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Front. V us from K l 3 decays: Theory. Federico Mescia (S.P.QcdR.) INFN-Frascati and University of Rome, “Roma Tre”. OUTLINE Motivations: V us and the CKM Unitarity The Lattice calculation of f + (0) [SU(3) breaking] Physical Results and Discussion

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  1. Front Vusfrom Kl3 decays: Theory Federico Mescia (S.P.QcdR.) INFN-Frascati and University of Rome, “Roma Tre” OUTLINE Motivations: Vus and the CKM Unitarity The Lattice calculation of f+(0)[SU(3) breaking] Physical Results and Discussion f+(0) = 0.960(9)  |Vus|2 +|Vud|2 +|Vub|2 -1=0.000(1) ICHEP04, August 16-22, Beijing

  2. Unitarity • PDG 2002 quotes a 2.2 deviation from unitarity • |Vud|= 0.9734 ± 0.0008. |Vus|= 0.2196 ± 0.0026.|Vub|= 0.0036 ± 0.0010. • Comparable uncertainties induced by|Vud|2and|Vus|2 • |Vub|2 can be neglected The most accurate test of CKM unitarity- Vus |Vus| possibly responsible!! Relies on old experimental and theoretical results of Kl3

  3. Rate (Andre 04’, Cirigliano 04’-02’) (Sirlin 82’) Accurately measured (ISTRA+,KTeV) For the CKM test, gives the largest uncertainty!! Vusfrom Kl3 decays . Accurately known

  4. F(0) chiral th cpT f+(0) = 1 + f2 + f4 + O(p8) DOMINANT UNCERTAINTY !! m-Independent O(ms-mu)2 – AG Vector Current Conservation ms=mu O((ms-mu)2/ms)[-0.023], Independent of Li, m (Ademollo-Gatto) O(p6)-cpT O(p6)-cpT Δloops Δloops The PDG-quoted estimate Leutwyler-Roos (1984), (QUARK MODEL) f4 = −0.016 ± 0.008 The most recent estimates Bijnens et al (2003),( + LR) f4 = −0.001±0.010 Jamin et al (2004),( + D. Analysis) f4 = −0.003±0.010 f+(0) and The Ademollo-Gatto Theorem Ambiguity: m= ???Δloops(1GeV) = 0.004,Δloops(Mρ) = 0.015,Δloops(0.5GeV) = 0.035 A lattice estimate of f4 is clearly needed! !!No Scale Ambiguity!!

  5. F4-strategy f4-Lattice QCD Challenge: Our Strategy 1. Evaluation of f0[q2 = (MK - Mp)2]with very high precision (<1%). Fermilab Double Ratio approach 2. Extrapolation of f0(q2max) to f0(0)=f+(0) estimating the slopeλ0 Suitable Double Ratios introduced for f0(q2)/ f+(q2) 3. We consider Δf ≡ f+(0)-1-f2Q (subtraction of the unphysical chiral logs) and extrapolate(ms/2 £mq£ ms)to the physical meson masses: Finally, Δf will be our estimate of f4.

  6. F0(q2max)-FNAL Stat. errors well below 1% 1) f0(q2max)- High precision measure(FNAL) • For MKMp , R1 + O(M2K-M2p)2 • Stat. and Syst. errors scale as (M2K-M2p)2, like the physical SU(3) breaking effects. • Independent of Zv and bv

  7. Q2 dependence Systematic uncertainty for the determination of f+(0) 2) Extrapolation off0(qMAX) to f+(0)

  8. F(0)-talavera 2) λ0 and λ+ slopes compairison with exp. Our Polar fit:λ+=0.025 ± 0.002λ0=0.012 ± 0.002 KTeV Polar fit:λ+=0.0250 ±0.0004λ0=0.0141±0.0010 Our values fortheslopes are consistent with the high precision KTeV measurement (June 2004-hep-ex/0406003) And substantially more precise than PDG quoted number λ+ = 0.028 ± 0.002 ISTRA+: High precision measurement (hep-ex/0404030)!! Polar fit not available but curvature visible λ+(Lin)=0.0277(6), λ+(Quad)=0.0232(16) ÜKe3 λ+(Lin)=0.0277(16)ÜKm3 Þλ0(Lin)=0.0183(13)

  9. F2-sub • At the simulated masses • =quenched artefacts: • well defined but non-trivial chiral behaviour Df 3) Df and subtraction of the chiral logs • Scale independent and no leading quenched artefacts • Hopefully suited for a smoth chiral behaviour

  10. F2-Extr. 3) Chiral extrapolation Having subtracted the leading log. correction, several extrapolations are tried

  11. Results & Ext. The final result is: Δf = - 0.017 ± 0.005stat ± 0.007syst [Leutwyler and Roos (PDG2002): ΔfLR = - 0.016 ± 0.008 ] f+ (0) = 0.960 ± 0.005stat ± 0.007syst K0π- + quenching error at O(p6) ! -Δf The dominant contributions to the systematic error come from the uncertainties on the q2 and mass dependencies of the form factor D.Becirevic,G.Isidori,V.Lubicz,G.Martinelli, F.M., S.Simula,C.Tarantino,G.Villadoro, hep-ph/0403217

  12. CKM Unitarity f+ (0) = 0.960 ± 0.005stat ± 0.007syst K0π- |Vus|Kl3 =(0.2259±0.0021) d|Vus| ~ 1% (dominated by the f+(0) theoretical uncertainty) • CKM-Unitarity recovered: |Vus|2 +|Vud|2 +|Vub|2=0.9997(14) • |Vud|=0.9740(5) • (Updated average: hep-ph/0406324) Values shifted with the KTeV slopes

  13. The end CONCLUSIONS ♦We presented a quenched lattice study of the SU(3) breaking effects in K→π ♦The calculation is the first one obtained by using a non-perturbative method based only on QCD, albeit in the quenched approximation ♦Our final result, f+ (0) = 0.960 ± 0.005stat ± 0.007systis in goodagreement with the estimate made by Leutwyler and Roos (PDG) ♦ Methodology now exists to reach 1% accuracy ♦The most important step is to remove the quenched approximation ♦Further steps: using lower masses(considering finite volume effects)

  14. F(0)-talavera 2) f+(0), λ0, c0 and Chiral Theory at O(p6) • From NNLO ChPT (Post, Schilcher (2001), Bijnens, Talavera (2003)), • C12 (μ)andC34 (μ) from the slope and curvature of the scalar form factor: • For the time being, (Lat. and Exp.) l0 and c0 not accurate enough • Our values for theslopes agree well with the KTeV measurements Mind: f+(0), λ0andc0related to the same LECs

  15. The end Charming: Unquenched & 6.5% uncertainty Disappointing: not better, d|Vus| ~ 1.2% Unquenched ♦ Hyperon beta Decays|Vus| =(0.2250±0.0027) ♦ fK/fp-1=0.210(4)(13)|Vus| =(0.2219±0.0026) Staggered-Fermions (MILC hep-lat/0407028) (Marciano hep-ph/0406324) Comments on other routes to Vus |Vus|Uni =(0.2265±0.0020) |Vus|Kl3 =(0.2259±0.0021) SU(3) breaking effects neglected, so far (Cabibbo-Swallow-Winston hep-ph/0307214) Lattice:Guadagnoli,Martinelli,Papinutto,Simula(preliminary)

  16. The end ♦ Hadronic t Decays|Vus| =(0.2208±0.0034) OPE (E.Gamiz hep-ph/0408244) Comments on other routes to Vus |Vus|Uni =(0.2265±0.0020) |Vus|Kl3 =(0.2259±0.0021) • Strange mass as inputms(2 GeV) =(95 ± 20) MeV(LATTICE+QCDSR) • Quark-hadron duality (analyze more moments) • Improve measure of spectral moments (BABAR, BELLE)

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