1. Claudio Gatti (KLOE Collaboration) LNF INFN K decay measurements with the KLOE detector XXII Rencontres de Physique de La Vallée d’Aoste Feb. 2008

2. Precision test of SM with kaons C.Gatti - La Thuile 2008 SM coupling to W  Same coupling for all fermionsUnitary matrix W u d, s l g q V ud,s glgl (g q g l ) 2 |V ud,s | 2 /M W 4 W  e gg gege (g  g e ) 2 /M W 4 K,  and nuclear  decays  decay (g q g l ) 2 (|V ud | 2 +|V us | 2 )= (g  g e ) 2 Left-handed Test of unitarity and universality V ub negligible

3. C.Gatti - La Thuile 2008 Precision test of SM with kaons H+H+ u d, s l W u d, s l Z'Z' Believe in SM coupling to W: Test the presence of scalar and right-handed currents and presence of new gauge bosons. With recent precise experimental results and progress in theoretical predictions (lattice QCD, ChPT...), kaon physics allows us to test the Standard Model at permil level, and probe new physics at the TeV scale.

4. Semileptonic kaon decays C.Gatti - La Thuile 2008  decay Short distance EW correction Long distance EM correction SU(2)-breaking correction Form factor at zero momentum transfer Phase space integral For the extraction of |V us | we need to measure  (Kl3): from measurement of BR’s and lifetimes. I kl : from measurement of the t-dependence of form factors. All measurements taking into account radiated photons.

5. Leptonic kaon decays C.Gatti - La Thuile 2008 EM correction Ratio of K and  decay constants Precise determination of the ratio |V us |/|V ud | from K  2 and   2 decay width. Combine measurement from K  2,   2, K e3, K  3 and from nuclear  decays to test electron-muon and lepton-quark universality and the unitarity of the CKM matrix.

6. The KLOE experiment C.Gatti - La Thuile 2008 Electromagnetic Calorimeter (pb/sci)  (E)/E = 5.7 %/  E(GeV)  (t) = 57 ps/  E(GeV)  100 ps  (x)~1 cm Drift Chamber (90%He 10% isobutane)  p /p  0.4 % (tracks with  > 45°)  x hit  150  m (xy), 2 mm (z)  x vertex ~ 1 mm  (M  ) ~ 1 MeV K S, K +  K L, K - K + K - BR~50% p=127 MeV ± =95 cm K S K L BR~30% p=110 MeV s =0.6 cm L =340 cm B=0.5 T Integrated luminosity L=2.5 fb -1 About 2.5×10 9 K S K L

7. Simulation of the final state photon C.Gatti - La Thuile 2008 Emission of final state photon included in the KLOE simulation. All measurements are inclusive of the final state radiation. Enriched Ke3 sampleDirect measurement of E  in Ke3

8. Kaon Tag C.Gatti - La Thuile 2008 KS  KS  KS  KS   KL  2KL  2KL  2KL  2 K L tagged by K S      Efficiency ~ 70%  (P K ) ~ 1 MeV K L “crash”  = 0.22 (TOF) K S    e  K S    e  K S tagged by K L interaction in EmC Efficiency ~ 30%  (P K ) ~ 1 MeV K ± tagged by K  ,  identified by the secondary particle momentum in the K rest frame: p * (m  ) Trigger from the tag side.  Tag ~10% Absolute BR’s: BR=N obs /N tag

9. K L,S decays and K L lifetime C.Gatti - La Thuile 2008 13×10 6 K L tagged decays. BR for 3  0,  +  -  0, Ke3 and K  3, identifying photons in the calorimeter and fit to E miss -p miss from p Trk.  L measurement from BR dependency on FV  BR/BR=  L ×0.0128 ns -1   BR=1 Measurement of  L from proper decay-time ditribution for K L  3  0. K L vertex from photon time of flight and K L direction. 8.5 million decays in ~0.4 L. 400 ×10 6 K S K L BR for K S   e PID from time of flight. 13,500 Ke3 events selected. Fit to E miss -p miss. First measurement of the charge asymmetry A S =(1.5±10)×10 -3

10. C.Gatti - La Thuile 2008 BR(Ke3) 0.4008(15) BR(K  3) 0.2699(14) BR(3  0 ) 0.1996(20) BR(       ) 0.1261(11) BR(     ) 1.964(21)  10 -3 BR(     ) 8.49(9)  10 -4 BR  ) 5.57(8)  10 -4  L 50.84(23) ns All correlations taken into account Only non-KLOE input BR(     )/BR(      =0.4391±0.0013 PDG ETAFIT BR(K L  +  - )  (K L  )=0.007275(68) ~45000  ~20000  BR(K L  )  (K L  3  0 )=0.00279(3) Other KLOE inputs BR(      69.196(51) BR(      30.687(51) BR(Ke + 3) 3.517(58)×10 -4 BR(Ke - 3) 3.528(62)×10 -4  2 /dof = 0.19/1 BR(K S       )/BR(K S      )=2.2549(54) The sum of measured K S BR’s is  BR  1-5×10 -4 K L,S decays and K L lifetime

11. K +        C.Gatti - La Thuile 2008 From 4 million tagged events. Found ~865,000 K  2 events in 225<p * <400 MeV Absolute BR. Counting by fit to p * distribution. Signal and background p * -shapes, and efficiency from data control samples. Small correction from MC checks, negligible dependence on  ±. BR(K +   )=(0.6366±0.0017) Same method used to measure BR(     . BR(K +       =(20.65±0.05 stat ±0.08 syst )% -1.2% of PDG 2006, shifts NA48/2 and ISTRA+ Kl3 measurements

12. C.Gatti - La Thuile 2008 K ± lifetime With 12 million tagged K, use 2 methods: K decay lenght t * =   L   K  K c  from DC info, taking into account dE/dX. K decay time t * = (t  -L   c)/  K from calorimeter info, measure photon time of flight.   =(12.347  0.030) ns  -  + = 1.004  0.004 K decay lenght 1.6  ±   =(12.364  0.044) ns K decay time 2.3  ±   =(12.337  0.036) ns PDG average 12.385(25) ns but CL 0.2%

13. K ± semileptonic decays C.Gatti - La Thuile 2008    e+e+e+e+   60 million tagged events. Apply kinematic cuts to reject background. Reconstruct photons and measure t K from tof. Measure lepton mass from tof and track momentum measurement. Counting from fit to m 2 l distribution. 300,000 Ke3 and 160,000 K  3. Using lifetime from KLOE: BR(Ke3)=(4.972±0.053)% BR(K  3)=(3.237±0.039)%

14. Form Factor: K 0 e3 C.Gatti - La Thuile 2008 High purity Ke3 sample, 2 million events, selected by kinematics and time of flight. e  by tof  measure t=(p K -p  ) 2 Independent measurement for the two charge modes. Ke3 sensitive only to vector FF. t/m 2 + =(25.5±1.5 stat ±1.0 syst )×10 -3  + =(1.4±0.7 stat ±0.4 syst )×10 -3 P(  2 ) ~ 90% Correlation –0.95 M V =(870±6 stat ±7 syst ) MeV Pole parametrization: P(  2 ) ~ 92%

15. C.Gatti - La Thuile 2008 Form Factor:  0  1.8 million K  3 selected. Sensitive to both vector and scalar FF’s. Bakground rejection with kinematic cuts and tof. Difficult  separation: Fit to E spectrum, less sensitive (errors 2-3 times larger)  combined fit with Ke3 data. Large correlations: impossible to measure 0 . +  + 0 1 -0.95 0.29 1 -0.38 0 =(15.4±2.2)×10 -3  2 /ndf =2.3/2

16. C.Gatti - La Thuile 2008 Form Factors New parametrizations based on dispersive relations (Bernard, Oertel, Passemar, Stern) and K  scattering data: f + and f 0 depend only on parameters + and 0 respectively. + =(25.7±0.6 stat+syst )×10 -3 0 =(14.0±2.1 stat+syst )×10 -3  2 /ndf =2.6/3 Correlation –0.26 Phase-space integrals change by 0.04% and 0.09% for Ke3 and K  3. t f + (0) f 0 (t CT ) t CT =(m K 2 -m  2 ) ml2ml2 (m K -m  ) 2 K   l f 0 (t) Test of lattice QCD Callan-Treiman f 0 (t CT )=f K  f  +  CT  CT O(10 -3 ) (Gasser, Leutwyler) f K  f  =1.189±0.007 (HPQCD/UKQCD) f + (0)=0.967±0.025 Compare with f + (0)=0.9644±0.0049 (RBC/UKQCD)

17. KLOE main publications related to V us C.Gatti - La Thuile 2008 Charged Kaons  ± JHEP 01 (2008) 073 d  0.25% K +   PLB632 (2006) 76 dBR  BR~0.26% K ±   l JHEP Accepted dBR(  l )  BR~1.1% Neutral Kaons  L PLB626 (2005) 15 d  0.5% K L BR’s PLB632 (2006) 43 dBR(  l )  BR~0.4-0.5% Ks   e PLB636 (2006) 173 dBR(  e )  BR~1.3% Form factors Ke3 FF PLB636 (2006) 166 d  ~7% d  50%  FF JHEP 12 (2007) 105 d 0  0  14% dI  I~0.3-0.5% |V us | and lepton universality @ KLOE arXiv:0802.3009

18. f + (0)×|V us | from KLOE results C.Gatti - La Thuile 2008 K Le3 0.2155(7) K L  3 0.2167(9) K Se3 0.2153(14) K ± e3 0.2152(13) K ±  3 0.2132(15) f + (0)×|V us |=0.2157±0.0006  2 /ndf =7.0/4 (13%) All correlations taken into account Only non-KLOE input  s Comparing charged and neutral K decays:  SU(2)=1.67(62)% (theory 2.36(22)%) Test of lepton universality: r  e =1.000±0.008 From  and  decays  ±0.4%

19. Test of CKM unitarity with KLOE results C.Gatti - La Thuile 2008 Using From lattice QCD: f + (0)=0.9644±0.0049 (RBC/UKQCD) f K  f  =1.189±0.007 (HPQCD/UKQCD) From 0 +  0 + nuclear  decays |V ud |=0.97418±0.00026 And using  (    ): |V us |=0.2237±0.0013 From Kl3 decays: |V ud | 2 +|V us | 2 -1=-0.0009±0.0008 |V us | 2  |V ud | 2 =0.0541±0.0007 From K  2: |V us |=0.2249±0.0010 |V ud |=0.97417±0.00026 |V ud | 2 +|V us | 2 -1=0.0004±0.0007  2 /ndf =2.34/1 (13%) Combined fit result: Unitarity condition verified to 0.1%

20. Bounds on new physics from K  2 decay C.Gatti - La Thuile 2008 From previous results: Unity in SM, affected by presence of scalar or right-handed currents. (Isidori, Paradisi) R l23 =1.008±0.008 We obtain: This places bounds on the charged Higgs mass and tan . Competitive and complementary to B decays.

21. C.Gatti - La Thuile 2008 Bounds on new physics from K e2 decay R K =  (K  e )/  (K   ) Accurate SM determination (0.04%) New physics effects up to 1% (Masiero, Paradisi, Petronzio). BR(K  e  ~10 -5 at most 4×10 4 events. No tag requested. Background from K  2, selection using DC info (M lep 2 ) and calorimeter PID: E RMS (MeV) M 2 lep (MeV 2 ) Fit region E RMS (MeV) M 2 lep (MeV 2 )   Data ° MC Fit  MC bkg 400 800 400 1200 4080 -4000-2000020004000

22. C.Gatti - La Thuile 2008 Bounds on new physics from K e2 decay tan  M H (GeV) Preliminary KLOE result with ~ 8100 observed events: R K =(2.55±0.05 stat ±0.05 syst )×10 -5 We place bounds on the charged Higgs mass and tan , for different values of the slepton- mass matrix element  13. SM: 2.477(1)×10 -5 (Cirigliano, Rosell) NA48 preliminary: 2.43(4)×10 -5

23. Conclusion C.Gatti - La Thuile 2008 We have measured: All the BR’s for K L K S and K ± The form factor parameters in semileptonic K L decays The K L and K ± lifetimes We obtain f + (0)×|V us |=0.2157±0.0006 with 0.3% accuracy We test lepton universality: r  e = g   /g e 2 =1.000±0.008 We measured the ratio |V us /V ud × f K /f  | 2 = 0.7650±0.0033 with 0.4% accuracy. Using lattice QCD determinations for meson form factor and decay constants we obtain: |V us |=0.2237±0.0013 and |V us /V ud |=0.2326±0.0015 with 0.6% accuracy Combining with a fit these results with the evaluation of |V ud | from nuclear  decay we obtain |V us |=0.2249±0.0010 with 0.4% accuracy. First-row CKM unitarity is satisfied to 0.1% (0.6  ) With our results we are able to exclude a large region in the m H+ -tan  plane. Preliminary results on the ratio BR(K  e  /BR(K   allow a test LFV and the exclusion of a large region in the m H+ -tan  plane. Complete dataset must still be analyzed, we expect improvements for lifetimes, BR’s and FF parameters, as well as from the theory side (Lattice QCD, ChPT......).

24. backup C.Gatti - La Thuile 2008 f + (0) fK/ffK/f

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