1. |Vus| and K S decays from KLOE Gaia Lanfranchi, LNF/ INFN On behalf the KLOE Collaboration XL Rencontres de Moriond 5-12 March, 2005

2. Kaon physics at KLOE: K L ,  e,  +  -  0,3  0 this talk K L lifetimethis talk K L  /K L  3  0 Phys. Lett. B566 61 (2003) K 0 mass KLOE Note 181 (http://www.lnf.infn.it/kloe) K S   e Phys. Lett. B535 37 (2002) Preliminary update with ’01-’02 data K S  π  First observation K S  0  0  0 this talk KS π+π-π0KS π+π-π0 In progress K S  +  - (  ) K S  0  0 Phys. Lett. B538 21 (2002) Update with ’01-’02 data in progress Vus from K + In progress K +  +  0  0 Phys. Lett. B 597 139 (2004) |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN

3. The KLOE Detector: Calorimeter Drift Chamber σ(E)/E = 5.7%/  E(GeV) σ(t) = 54 ps/  E(GeV)  50 ps  p /p  0.4 % (tracks with  > 45°)  x hit  150  m (xy), 2 mm (z)  x vertex ~ 1 mm  (M  ) ~ 1 MeV |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN

4. V us is a fundamental parameter of SM PDG 2004: violation of unitarity? To measure V us we need Γ Le3 …. We need to measure: BR(K Le3 ), τ L |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN

5. K L lifetime: direct measurement K L lifetime: direct measurement  K L lifetime is “hard” to measure ! Last measurement 30 years ago (Vosburgh et al, PRD 6 (1972), 1834):  Can’t stop K L ’s!  Knowledge of the K L momentum spectrum is required.  Measure K L lifetime @ KLOE is possible because:  K L ’s are slow (βγ  0.22, λ L  340 cm);  K L ’s are (almost) monochromatic (P(K L )  110 MeV);  K L ’s are background free (unambiguously tagged ). |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN

6. K L lifetime: statistical error vs fit region K L lifetime: statistical error vs fit region |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN T = ΔL/λ Number of events δτ/τ  0.40 8,000,000 0.3%  0.04 8,000,000  2.4%  0.004 8,000,000  20% To reach the 0.3% statistical accuracy you need a factor 3.5  10 3 more events!! KLOE Statistical error Number of events in the fit region T = fit region in lifetime units

7. K L dominant BR’s: present experimental situation K L  e K L  K L  3  0 NA48: 0.4010±0.0045 KTeV: 0.4067±0.0011 PDG 2004: 0.3881±0.0027 KTeV: 0.2701 ±0.0009 PDG 2004: 0.2719±0.0022 K L  π + π -  0 KTeV: 0.1252±0.0007 PDG 2004: 0.1258±0.0019 KTeV: 0.1945±0.0018 PDG 2004: 0.2105±0.0023 |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN

8. K L dominant BR’s: K L dominant BR’s: |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN What is KLOE’s role in this scenario? KLOE can measure:  absolute branching fractions (instead of ratios!);  K L lifetime. Therefore KLOE can provide a complete and self- consistent set of measurements of the dominant K L decay widths without relying on external inputs.

9. The KLOE K L “beam”: K S  +  - KL  2KL  2KL  2KL  2 K L tagged by K S  +  - events: Efficiency ~ 70% (mainly geometrical) K L angular resolution: ~ 1° K L momentum resolution: ~ 1 MeV 1) Pure and tagged K L beam:  we can measure absolute BRs since the normalization is provided by tagging events. 2) Low energy, monochromatic beam: P (K L )  110 MeV, βγ  0.22, λ L  340 cm  a big fraction of K L (50%) decays inside the detector  We can measure K L lifetime. |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN  KSKS KLKL BR = 34% p  110 MeV

10. K L absolute BR’s and lifetime: DATA SAMPLE: 2001+2002 data sample: 400 pb -1 statistics, 50  10 6 tagged K L :  13 million tagged K L used to evaluate the absolute BR’s;  40 million tagged K L used to evaluate systematic uncertainties;  15 million of K L  3π 0 for the direct measurement of the lifetime. |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN

11. K L absolute BR’s: K L absolute BR’s: For each K L decay mode (i=π ,πe,3  0,  +  -  0 ) we count the number of events in a given fiducial volume: Reconstruction efficiencies: K L  π , πe ε (rec)  60% K L  π+π-π0 ε (rec)  45% K L  3π 0 ε (rec)  100% Integral over the fiducial volume: ε (FV, τ L )  26%, depends on τ L Tagging efficiency: Depends on the channel Can introduce a BIAS |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN

12. K L absolute BR’s: tag bias K L absolute BR’s: tag bias |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN Slightly different tagging efficiencies for different K L topologies:  tag i /  tag all  1 1) Different trigger efficiency for K L decays in FV / K L interactions in calo / K L punch-through:  require that K S pions satisfy trigger conditions by themselves  trigger efficiency cancels out 2) Interference effect between K S and K L tracks lowers reconstruction efficiency for K S  π+π- decays at small R L :  cut on the opening angle of K S pions       Ke3 K  3 3  0  tag i /  tag all.998(4).986(2).984(3) 1.017(3) After these cuts the tag bias is reduced to 1-2 %:

13. K L absolute BR’s: K L  charged Charged decays selected by closing the kinematics at the vertex: P mis - E miss. Fit data with linear combination of 3 MC shapes. Large statistics, accuracy is dominated by systematics. Lesser of P miss  E miss in  or  hyp. (MeV) |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN

14. K L absolute BRs: K L  charged P miss  E miss (MeV) (πe hypothesis) P miss  E miss (MeV) (πμ hypothesis) P miss - E miss distribution very sensitive to radiation and momentum resolution Check data/MC agreement via independent PID: e/μ/π from TOF and shower shape Radiative corrections properly included in the Monte Carlo generators. Enriched sample of K L  πe events Enriched sample of K L  π  events |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN

15. K L absolute BR’s: K L   0  0  0 |Vus| and K S decays from KLOE, G. Lanfranchi – LNF/INFN L LγLγ LKLK e+ e- π+ π+ π - π -   solved for the two variables Lγ, L K  Use events with  3 photons “clustering” a vertex  99.2% selection efficiency  Residual background (1.3%, mainly π + π - π 0 events) is subtracted..  The photon vertex of K L  3  0 is reconstructed by TOF, using cluster time/position and K L momentum (from K S      ). (X γ,Y γ,Z γ,T γ )

16. K L absolute BR’s: final results BR(K L  e ) = 0.4049  0.0010 stat  0.0031 syst BR(K L  ) = 0.2726  0.0008 stat  0.0022 syst BR(K L  3   ) = 0.2018  0.0004 stat  0.0026 syst BR(K L       ) = 0.1276  0.0006 stat  0.0016 syst  Absolute BR's results (  KL = 51.54  ns, PRD 6 (1972), 1834)  S ystematics: |Vus| and K S decays from KLOE, G. Lanfranchi – LNF/INFN

17. K L dominant BR’s: unitarity and lifetime K L dominant BR’s: unitarity and lifetime The sum of the dominant branching fractions (plus K L rare decays from PDG) gives: |Vus| and K S decays from KLOE, G. Lanfranchi – LNF/INFN ε = 25% 340 cm The BR depend on the K L lifetime through the acceptance: Assuming  BR(K L  X) =1 we have an indirect measurement of the K L lifetime:  KL = (50.72  stat   syst  ns (K L ) (cm)  FV

18. K L dominant BR’s: results imposing unitarity BR(K L  e ) = 0.4007  0.0006  0.0014 BR(K L  ) = 0.2698  0.0006  0.0014 BR(K L  3   ) = 0.1997  0.0005  0.0019 BR(K L       ) = 0.1263  0.0005  0.0011 |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN

19. K L dominant BR’s: comparison K L  e (no PDG) 0.4045±0.0009 χ 2 = 5.1 K L  0.2702±0.0007 χ 2 = 0.3 K L  3  0 (no PDG) 0.1968±0.0012 χ 2 =1.9 K L  π + π -  0 0.1255±0.0006 χ 2 = 0.4 KLOE NA48 KTeV PDG04 KLOE KTeV PDG04 KLOE NA48* KTeV PDG04 KLOE KTeV PDG04 * Presented by L.Litov @ICHEP04 15

20. |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN L LγLγ LKLK e+ e- π+ π+ π - π -   solved for the two variables Lγ, L K  We use K L  π 0 π 0 π 0 events tagged by K S  π + π - events:  “tagging” and “tagged” events are fully decoupled.  trigger efficiency is 100%, almost flat in the fiducial volume  The K L vertex is reconstructed by TOF, using cluster time/position and K L momentum (from K S  π+π-). (X γ,Y γ,Z γ,T γ ) K L lifetime: direct measurement K L lifetime: direct measurement

21. K L lifetime: control sample ++ π-π- KSKS KLKL We use K L  π + π - π 0 events to measure :  EmC time scale calibration;  Vertex resolution;  Vertex reconstruction efficiency. |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN ++ -- γ γ e+ e-   (vertex,π + π - )  1 mm

22. K L lifetime: EmC time scale and vertex resolution Plot di time scale EmC Time Scale : Plot di risoluzione π + π - π 0 data: L K (+-) (cm) Vertex resolution:  2.5 cm set at 0.1% level |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN L(γγ) – L(π+π-) (cm) L(π + π - ) (cm)

23. K L lifetime: final result K L lifetime: final result τ L (KLOE) = (50.87 ±0.16 (stat) ± 0.26 (syst)) ns |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN  14 x 10 6 events Fit region = 6 -26 ns ( 40% τ L ) t*= L K /βγc (ns) + data Yes, it’s going down!! Events/0.3 ns

24. K L lifetime: comparison K L lifetime: comparison |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN KLOE direct KLOE indirect Vosburgh et al, PRD 6 (1972), 1834 average: τ L = (50.98 ± 0.21) ns PDG 2004 = (51.8 ± 0.4) ns

25. | V us | from K e3 decays and τ L : Most precise test of CKM unitarity comes from 1 st row: |V ud | 2 + |V us | 2 + |V ub | 2 ~ |V ud | 2 + |V us | 2  1 –  where it can be tested at 10 -3 level: 2|V ud |  V ud = 0.0015 from super-allowed 0 +  0 + Fermi transitions, n  -decays 2|V us |  V us = 0.0011 from semileptonic kaon decays (PDG 2002 fit) |V us | from neutral K l3 partial decay widths: V us f + (0) = G 2  M 5 K S ew I l ( +, 0 + ´,...) 128  3  Kl3 K0K0 1 +  em,l 1 ½ f + K  (0) form factor at zero momentum transfer, pure theory calculation (  PT, lattice) I( ) phase space integral, S ew short distance corrections (1.0232) +,  0 momentum dependence of vector and scalar form factors (f + (t), f 0 (t),t =q 2 )  em electromagnetic correction (amplitude and phase space): 0.5%K e3 - 0.8%K 

26. |V us | from K e3 decays and τ L : Prescription from hep-ph/0411097 (F. Mescia @ICHEP04): 1) Quadratic parametrization of the form factor momentum dependence:       from KTeV + ISTRA 2) K L lifetime from KLOE (average of the two measurements) :  KL = (50.81  ns 3) BRs from KLOE set the sum = 1: 4) Form factor f + K  (0) from Leutwyller-Roos: 0.961(8) confirmed by D. Becirevic et al (Lattice+CHPT) 0.960(9) M. Okamoto et al. (MILC) (Lattice+CHPT) 0.962(11) BR(K L  e ) = 0.4007  0.0006  0.0014 BR(K L  ) = 0.2698  0.0006  0.0014

27. | V us |  f + Kπ (0) KLOE results: |V us |  f + K  (0) (K Se3 ) = 0.2169  0.0017 |V us |  f + K  (0) (K Le3 ) = 0.2164  0.0007 |V us |  f + K  (0)(K L  3 ) = 0.2174  0.0009 From Unitarity : (1-|V ud | 2 ) 1/2 f + K  (0) = 0.2177  0.0028 |V us | from K l3 decays and τ L : PRD 6 (1972), 1834 KLOE

28. K S physics: first observation of K S  π  decay: K S physics: first observation of K S  π  decay: |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN  2001 Data signal +  +  Selection à la K S  πe : K crash tag + 2 tracks from IP with M ππ < 490 MeV (reject K S  ππ(γ)) TOF identification: compare πμ expected flight times, reject ππ,πμ bkg Kinematic closure: use K L to obtain K S momentum P K and test for presence of neutrino: E miss =  M K 2 + P K 2 – E  – E  P miss = |P K – P  – P  |

29. The KLOE K S “beam”: The KLOE K S “beam”: |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN K L “ crash ” βγ  0.22, TOF  30 ns K S  πe K S  πe K S tagged by K L interaction in EmC:  efficiency  30 %  K S angular resolution:  1  (0.3  in  )  K S momentum resolution: 1 MeV  3 · 10 5 tags/pb-1

30. |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN Direct search for K S  π 0 π 0 π 0 decay: K S  3  0 is pure CP violating decay, never observed: SM prediction:  S000 =  L000 |  +  000 | 2, giving BR(K S  3  0 ) = 1.9 10  9 : Best result: BR(K S  3π 0 ) < 7.4 10 -7 (90% CL) (NA48, hep-ex/0408053) Data MC K S  3  0 0 0 20 40 80 60 40102030       Analysis Outline: Signal selection: K L crash tag + 6 prompt photons, no tracks from IP Background: K S  π 0 π 0 + 2  split/accidental clusters Background rejection: compare 3  vs 2  hypotheses:     pairing of 6  clusters with better  0 mass estimates     best  pairing of 4  ’s out of 6:  0 masses, E(K S ), P(K S ), c.m.  0   0 angle Signal BOX

31. |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN K S  π 0 π 0 π 0 upper limit: final result Using the PDG values and our limit we have: KLOE NA48 90 % CL N bkg = 3.13 ± 0.82 stat ± 0.37 sys N obs = 2  (events with K L tag) = 24.3% BR(K S  π 0 π 0 π 0 ) < 1.2  10 -7 @ 90% CL A(K S   0  0  0 ) A(K L   0  0  0 ) |  000 | = < 1.8 10 -2, 90% CL NA48 (hep-ex/0408053) A factor 5 better than the previous limit!

32. |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN K S  π 0 π 0 π 0 decay and Bell-Steinberger relation: K S  π 0 π 0 π 0 decay and Bell-Steinberger relation:  Uncertainty on K S  3  0 amplitude enters in the Bell-Steinberger relation: K S,L = K 1,2 +(  ± δ) K 2,1 (1 + i tan  SW )(Re  iIm  f A*(K S  f) A(K L  f) CPTCP Exp. input (  and phases) 1ΓS1ΓS A limit on BR(K S  π 0 π 0 π 0 )  10 -7  error on Im δ  2 · 10 -5 (dominated now by η +- ) 29

33. |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN Summary: NA48 What we have now:  Measurements of all the dominant K L BR’s at 0.5% accuracy;  Two measurements of the K L lifetime at 0.6% accuracy;  Best upper limit on K S  π 0 π 0 π 0 decay;  First Observation of K S  π  decay Coming soon:  Final result on K S semileptonic BR;  Analysis of K L semileptonic form factor slopes;  Analysis of K ±, BR’s and lifetime. 30

34. BACKUP SLIDES

35. |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN The present data taking: NA48 Daily Lum (nb -1 ) Int Lum (pb -1 ) Peak Lum (cm -2 s -1 ) L  770 pb -1  goal is 2 fb -1 within december 2005 a factor 4 more than the present statistics Luminosity collected since may 2004:  Limit on K S -> 3π 0 at the 10 -8 level  K S semileptonic asymmetry to 4 × 10 -3  First interferometry studies of K S K L system Next in line:

37. The KLOE detector: Be beam pipe (0.5 mm thick) Instrumented permanent magnet quadrupoles (32 PMT’s) Drift chamber (4 m   3.3 m) 90% He + 10% IsoB, CF frame 12582 stereo sense wires Electromagnetic calorimeter Lead/scintillating fibers 4880 PMT’s Superconducting coil (5 m bore) B = 0.52 T (  B dl = 2 T·m) e + e -  |Vus| and K S decays from KLOE, G. Lanfranchi – LNF/INFN

38. K L lifetime: vertex reconstruction efficiency |Vus| and K S decays from KLOE G. Lanfranchi – LNF/INFN vertex efficiency for 3π 0 MC (%) L K (true) (cm) vertex efficiency for π + π - π 0 (data & MC) (%) MC DATA L K ( π+π-) (cm)

39. K L absolute BR’s: K L   0  0  0 KLOE photons are very low energy photons! Photon efficiency measured on data using K L  π + π - π 0 events Plot dell’energia totale per 6 fotoni O della massa totale. Photon energy spectrum + DATA - Monte Carlo 7 MeV <E γ < 250 MeV |Vus| and K S decays from KLOE, G. Lanfranchi – LNF/INFN

40. 000000 +-0+-0  e  Effect of the tag bias: ε (tagging) L K (cm) ε (tagging) Before cuts:After cuts:

41. T(measured) = T(stop)-T(start) T(stop) = T +  1 (cables+FEE) T(start) = Ttrg +  2 (cables+FEE) +  rephasing T(measured) = T + (  2 -  1 ) - (Ttrg+  rephasing ) = T + T0 The t 0 of the event:

42. T(measured) = T(stop)-T(start) T(stop) = T +  1 (cables+FEE) T(start) = Ttrg +  2 (cables+FEE) +  rephasing T(measured) = T + (  2 -  1 ) - (Ttrg+  rephasing ) = T + T0 In the simplest case of a photon we have: T = L/c  T measured -L/c = T0 For each event we have to find one particle that can fix the T0 for that event ! The t 0 of the event:

43.  S  π 0 π 0 π 0 search: background calibration A good agreement is observed in each scatter plot region  DATA -- MC ALL  2 2  >40  2 2  <14  2 2  <40 ALL 2323 2323 2323 2323

44.  S  π 0 π 0 π 0 search: background calibration A good agreement is observed in each scatter plot region  DATA -- MC ALL  2 3  <4  2 3  >4 ALL 2222 2222 2222