1. (Semi)leptonic kaon decays: experimental results & prospects
Evgueni Goudzovski
(University of Birmingham)
Outline:
Overview of recent and planned kaon experiments;
Global analysis of (semi)leptonic kaon decay data;
CKM unitarity and SM tests;
Summary and prospects.
Lattice QCD meets Experiment  University of Glasgow
3 June 2010

2. Overview of kaon experiments
E. Goudzovski / Glasgow, 3 June 2010

3. Major recent & future K experiments
FNAL
KTeV,P996
BNL
E865,787,949
CERN
NA48,NA62
LNF
KLOE,KLOE2
IHEP
ISTRA+,OKA
KEK/J-PARC E391,KOTO,TREK
NA62, KOTO, P996 aim at the “golden modes” K.
Several experiments plan |Vus| measurements with (semi)leptonic decays: lattice QCD is a crucial ingredient!
E. Goudzovski / Glasgow, 3 June 2010

4. Future K experiments
decays in flight
Unseparated 75 GeV K+ beam
Starting in 2013
decays in flight
30 GeV KL beam
Expect to reach KL SES Starting in 2011
proposal to collect ~103 KL events with a low-energy KL beam
E. Goudzovski / Glasgow, 3 June 2010

5. Other major experiments
K0, K decays in flight (~100 GeV beams)
Frascati:
low energy (~100 MeV) kaons
at DAFNE  factory (e+e– at 1.02GeV)
KLOE: , KLOE2: 2010-
Protvino:
K decays in flight (~26 GeV beams)
E. Goudzovski / Glasgow, 3 June 2010

6. (semi)leptonic K decay data
Global analysis of
(semi)leptonic K decay data
E. Goudzovski / Glasgow, 3 June 2010

7. |Vus|f+(0) from Kl3 decays
Kl (Kl3) decays: ideal channels for |Vus| determination
(with K=KS, KL, K+; l=e,; CK2 = ½ for K+, CK2 = 1 for K0)
Inputs from experiment
Inputs from theory
(Kl3()):
radiation-inclusive decays rates;
in practice, branching ratios & lifetimes.
IKl():
Phase space integrals;
s parameterize form factor dependence on momentum transfer t=(PK–P)2.
E.g. Taylor expansion parameterization:
(+’, +’’) for Ke3, (+’, +’’,0’) for K3.
SEW=1.0232(3):
short-distance EW correction
f+(0):
vector form factor at zero momentum transfer (t=0)
SU(2) and EM:
channel-dependent isospin breaking
and long-distance EM corrections
E. Goudzovski / Glasgow, 3 June 2010

8. |Vus| from Kl3: recent history
2002: |Vud|2 + |Vus|2 – 1 = –0.0035(15).
(PDG 2004) A 2.3 hint for CKM unitarity violation.
2003: BNL E865 measured higher BR(K+e3)=0.0513(10).
Start of the |Vus| revolution:
first modern measurement, consistent with unitarity.
2004-present: Many new measurements (KLOE,KTeV,ISTRA+,NA48)
2008-beyond: Value of |Vus| used in precision tests of the SM
 1.9%
BRs, lifetimes, form factor shapes;
Much higher statistical precision than early measurements;
Adequate treatment of radiative corrections;
Correlations between measurements properly reported.
FlaviaNet Kaon WG [ arXiv: update arXiv:
E. Goudzovski / Glasgow, 3 June 2010

9. BR &  measurements: KL FlaviaNet’10 fit: 21 input measurements
(published final results, mostly )
Evolution of main KL BRs
KLOE: 4 absolute BRs, BR(+–)/BR(Kl3)
BR()/BR(30), KL with KL30
KTeV: 5 ratios fo BRs, BR(+–)/BR(+–)
2 meas. of BR(+–DE)/BR(+–)
NA48: BR(Ke3)/BR(2-track),
BR(+–)/BR(Kl3), BR()/BR(30)
PDG: BR(00)/BR(+–)
E731: BR(+–DE)/BR(+–)
Vosburgh (1972): KL
PDG’04
PDG’09
FlaviaNet’10
Free parameters: 9 main BRs, lifetime KL.
Constraint: BRi = 1.
Fit quality: 2/ndf=19.8/12 (P=7.1%).
Cf. PDG’09: 2/ndf=35.7/17 (P=0.5%).
PDG’04
PDG’09
~5 shifts wrt PDG’04: many new results, elimination of old results with no radiative corrections or not reporting correlations.
FlaviaNet’10
E. Goudzovski / Glasgow, 3 June 2010

10. BR &  measurements: K Evolution of main K BRs
FlaviaNet’10 fit: 17 input measurements
(many 2000s but also earlier results)
KLOE: 5 absolute BRs, K with K
NA48/2: BR(Ke3)/BR(0), BR(K3)/BR(0),
E865: BR(Ke3)/BR(0+K3+K3, 0 Dalitz)
KEK246: BR(Ke3)/BR(K3)
Early: BR(K3), 3 meas. of K,
3 meas. of BR(K)/BR(0)
Free parameters: 6 main BRs, lifetime K.
Constraint: BRi = 1.
Fit quality: 2/ndf=25.8/11 (P=0.7%).
Cf. PDG’09: 2/ndf=52/24 (P=0.1%).
E. Goudzovski / Glasgow, 3 June 2010

11. BR &  measurements: KS
|Vus| with KS decays: the most recent development
KLOE (2006):
BR(KSe) / BR(KS+–) = 10.19(13)  10–4
BR(KS+–) / BR(KS00) = (54)
NA48 (2007):
BR(KSe)/BR(KLe) = 0.993(34)
NA48 (2002):
KS = (70) ps
KTeV (2003):
KS = 89.58(13) ps
Assuming lepton universality and using measured form factors:
BR(Ke3)/BR(K3) = (15)
 1.3%
dominated by statistics
FlaviaNet’10 fit: 6 inputs. Free parameters: 4 BRs and lifetime.
Constraint: BRi = 1.
2/ndf = 0.015/1 (P=90%)
Fit result:
BR(Ke3) = 7.05(8)  10–4
E. Goudzovski / Glasgow, 3 June 2010

12. Form factors with Ke3: (’+,’’+)
Polynomial parameterization:
f+(t)/f+(0) = 1 + ’(t/m2) + ½’’(t/m2)2 + …
Slope parameters x103
’ = 25.10.9
’’ = 1.60.4
(’,’’) = –0.94
2/ndf = 3.5/6 (P=51%)
Phase Space Integrals:
I(K0e3) = (21)
I(Ke3) = (22)
4 significance of ’’
Slope measurements
 0.14%
Fits to pole and dispersive parameterizations lead
to similar PSIs within 0.1%
E. Goudzovski / Glasgow, 3 June 2010

13. Form factors, Ke3+K3: (’+,’’+,0)
NA48 K3 measurement is inconsistent and has been excluded
Phase Space Integrals:
I(K0e3) = (20) I(K03) = (20)
I(Ke3) = (21) I(K3) = (20)
2/ndf=5.6/5 (P=34%)
E. Goudzovski / Glasgow, 3 June 2010

14. |Vus|f+(0) measurements with Kl3
Global fit result:
|Vus|f+(0) = (5)
2/ndf = 0.77/4
(P=94%)
Main error sources
0.2163(6)
KL lifetime
0.2166(6)
0.23% relative precision
0.2155(13) BR
(statistics)
Prospects:
KLOE-2/step-0 alone expect
0.14% precision on |Vus|f+(0)
by improving on BR(KSe3) and KL, K lifetimes.
(arXiv: )
NA48/NA62 plan improvements on K+ BRs and FFs.
0.2160(11)
BRs, isospin breaking corrections
0.2158(14)
Measurements of |Vus|f+(0)
E. Goudzovski / Glasgow, 3 June 2010

15. |Vus|/|Vud| from (K,)
SM ratio of radiation-inclusive leptonic decay widths:
Extracted
Lattice QCD input
Experimental input
(1) from K BR fit
BR(K2) = (18)
(K) = (15) ns
(2) from PDG 2009
() = (7) s–1
Experimental result:
|Vus/Vud| fK/f = (5)
Long-distance EM correction
 0.28%
(Marciano, PRL 93 (2004) )
 0.18%
E. Goudzovski / Glasgow, 3 June 2010

16. CKM unitarity and SM tests
E. Goudzovski / Glasgow, 3 June 2010

17. CKM unitarity |Vus| vs |Vud| fit |Vus| |Vud| Experimental input:
|Vus|f+(0) = (5)
|Vus/Vud| fK/f = (5)
|Vud| = (22)
(average from 20 nuclear beta decays,
Hardy & Towner, PRC79 (2009) )
Lattice input:
f+(0) = 0.959(6)
fK/f = 1.193(6)
Fit result:
|Vus| = (9)
Fit imposing unitarity:
|Vus| = (6)
CKM unitarity test:
|Vus|2 +|Vud|2 –1 = –0.0001(6)
~0.2%
|Vus|
|Vus| vs |Vud| fit
0.6%
0.4%
Other (less precise) |Vus| evaluations have been made
with hyperon and tau decays
|Vud|
E. Goudzovski / Glasgow, 3 June 2010

18. K2: sensitivity to new physics
Comparison of |Vus| determined from helicity-suppressed K2 decays vs helicity allowed Kl3 decays W+
or H+ ?
To reduce uncertainties of hadronic and EM corrections to K2,
tan vs H+ mass exclusion
tan
Lattice QCD input
Measured with K2/2
Measured with Kl3
SM expectation: R23 = 1.
Charged Higgs mediated currents lead to
Experiment: R23 = 0.999(7), limited by lattice input.
Charged Higgs mass [GeV/c2]
E. Goudzovski / Glasgow, 3 June 2010

19. Kl3: lepton universality test
Comparison of |Vus| determined from Ke3 vs K3 decays SM
= (g/ge)2 = 1
lepton coupling
at the Wl vertex
Experimental results
K: re = 0.998(9)
K0: re = 1.003(5)
Non-kaon measurements:
l: re = (33)
l: re = 1.000(4)
The sensitivity in kaon sector approaches those obtained in the other fields.
 re = 1.002(4)
(PRD 76 (2007) )
(Rev.Mod.Phys. 78 (2006) 1043)
E. Goudzovski / Glasgow, 3 June 2010

20. Kl2: lepton universality test
LFV H exchange contribution:
(MH, tan) 95% exclusion limits
100
2HDM-II
tan
can reach ~1% without contradicting any known experimental limits 80 60
ATLAS fb–1 (by 2014?) 40
SuperB excludes 20
200
400
600
800
1000
Charged Higgs mass [GeV/c2]
Experiment: RK=2.498(14)10–5; SM: RK=2.477(1)10–5
E. Goudzovski / Glasgow, 3 June 2010

21. Summary Tremendous progress in measurements and interpretation of
(semi)leptonic kaon decays during the last decade!
Thanks to advances of both experiment and theory, |Vus|f+(0) has been measured to 0.23% precision, and |Vus| has been evaluated to 0.4% precision with kaon decays.
CKM unitary with |Vud|2+|Vus|2 tested at 0.06% precision:
 O(10 TeV) bound on the scale of new physics.
K2/2 and Ke2/K2 put non-trivial constraints of 2HDM.
Experimental precision on |Vus|f+(0) is expected to be improved to the level of ~0.1% in mid-term: a similar precision on f+(0) and an improvement on radiative corrections for |Vud| would allow for a CKM unitarity test at ~0.02% level.
Interpretation of Ke3 data is currently limited by lattice QCD input
E. Goudzovski / Glasgow, 3 June 2010