Test of the Standard Model with Kaon decays. Barbara Sciascia LNF-INFN for the Kaon WG, FlaviaNet PhiPsi08 - LNF, 7 April 2008

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1 Test of the Standard Model with Kaon decays Barbara Sciascia LNF-INFN for the Kaon WG, FlaviaNet PhiPsi08 - LNF, 7 April FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

2 Introduction Analysis of leptonic and semileptonic kaon decays data provide precise determination of fundamental SM couplings; set stringent SM tests, almost free from hadronic uncertainties; discriminate between different NP scenarios. Test unitarity of the quark mixing matrix (V CKM ): present precision on V us (dominant source of error) and V ub negligible ( V ub2 ~10 5 ) set bounds on NP well above 1 TeV. Comparison of Ke3 and Kµ3 modes, tests the lepton universality. 2 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

3 The FlaviaNet Kaon working group The FlaviaNet Kaon WG ( Recent kaon physics results come from many experimental (ISTRA+, KLOE, KTeV, NA48) and theoretical (Lattice, χ PT,). The main purpose of this working group is to perform precision tests of the Standard Model and to determine with high accuracy fundamental couplings (such as V us ) using all existing (published and/or preliminary) data on kaon decays, taking correlations into account. WG note: Precision tests of the Standard Model with leptonic and semileptonic kaon decays, arxiv: [hep-ph] 11 Jan FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

4 Summary of the talk Global fits and averages: K L, K S, and K ±, dominant BRs and lifetime. Parameterization of the K π interaction (form factor) Physics results: V us f + (0) Test of lepton universality with K l3. V us / V ud f K /f π. Theoretical estimations of f + (0) and f K /f π. V us and V ud determinations. Bounds on helicity suppressed amplitudes. The special role of BR(K ± e2)/br( K ± µ2) 4 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

5 K L leading branching ratios and τ L 18 input measurements: 5 KTeV ratios NA48 K e3 /2t and Γ(3π 0 ) 4 KLOE BRs KLOE, NA48 π + π /K l3 KLOE, NA48 γγ/3π 0 PDG ETAFIT for π + π /π 0 π 0 KLOE τ L from 3π 0 Vosburgh 72 τ L 8 free parameters, 1 constraint: ΣBR=1 Main differences wrt PDG06: For KLOE and KTeV, use values obtained before applying constraints. Make use of preliminary BR(3π 0 ) and new BR(π + π )/BR(Ke3) from NA48 Fit parameter BR(π + π ) is understood to be inclusive of the DE component. 5 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

6 Evolution of the average BR values This fit χ 2 /ndf = 20.2/11 (4.3%); PDG06 fit: χ 2 /ndf = 14.9/9 (14.0%) Minor differences wrt PDG06: contrast between KLOE BR(3π 0 ) and other inputs involving BR(2π 0 ) and BR(3π 0 ) treatment of the correlated KLOE and KTeV inputs: more uniform scale factor in this fit and significantly smaller uncertainty for BR(Ke3). 6 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

7 K S leading branching ratios and τ S 4 input measurements: KLOE BR(Ke3)/BR(ππ ππ) KLOE BR(ππ ππ)/br(π 0 π 0 ) Universal lepton coupling NA48 BR(Ke3) τ S : non CPT-constrained fit value, dominated by 2002 NA48 and 2003 KTeV measurements 4 free parameters: K S ππ, K S π 0 π 0,K S e3,k S µ3, 1 constraint: ΣBR=1 KLOE meas. completely determine the leading BR values. NA48 Ke3 input improve the BR(Ke3) accuracy of about 10%. BR(K S e3)/br(k L e3) from NA48 not included (need of a K L and K S combined fit) Combined fit would be useful in properly account for preliminary NA48 Γ(K L 3π 0 ) and PDG ETAFIT, used in the K L fit. 7 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

8 K ± leading branching ratios and τ ± 26 input measurements: 5 older τ values in PDG 2 KLOE τ KLOE BR(µν µν) KLOE Ke3, Kµ3, and Kπ2 BRs ISTRA+ K e3 /π π 0 NA48/2 K e3 /π π 0, K µ3 /π π 0 E865 K e3 /Kdal 3 old ππ 0 /µν 2 old Ke3/2 body 3 Kµ3/Ke3 (2 old) 2 old + 1 KLOE results on 3π 7 free parameters, 1 constraint: ΣBR=1 Don t use the 6 BR meas. from Chiang; no implementation of radiative corrections 6 BR constrained to sum to unit. the correlation matrix not available. Try to discard many other old meas.: no recent meas. involving BR(πππ πππ) fit instable if only recent are used. 8 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

9 Evolution of the average BR values This fit χ 2 /ndf = 42/20 (0.31%); PDG06 fit: χ 2 /ndf = 30/19 (5.2%) If 5 older τ ± measurements replaced by PDG avg (with S=2.1), χ 2 / ndf = 24/16 (8.4%) with no significant changes to central values or errors. include many new results some conflict among newer meas. involving BR(Ke3): the pulls are +1.04, -0.26, -0.73, and -2.13, for NA48, BNL-E865, ISTRA+, and KLOE respectively. Evolution of the BR(K l3 ) and for the important normalization channels. 9 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

10 Parameterization of K l3 form factors Hadronic K π matrix element is described by two form factors f + (t) and f 0 (t) defined by: Experimental or theoretical inputs to define t-dependence of f +,0 (t). f (t) term negligible for K e3. Taylor expansion: Obtain λ,λ, from fit to data distributions (more accurate than theor. predictions). λ and λ are strongly correlated: 95% for f + (t), and 99.96% for f 0 (t). One parameter parameterizations: Pole parameterization (what vector/scalar state should be used?) Dispersive approach plus Kπ scattering data for both f + (t) and f 0 (t) 10 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

11 Vector form factor Quadratic expansion: Measurements from ISTRA+, KLOE, KTeV, NA48 with K L e3 and K e3 decays. Good fit quality: χ 2 /ndf=5.3/6(51%) for all data; χ 2 /ndf=4.7/4(32%) for K L only The significance of the quadratic term is 4.2σ from all data and 3.5σ from K L only. Using all data or K L only changes the space phase integrals I 0 e3 and I ± e3 by 0.07%. Errors on I e3 are significantly smaller when K data are included. A pole parameterization is in good agreement with present data: λ = (m π +/M) 2 ; λ = 2λ 2 KLOE, KTeV, NA48 quote value for M V for pole fit to K L e3 data (χ 2 /ndf=1.8/2) The values for λ + and λ + from pole expansion are in agreement with quadratic fit results. Using quadratic averages or pole fit results changes I 0 e3 by 0.03%. Improvements: dispersive parameterization for f + (t), with analytical and unitarity properties and a correct threshold behavior, (e.g.passemar arxiv: [hep-ph]) Dispersive results for λ + and λ 0 are in agreement with pole parameterization. 11 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

12 Vector and scalar form factor from K µ3 λ +, λ + and λ 0 measured for Kµ3 from ISTRA+, KLOE, KTeV, and NA48. NA48 result lies out of correlation directions in the [λ +, λ +, λ 0 ] space. Fit probability varies from (with NA48) to 22.3% (without NA48). 1σ contour for all the experimental results. Neglecting a quadratic term in the param. of scalar FF implies: λ 0 λ λ 0 Because of correlation, is not possible measure λ 0 at any plausible level of stat. 12 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

13 Vector and scalar form factor from K l3 Slope parameters λ +, λ + and λ 0 from ISTRA+, KLOE, KTeV, and NA48. Space integral used for the V us f + (0) determination Averages of quadratic fit results for Ke3 and Kµ3 slopes. Adding Kµ3 data to the fit doesn t cause significant changes to I 0 e3 and I ± e3. The significance of the quadratic term λ + is strong (3.6σ from to fit to all data). NA48: [I(Kµ3)] = 0.6%, but Ke3+Kµ3 average gives [V us f + (0)] = 0.08%. 13 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

14 Determination of V us f + (0) Γ(K l3(γ) ) = C K 2 G F2 M K 5 K 0 π (λ +,0 S 192π 3 EW V us 2 f + (0) 2 I Kl (λ with K = K +, K 0 ; l = e, µ and C K2 = 1/2 for K +, 1 for K 0 +,0 ) (1+δ K SU(2) +δkl em )2 Inputs from theory: Inputs from experiment: S EW δ K SU(2) δ Kl em K f 0 π (0) + Universal short distance EW correction (1.0232) Form factor correction for strong SU(2) breaking Long distance EM effects Hadronic matrix element at zero momentum transfer (t=0) Γ(K l3(γ) ) I Kl (λ) Branching ratios with well determined treatment of radiative decays; lifetimes Phase space integral: λ s parameterize form factor dependence on t : K e3 : only λ + K µ3 : need λ + and λ 0 14 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008 CT

15 SU(2) and em corrections K 0 e3 K 0 µ3 K + e3 K + µ3 δ Κ SU(2) (%) (22)% +2.36(22)% δ Kl em (%) +0.57(15) +0.80(15) +0.08(15) +0.05(15) (values used to extract V us f + (0)) δ em for full phase space: all measurements assumed fully inclusive. Different estimates of δ em agree within the quoted errors. Available correlation matrix between different corrections. 15 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

Determination of V us f + (0) Γ(K l3(γ) ) = C K 2 G F2 M K 5 K 0 π % err (λ +,0 S 192π 3 EW V us 2 f + (0) 2 I Kl (λ +,0 ) (1+δ K SU(2) +δkl em )2 Approx. contr. to % err from: BR τ δ I Kl K L e3 0.

16 Determination of V us f + (0) Γ(K l3(γ) ) = C K 2 G F2 M K 5 K 0 π % err (λ +,0 S 192π 3 EW V us 2 f + (0) 2 I Kl (λ +,0 ) (1+δ K SU(2) +δkl em )2 Approx. contr. to % err from: BR τ δ I Kl K L e (6) K L µ (7) K S e (13) K ± e (8) K ± µ (11) Average: V us f + (0) = (5) χ 2 /ndf = 2.74/4 (60%) 16 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

17 Test of Lepton Universality from Kl3 Test of Lepton Flavor Universality: comparing Ke3 and Kµ3 modes constraints possible anomalous LF dependence in the leading weak vector current. Evaluate R Kµ3/Ke3 : Compare experimental results with SM prevision: Using FlaviaNet results get accuracy 0.5%, K L r µe = (61) K ± r µe = (86) Average r µe = (52) Comparable with other determinations: τ decays: (r µe ) τ = (41) (PDG06) π decays: (r µe ) π = (33) Comparing values obtained for K L and K ± (without δ Κ SU(2) correction) allows the empirical evaluation of SU(2) breaking correction : 2.81(38)%. To be compared with χ PT prediction 2.36(22)%. Recent analyses point to 3%. 17 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

18 Γ(K l3(γ) ) = C K 2 G F2 M K 5 Leutwyler & Roos estimate still widely used: f + (0) = 0.961(8). Theoretical estimate of f + (0) K 0 π (λ +,0 S 192π 3 EW V us 2 f + (0) 2 I Kl (λ +,0 ) (1+δ K SU(2) +δkl em )2 Lattice evaluations generally agree well with this value; use RBC-UKQCD07 value: f + (0) = (49) (0.5% accuracy, also syst. err.). 18 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

19 V us /V ud determination from BR(K µ2 ) Γ(K µ2(γ) ) Γ(π µ2(γ) ) = V us 2 f K M K (1-m 2 µ /M K2 ) 2 (1+α(C K -C π )) V ud 2 m π (1-m 2 µ /m 2 π ) 2 f π Inputs from experiment: Γ(π,K l2(γ) ) BR with well determined treatment of radiative decays; lifetimes Inputs from theory: C K,π Rad. inclusive EW corr. f K /f π Not protected by the Ademollo-Gatto theorem: only lattice. Lattice calculation of f K /f π and radiative corrections benefit of cancellations. Use HPQCD-UKQCD07 value: f K /f π = 1.189(7). 19 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

20 A test of lattice calculations ~ Scalar form factor f 0 (t) = f 0 (t) f + (0) extrapolation at Callan-Treiman point: links f + (0) and f K /f π with λ 0 measured in Kµ3 decays. ~ f 0 ( Kπ ) is evaluated fitting K L µ3 with a dispersive parameterization G(t) from Kπ scattering data. To fit we use a 3 rd order expansion Not allowed From CT, using f K /f π =1.189(7) [HPQCD- UKQCD07] obtain: f + (0)=0.964(23) in agreement with RBC/UKQCD07 value: f + (0) = (49). 20 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

V ud, V us and V us /V ud Kl3: V us f + (0) = 0.2166(5) and f + (0) = 0.964(5), obtain V us = 0.2246(12) Kl2: V us / V ud f K /f π = 0.2760(6) and f K /f π = 1.189(7), obtain V us / V ud =0.

21 V ud, V us and V us /V ud Kl3: V us f + (0) = (5) and f + (0) = 0.964(5), obtain V us = (12) Kl2: V us / V ud f K /f π = (6) and f K /f π = 1.189(7), obtain V us / V ud =0.2321(15) V ud from nuclear β decay: V ud = (26) [Hardy-Towner, nucl-th ] Fit (no CKM unitarity constraint): V ud = (26); V us = (9) χ 2 /ndf = 0.65/1 (41%) Unitarity: 1 V ud2 V us2 = (6) The test on the unitarity of CKM can be also interpreted as a test of the universality of lepton and quark gauge coupling: Fit (with CKM unitarity constraint): V us = (7) χ 2 /ndf = 0.8/2 (67%) 21 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

K µ2 : sensitivity to NP Comparison of V us from K l2 (helicity suppressed) and from K l3 (helicity allowed) To reduce theoretical uncertainties study the quantity: Within SM R l23 = 1; NP effects

22 K µ2 : sensitivity to NP Comparison of V us from K l2 (helicity suppressed) and from K l3 (helicity allowed) To reduce theoretical uncertainties study the quantity: Within SM R l23 = 1; NP effects can show as scalar currents due to a charged Higgs: R l23 is accessible via BR(K µ2 )/BR(π µ2 ), V us f + (0), and V ud, and f K /f π /f + (0) determinations. Using K ± fit results, assuming unitarity for K l3, and using f K /f π /f + (0) from lattice: R l23 = 1.004(7). Uncertainty dominated by f K /f π /f + (0). 95% CL excluded region (with ε ). In tanβ-m H± plane, R l23 fully cover the region uncovered by BR(B τν τν). M H± (GeV) 22 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

Measurement of R K =Γ(K e2 )/Γ(K µ2 ) PDG06: 5% precision from 3 old mnts 2 preliminary meas. from NA48 (see M.Raggi talk); waiting for new data result. 1 preliminary from KLOE see (A.

23 Measurement of R K =Γ(K e2 )/Γ(K µ2 ) PDG06: 5% precision from 3 old mnts 2 preliminary meas. from NA48 (see M.Raggi talk); waiting for new data result. 1 preliminary from KLOE see (A.Passeri talk); waiting for final. New average: R K =2.457(32) Perfect agreement with SM expectations: R K SM =2.477(1) In SUSY(MSSM) LFV appear at 1-loop level (effective H + lν τ Yukawa interaction). For moderately large tanβ values, enhance R K up to few %. The world average gives strong constrains for tanβ and M H±. 95%-CL excluded regions in the tanβ - M H plane, for 13 = 10-4, , M H± (GeV) 23 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

24 Conclusions Dominant K S, K L, and K ± BRs, and lifetime known with very good accuracy. Dispersive approach for form factors. Constant improvements from lattice calculations of f + (0) and f K /f π : Callan-Treiman relation allows checks from measurements; lack of sys. errors; need to average different evaluations. V us f + (0) at 0.2% level. Test of LU with Kl3 decays with 0.5% accuracy. V us measured with 0.4 accuracy (with f + (0)= (49)) Dominant contribution to uncertainty on V us still from f + (0). CKM unitarity test satisfied at 0.3σ level test of lepton-quark universality Comparing V us values from Kµ2 and Kl3, exclude large region in the (m H,tanβ) plane, complementary to results from B τν decays. 24 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

25 Additional information 25 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

26 K ± leading branching ratios and τ ± No significant differences in the fit if the final KLOE measurement of K ± lifetime is used instead of the preliminary one (FlaviaNet note): FlaviaNet note τ ± (KLOE) = (30) ns 5.593(30)% 1.749(26)% (19) ns 26 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

27 Dispersive parameterization 27 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

28 With or without NA48 Kµ3 data wna48-w/ona48: (0.01%) (0.04%) I(K 0 e3) (0.01%) (0.07%) I(K ± e3) (0.55%) (0.75%) Ι(Κ 0 µ3) (0.49%) (0.69%) I(K ± µ3) 28 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

29 Lepton universality from K e2 /K µ2 SM: no hadronic uncertainties (no f K ) In MSSM, LFV can give up to % deviations [Masiero, Paradisi, Petronzio] NP dominated by contribution of eν τ R K Γ(K eν e )+Γ(K eν τ ) Γ(K µν µ ) ν e ν µ ν τ with effective coupling: m K 4 m τ 2 R K R SM K [ 1+ R 31 2 tan 6 β] 4 2 m H m e 1% effect ( R 31 ~5x10-4, tanβ 40, m H ~500GeV) not unnatural Present accuracy on R 6% ; need for precise (<1%) measurements 29 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

30 Vector form factor from K e3 Quadratic from ISTRA+, KLOE, KTeV, NA48 with K L and K decays. The significance of the quadratic term is 4.2σ from all data and 3.5σ from K L only. Using all data or K L only changes the space phase integrals I 0 e3 and I ± e3 by 0.07%. Errors on I e3 are significantly smaller when K data are included. 30 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

31 Vector form factor from K e3 KLOE, KTeV, NA48 quote value for M V for pole fit to K L e3 data. The values for λ + and λ + from pole expansion are in agreement with quadratic fit results. Using quadratic averages or pole fit results changes I 0 e3 by 0.03%. 31 FlaviaNet: WG on precise SM tests in K decays B. Sciascia PhiPsi08, LNF, 7 Apr 2008

Lepton Universality Tests with Kaons

Lepton Universality Tests with Kaons Rainer Wanke Institut für Physik, Universität Mainz for the Flavianet Working Group on Kaon Decays KAON 2007 Frascati, May 24, 2007 Rainer Wanke, Universität Mainz,