E. Blucher

1
Kaons and the CKM Matrix
Ed Blucher University of Chicago

• Kaons and the Unitarity Triangle
• Vus and related measurements
• Conclusions

2
Kaons and the CKM Matrix

• 1964 observation of KL????? demonstrated CP
  violation and
• presented 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.
• Until 1999, however, there was only one measured
  CP violating
• parameter, ?.

KL Kodd ?Keven
Indirect from asymmetric mixing
??
Direct in decay process
??
3
KTeV Detector
NA48 Detector
KL
KL ?KS
4
NA48 LKr Calorimeter
KTeV CsI Calorimeter
5
Calorimeter Performance
KTeV
NA48
6
Measurements of Re(????)
World average Re(????) (16.6 ? ??6) ? ????
(confidence level 10)
7
Calculations of Re(????)
Bertolini, Sozzi
Re(????) ? ?, but large hadronic uncertainties
currently make it impossible to convert
measurement of Re(????) into a meaningful CKM
constraint.
8
K decays and the Unitarity Triangle
B(KL?????) and B(K????) can be used to
determine (?,?) with little systematic
uncertainty.
9
Measurement allows clean determination of Vtd
(5 th. error)
BNL E787 (95-98) observed 2 K???? events. E949
involved modest detector upgrades and more data
goal 5-10 evts but, run ended after 20 of
proposed exposure.
Combined E787/E949 Result
Standard Model 0.8?1????
Analysis underway for p?lt195 MeV/c
10
Pure direct CP violation - clean measurement of ?
(1 th. error)
SM
Signature Single unbalanced ?0 Backgrounds
KL????, KL?3??, neutron interactions, etc.
Best limit came from KTeV using ???ee?
Model-independent limit (Grossman, Nir)
E391 (KEK), the first experiment dedicated to
began taking data in 2004.
11
E391a Experimental Method
12
E391a Experiment
13
E391a Preliminary Limit
Preliminary result from 1 week of data during
first run
Severe cuts required to reduce background from
membrane. Resulting acceptance 0.75, an
order of magnitude lower than design.

• Runs II and III will have higher acceptance lower
  background.

• Goal with run III Single event sensitivity near
  Grossman-Nir bound.

14
Current Constraints on ? and ?
Isidori
Planned experiments with goal of 100 SM events
in 2-3 year run

• JPARC

• P326-aka NA48/3 (CERN)

15
New Determinations of Vus
Unitarity Tests of CKM Matrix
Uncertainty on ?j Vij2
0.2
2.7
30
For first row, PDG quotes 2.2 ? deviation from
unitarity
16
2002 PDG Vux Evaluations
Vud 0.9734 ? 0.0008 from 0?0 nuclear ?
decays, neutron decay Vus 0.2196 ? 0.0023
from K, K0 decays to ?e? (??? not used by
PDG because of large uncertainties in form
factor measurements). Vub (3.6 ? 0.7) ?
10?3 from semileptonic B decay
2003 K measurement from BNL E865 consistent with
unitarity.
Interesting to revisit K0 measurements (PDG fit
values based on averages of many old experiments
with large errors)
17
Determination of Vus in Semileptonic K Decays
Vus2
Experiment form factors needed to calculate
phase space integrals
Experiment B(K??e?) and B(K????), ?
SU2 corr. for K (theory)
Form factor at t0 (theory)
Rad. Corrections (theory)
18
2003 BNL E865 Measurement of B(K???e?)

• Using 70,000 Ke3 decays normalized to K?????,
  K??????,
• K ???????, they found B(Ke3) 5 higher than
  PDG.
• Result consistent with CKM unitarity at 1 level.
• Assumes other K branching ratios are correct
  B(Ke3) is only 5.

Data/MC comparison for e momentum from ???ee??
decay for signal and normalization decay modes.
19
New Measurements since 2003
(the kaon revolution Marciano)

• KTeV measured 6 largest KL branching fractions
  and KL
• semileptonic form factors (Ke3 and K?3) Ke3?,
  K?3?
• NA48 measured KL??e?/charged fraction,
  B(KL???????),
• Ke3 FF, B(Ke3) Ke3?, K?3?
• KLOE measured main KL branching fractions, KL
  lifetime,
• B(KS ??e?), B(K????), and recently, B(KL????).
• ISTRA has measured Ke3 branching fraction and
  FF

20
KL Branching Ratio Measurements
3?0
K?3
??-?0

• KTeV measures the following 5 ratios

Ke3
These six decay modes account for 99.93 of KL
decays, so ratios may be combined to determine
branching fractions.

• NA48 measures

These may be combined to measure B(Ke3).

• KLOE (ee????KK?, KLKS) can tag one kaon and
  measure
• branching fractions using accompanying kaon they
  measure branching
• fractions for 4 main KL decay modes assuming ?
  B(KL?i)1??small

21
Simple event reconstruction and selection may be
used to distinguish different decay modes with
very little background.
KLOE
NA48
Dmp Minimum cPmiss - Emiss for
????? hypothesis
22
KTeV Particle Identification
23
Note branching fractions include inner
bremsstrahlung contributions for all decay modes
with charged particles.
KTeV Data MC Comparison for Radiative Photon
Candidates
It is critical to include radiation properly in
Monte Carlo simulation.
E.g., for KTeV, radiation changes Ke3 acceptance
by 3 effect on other modes is lt 0.5.
Both KTeV and NA48 have published new
measurements of B(Ke3?) and B(K?3?)
24
KTeV Measured Partial Width Ratios
25
Comparison of KTeV, NA48, KLOE, PDG KL Branching
Fractions
Value based on PDG-style fit to all new
measurements (KTeV, KLOE, NA48)
26
How could PDG averages be so far off?
Comparison with Individual Experiments

• PDG fit combined different width ratios from many
  (40) experiments.
• Its likely that many (most?)
• experiments did not treat
• radiation adequately,
• particularly for electron modes.
• These potentially large correlated systematic
  errors were not taken into account in the PDG fit.

27
KLOE KL Lifetime Measurements

• Indirect method from branching fraction
  measurement.
• Detector acceptance depends on ?L.
  Comparison of
• ?B(KL?i) ?small with 1 can be used to
  determine
• ? ?L (50.72?0.14?0.33) ns

2. Direct method using using KL??0?0?0
?L(50.87?0.16 ?0.26) ns Combining both KLOE
results ?L(50.81?0.23)ns PDG Average
?L(51.5?0.4)ns New average ?L(50.98?0.21)ns
Events/0.3 ns
t LK/??c (ns)
28
Determination of ?? Using B(KL???)
KL-KS Interference
29
Semileptonic Form Factor Measurements
(to determine IK integrals)
IK depends on the two independent semileptonic
FFs f(t), f?(t)
30
KL Form Factor Results
31
Input to Calculate Recent Vus (on next page)
B(KLe3) KTeV, KLOE, NA48 B(KL?3) KTeV,
KLOE B(KSe3) KLOE B(Ke3) E865, NA48, KLOE,
ISTRA ?L KLOEPDG average ?S KTeV, NA48
average ? PDG
K0 KTeV quadratic FF (including 0.7 model
dep.) K ISTRA quadratic FF (including
0.7 model dep.)
SEW (short-distance rad. corr) 1.023
(Sirlin) Long-distance radiative corrections
(Andre, Cirigliano et al.) ?e0.0104? 0.002
(was 2 from Ginsberg) ??0.019 ? 0.003
?e0.0006 ? 0.002 ?SU20.046?0.04
(Cirigliano) f(0) 0.961 ? 0.008 (Leutwyler
Roos) recent calculations
32
Comparison with Unitarity
Average of all recent results accounting for
correlations
? theory
Uses updated Vud 0.9739?0.0003 (Hardy,
Towner Marciano,Sirlin -- Kaon 2005)
Using f(0) 0.961 ? 0.008 (Leutwyler Roos),
Assuming unitarity, ? 0.227 ? 0.001.
33
Conclusions

• New K?3 measurements result in 3 shift in Vus
  compared to PDG 2002, and are consistent with
  CKM unitarity (depending on f(0))
• Other methods (K?2/??2, ?) give somewhat lower
  Vus new
• measurements of 0?0 nuclear ? decays in
  progress.
• 5-8 shifts observed in main KL branching
  fractions.
• Value in repeating old measurements with
  modern, high
• statistics experiments.
• First results from dedicated KL???? experiment
  E391a.
• Next generation of rare K decay experiments hold
  promise of
• precision determination of ?, ? to compare
  with B system.