. Shanahan – FNAL SLAC - July 26, 2001

5. P. Shanahan – FNAL SLAC - July 26, 2001
Direct CP Violation
KL  e K1 + K2
p p e
Direct (decay)
Indirect
(mixing)
Direct CP Violation:
CP Violation in Decay Amplitudes: EW and Stong Penguins
Small effect on CP violating KL Amplitudes: d d W d s q
u,c,t
Z,g q
P. Shanahan – FNAL SLAC - July 26, 2001

6. e’/e in the Standard Model
e’Im(A2/A0) : A0,2– I=0,2 Final State
e’/e =Im(lt) x [ c0 + Rs(c6B6(1/2)+c8B8(3/2))]
c0,6,8 – Wilson Coefficients, NLO (~ 10%)
Im(lt) – Im(VtdVts*) (~ 40%)
B6,8(1/2) – Hadronic matrix elements of effective 4 quark
operators – non perturbative, difficult to calculate.
e’/e calculations vary…
(4.63.0)x Ciuchini, et al. 97
(5.73.6)x ms=130 20 MeV
(9.15.7)x ms=110 20 MeV
(17 )x Bertolino, et al., 98
Buras, et al., 99 {
+14
-10
P. Shanahan – FNAL SLAC - July 26, 2001

7. Previous Measurements
Pre-June, 2001: World Average e’/e=(18.02.0)x10-4,
poor agreement among experiments.
P. Shanahan – FNAL SLAC - July 26, 2001

8. P. Shanahan – FNAL SLAC - July 26, 2001
KTeV at Fermilab
University of Arizona, UCLA ,UCSD, Universidade Estadual de Campinas, University of Chicago, University of Colorado, Elmhurst College, Fermilab,
Osaka University, Rice University, Universidade de São Paulo, University of Virginia, University of Wisconsin
Kaons at the TeVatron
Three Physics Programs:
Rare K decays: E799
Hyperon Physics: E799/E832
e’/e: E832
d(e’/e)=O(10-4)
P. Shanahan – FNAL SLAC - July 26, 2001

9. P. Shanahan – FNAL SLAC - July 26, 2001
Measuring e’/e
Simultaneous KL and KS beams: GeV
Produce 2 KL beams 160 m upstream of the detector
Coherent regeneration of KS in 1.8m of plastic scintillator 35 m upstream of detector
Detector
Spectrometer for p+p-
CsI EM Calorimeter for p0p04g
KL (VAC Beam) KL
KL+rKS (REG Beam)
Regenerator
switches beam
every spill
P. Shanahan – FNAL SLAC - July 26, 2001

10. P. Shanahan – FNAL SLAC - July 26, 2001
KTeV Detector
P. Shanahan – FNAL SLAC - July 26, 2001

11. Coherent Regeneration
Difference in K0 and K0 forward scattering amplitude in matter
r , with power law dependence in PK
Coherent effect
Distinguish from inelastic KS production via scintillation light from recoil in interactions
Subtract diffractive and remaining inelastic and background offline
Coherent
Inelastic
P. Shanahan – FNAL SLAC - July 26, 2001

12. P. Shanahan – FNAL SLAC - July 26, 2001

13. Cesium Iodide Calorimeter
3100 Crystals of 27 X0 Pure CsI (50cm)
High Linearity Phototubes
8 Range, Deadtimeless, Pipelined ADC
1.9m
P. Shanahan – FNAL SLAC - July 26, 2001

14. P. Shanahan – FNAL SLAC - July 26, 2001

15. P. Shanahan – FNAL SLAC - July 26, 2001
CsI Performance
CsI Calibrated with e from 420 Million Kpen
Energy Resolution
P. Shanahan – FNAL SLAC - July 26, 2001

16. P. Shanahan – FNAL SLAC - July 26, 2001
KTeV Trigger
P. Shanahan – FNAL SLAC - July 26, 2001

17. e/e Standard Analysis
Count KL,S to p+p- and p0p0
Background Subtraction – non pp and non-coherent Kpp
Very different KL and KS lifetimes:
Need acceptance correction from Monte Carlo simulation of detector + overlay of accidental activity
Fit for e’/e
Account for full kaon wave function in each beam
P. Shanahan – FNAL SLAC - July 26, 2001

18. P. Shanahan – FNAL SLAC - July 26, 2001
KTeV Data Taking
1996
1997
1999
2000
E799
E832
1st KTeV result, and re-analysis
New result
P. Shanahan – FNAL SLAC - July 26, 2001

19. P. Shanahan – FNAL SLAC - July 26, 2001
Event Sample
Year KL
p+p-
(106)
p0p0 KS
Statistical error
(10-4)
96/97a
(PRL)
2.6
0.9
4.5
1.4
3.0 97
8.6
2.5
14.9
4.2
1.73
Combined
11.2
3.4
19.4
5.6
~1.5
P. Shanahan – FNAL SLAC - July 26, 2001

20. Reconstructed Invariant Masses
P. Shanahan – FNAL SLAC - July 26, 2001

21. P. Shanahan – FNAL SLAC - July 26, 2001
p+p Reconstruction
2 good tracks, forming a good vertex
Cuts
PT2
Track Quality
Vertex 2
Muon Veto reject Kpmn
E/p reject Kpen
“pp” Mass reject Lpp
Regenerator Veto noncoherent KS
PT nocoherent KS, non pp
Regenerator
mpp E
Zvtx
P. Shanahan – FNAL SLAC - July 26, 2001

22. P. Shanahan – FNAL SLAC - July 26, 2001
Interference in Kpp
Dwell on scale of meters
P. Shanahan – FNAL SLAC - July 26, 2001

23. P. Shanahan – FNAL SLAC - July 26, 2001
Backgrounds to p+p-
Non-coherent KS regeneration
Scattering in regenerator
Scattering in collimators
Kpln
Beam interactions in REG Pb
Total: .098% VAC
.081% REG
P. Shanahan – FNAL SLAC - July 26, 2001

24. Monte Carlo Simulation
Detector apertures/ performance
Overlay real random activity
E.g.: Delayed hit problem
Worst for tracks near Drift Chamber sense wires
P. Shanahan – FNAL SLAC - July 26, 2001

25. P. Shanahan – FNAL SLAC - July 26, 2001
Simulation Results
P. Shanahan – FNAL SLAC - July 26, 2001

26. P. Shanahan – FNAL SLAC - July 26, 2001
Acceptance
Data-MC comparison of p track illumination at CsI
MC tuned with 10s of millions of CP conserving decays
P. Shanahan – FNAL SLAC - July 26, 2001

27. P. Shanahan – FNAL SLAC - July 26, 2001
Acceptance Test
Comparison of Data and MC Z vertex Distributions
Test of acceptance in variable most relevant to KL-KS difference
Set systematic uncertainty based on p+p-:
d(e’/e)=0.53x10-4
P. Shanahan – FNAL SLAC - July 26, 2001

28. P. Shanahan – FNAL SLAC - July 26, 2001
p0p0 Reconstruction
Vertex for each pair of photons found assuming p0 mass
Choose pairing with most consistent p0 vertices
Calculate p0p0 mass
No direction information – use energy centroids
Good pairing
Bad pairing
Cuts:
Photon Veto p0
Cluster Shape  “Fused” gs (3p0)
Vertex Pairing c Mispairs, 3p0
Regenerator Activity Non-coherents
(X,Y)CE Non-coherents
Mp0p0, EK, Zvtx
Extra intime photons in CsI p0
P. Shanahan – FNAL SLAC - July 26, 2001

29. P. Shanahan – FNAL SLAC - July 26, 2001
p0p0 Center of Energy
Cut on center of energy
In 1 cm2 square rings
Simulate Regenerator scattering spectrum using pt2 shape from p+p-
P. Shanahan – FNAL SLAC - July 26, 2001

30. P. Shanahan – FNAL SLAC - July 26, 2001
Backgrounds to p0p0
Dominant BG: Regenerator Scatters
Modeled from Kp+p- pT2 Spectrum
Separate normalization of diffractive and inelastic KS production
REG Beam: 1.27%
VAC Beam: 0.50%
P. Shanahan – FNAL SLAC - July 26, 2001

31. P. Shanahan – FNAL SLAC - July 26, 2001
Energy Scale
Energy Scale:
Apply correction (1+d)-1
Relative Data-MC energy scale correction:
Make data and MC regenerator edge line up.
P. Shanahan – FNAL SLAC - July 26, 2001

32. Energy Scale Cross Check
Beam interactions
Regenerator Pb
Vacuum window
Kp+p-p0
For systematic:
Apply extra energy scale, varying linearly from Regenerator, to fix ZVACWIN
d(e’/e)=1.37x10-4
P. Shanahan – FNAL SLAC - July 26, 2001

33. P. Shanahan – FNAL SLAC - July 26, 2001
Acceptance Test
Set systematic uncertainty from 3p0
d(e’/e)=0.26x10-4
P. Shanahan – FNAL SLAC - July 26, 2001

34. Systematic Uncertainties
P. Shanahan – FNAL SLAC - July 26, 2001

35. P. Shanahan – FNAL SLAC - July 26, 2001
KTeV 1997 e’/e Result
Re(e’/e)=(19.81.7(stat) 2.3(syst) 0.6(mc stat))x10-4
P. Shanahan – FNAL SLAC - July 26, 2001

36. P. Shanahan – FNAL SLAC - July 26, 2001
Reweighting Analysis
MC acceptance correction is only ~5% on the double ratio
… but this is ~90x10-4 on e’/e
We have strong cross checks on our acceptance calculation
E.g., purely geometrical MC accounts for about 90% of the acceptance correction
However, an “MC independent” measurement is desirable:
Reweighting:
reweight VAC beam to have same p,Z distribution as REG
Similar to NA48 method (CERN), but more complicated due to substantial interference of KL and KS
P. Shanahan – FNAL SLAC - July 26, 2001

37. Pros and Cons of Reweighting
Reweighting completely removes biases from lifetimes and geometry
Reweighting de-emphasizes tracks near beam regions
Less susceptibility to rate and accidental effects
Statistically weaker
- d(e’/e): 1.7x10-43.0x10-4
P. Shanahan – FNAL SLAC - July 26, 2001

38. Examples of Reweighting
Data
vs.
P. Shanahan – FNAL SLAC - July 26, 2001

39. P. Shanahan – FNAL SLAC - July 26, 2001
Reweighting Result
With preliminary
understanding of
correlated
uncertainties,
D(e’/e)=(1.5
2.1(stat)
3 (syst) )
x10-4
Preliminary reweighting results (NOT the official KTeV Number….)
Re(e’/e)=21.32.9(stat) 4.0(syst)
Hope to reduce systematic…
P. Shanahan – FNAL SLAC - July 26, 2001

40. P. Shanahan – FNAL SLAC - July 26, 2001
Other Cross Checks
P. Shanahan – FNAL SLAC - July 26, 2001

41. Re-Analysis of 1996/97a Result
Miscellaneous improvements
e.g. recalibration, Mask Anti, DC Simulation
Mistake found in p0p0 scattering background
External parameters
Dm, tS from KTeV (was PDG98)
P. Shanahan – FNAL SLAC - July 26, 2001

42. P. Shanahan – FNAL SLAC - July 26, 2001
Updated 1996/97a Results
New 1996 Result:
e’/e=(23.2
 3.0 (stat)
 3.2 (syst)
 0.7 (MC st))x10-4
Old Result: (superceded)
e’/e=(28.0
 3.0 (stat)
 2.7 (syst)
 1.0 (MC st))x10-4
P. Shanahan – FNAL SLAC - July 26, 2001

43. Shifts in Updated Analysis
Each consistent
With quoted
Systematic uncertainty
P. Shanahan – FNAL SLAC - July 26, 2001

44. P. Shanahan – FNAL SLAC - July 26, 2001
Combined 1996 and 1997 Results
Re(e’/e)=(20.7
1.5(stat)
2.4(syst)
0.5(MC Stat)
)x10-4
Re(e’/e)=( 20.7  2.8 )
x 10-4
P. Shanahan – FNAL SLAC - July 26, 2001

45. P. Shanahan – FNAL SLAC - July 26, 2001
World Data on Re(e’/e)
World Average:
(17.21.8)x10-4
Probability=13%
P. Shanahan – FNAL SLAC - July 26, 2001

46. Kaon System Parameters
KS, KL, and Interference in REG
Beam allows measurement
Of several Kaon system parameters
P. Shanahan – FNAL SLAC - July 26, 2001

47. P. Shanahan – FNAL SLAC - July 26, 2001

48. P. Shanahan – FNAL SLAC - July 26, 2001
Conclusions
KTeV has new Re(e’/e) result with improved error
Re-analysis of 1996 result
Combined KTeV Result:
Re(e’/e)=(20.72.8)x10-4
World data now in significantly better agreement
World Average: (17.21.8)x10-4
13% CL
e’/e now known to ~10%
More data from 1999 run!
P. Shanahan – FNAL SLAC - July 26, 2001