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LATTICE QCD AND FLAVOR PHYSICS

Vittorio Lubicz. LATTICE QCD AND FLAVOR PHYSICS. OUTLINE Motivations for flavor physics Quark masses (see talk by F.Knechtli) CKM matrix a) The Cabibbo angle and the first row unitarity test

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LATTICE QCD AND FLAVOR PHYSICS

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  1. Vittorio Lubicz LATTICE QCD AND FLAVOR PHYSICS OUTLINE Motivations for flavor physics Quark masses (see talk by F.Knechtli) CKM matrix a) The Cabibbo angle and the first row unitarity test b) The Unitarity Triangle Analysis and CP violation DESY THEORY WORKSHOP 2005September 27 - 30DESY, Hamburg, Germany

  2. 1 MOTIVATIONS FOR FLAVOR PHYSICS

  3. Flavor physics is (well)described but not explained in the Standard Model: Flavor A large number of free parameters in the flavor sector (10 parameters in the quark sector only, 6 mq + 4 CKM) • Why 3 families? • Why the spectrum of quarks and leptons covers 5 orders of magnitude? (mq v  GF-1/2…) • What give rise to the pattern of quark mixing and the magnitude of CP violation?

  4. E.g. K0-K0 mixing: Flavor physics is an open window on New Physics:FCNC, CP asymmetries,… x x ˜ ˜ ˜ ˜ g g sL sL ˜ ˜ dR dR K K K K Flavor physics is not the only open question in the Standard Model Conceptual problems: gravity, gauge hierarchy,… Phenomenological indications of New Physics: unifications of couplings, neutrino masses, dark matter, vacuum energy, baryogenesis,…

  5. δmH = mtΛ≈ (0.3 Λ) 2 2 2 2 x x ˜ ˜ ˜ ˜ g g sL sL ˜ ˜ dR dR K 3GF √2π 2 K ΛK0-K0≈O(100 TeV) New Physics can be conveniently described in terms of a low energy effective theory: The “natural” cut-off: Λ=O(1TeV) THE FLAVOR PROBLEM: ΛNPΛEWSB~ O(1TeV) New Physics must be very special !!

  6. THEORY EXPERIMENTS We need to control the theoretical input parameters at a comparable level of accuracy !! εK= 2.280 10-3 ± 0.6% Δmd= 0.502 ps-1 ± 1% sin(2β)= 0.687 ± 5% ……… DETERMINATION OF THE SM FLAVOR PARAMETERS THE PRECISION ERA OF FLAVOR PHYSICS …… Challenge for LATTICE QCD

  7. 2 LATTICE QCD AND QUARK MASSES

  8. QUARK MASSESCANNOT BE DIRECTLY MEASURED IN THE EXPERIMENTS, BECAUSE QUARKS ARE CONFINED INSIDE HADRONS • BEING FUNDAMENTAL PARAMETERS OF THE STANDARD MODEL, QUARK MASSES CANNOT BE DETERMINED BY THEORETICAL CONSIDERATIONS ONLY. QUARK MASSES CAN BE DETERMINED BY COMBINING TOGETHER A THEORETICALAND AN EXPERIMENTAL INPUT. E.G.: [MHAD(ΛQCD,mq)]TH. = [MHAD]EXP. LATTICE QCD

  9. LATTICEDETERMINATIONOFQUARK MASSES mq(μ) = mq(a) Zm(μa) ^ PERTURBATION THEORY OR NON-PERTURBATIVE METHODS ADJUSTED UNTIL MHLATT = MHEXP Extrapolation to m = ms Extrapolation to m = mu,d

  10. UNQUENCHED T.Izubuchi, plenary at Lattice 2005 V.Lubicz, plenary at Lattice 2000 ms (2 GeV )  (105  15  20) MeV [PDG 2002: ms= (120 40) MeV] 2004 THE STRANGE QUARK MASS The highest values obtained with NPR

  11. RATIOSOF LIGHT QUARK MASSES ARE PREDICTED ALSO BYCHIRAL PERTURBATION THEORY: 2 ms/(mu+md)  24.4  1.5  0.553  0.043 ms mu (mu+ md)/2 md THE AVERAGE UP/DOWN QUARK MASS From S. Hashimoto ICHEP 2004 Good agreement with the ChPT prediction

  12. 3 CKM MATRIX a) THE CABIBBO ANGLE AND THE “FIRST ROW” UNITARITY TEST

  13. The most stringent unitarity test: |Vud|2 + |Vus|2 + |Vub|2 = 1 PDG 2004 quotes a 2σ deviation from unitarity: |Vud|2 + |Vus|2 + |Vub|2- 1 = - 0.0029 ± 0.0015 |Vud| = 0.9740 ± 0.0005 SFT and neutron β-decay |Vus| = 0.2200 ± 0.0026 K→πlν(BNL-E865 + old exps) |Vub| = 0.0037 ± 0.0005 b→u incl. and excl. (|Vub|2≈ 10-5 ) BUT: the PDG average for |Vus|is superseded by NEW experimental and theoretical results

  14. Kl3: the NEW experimental results BNL-E865 PRL 91, (2003) 261802 F.Mescia ICHEP ‘04 KTeV PRL 93, (2004) 181802 NA48 PLB 602, (2004) 41 KLOE hep-ex/0508027

  15. Vus = λ l v s u K π d Vector Current Conservation f2 = − 0.023 Independent of Li (Ademollo-Gatto) THE LARGEST UNCERTAINTY Kl3 theory Ademollo-Gatto: f+(0) = 1 - O(ms-mu)2 O(1%). But represents the largest theoret. uncertainty ChPT “Standard” estimate: Leutwyler, Roos (1984) (QUARK MODEL) f4 = −0.016 ± 0.008 f+(0) = 1 + f2 + f4 + O(p8)

  16. f4 =Δloops(μ)− [C12 (μ) + C34 (μ)] (MK − Mπ) 2 2 2 8 (μ = ???) LOC Jamin et al., f4= -0.018 ± 0.009[Dispersive analysis] LOC Leutwyler and Roos,f4= -0.016 ± 0.008[Quark model] LOC Cirigliano et al.,f4= -0.002 ± 0.008[1/Nc+Low resonance] Fπ 4 f4: the ChPT calculation… Post and Schilcher, Bijnens and Talavera C12 (μ)andC34 (μ)can be determined from the slope and the curvature of the scalar form factor. But experimental data are not accurate enough … and model estimates Lattice QCD: VERY CHALLENGING A PRECISION OF O(1%) MUST BE REACHED ON THE LATTICE!!

  17. 1) Evaluation of f0(qMAX) 2 1% The first Lattice QCD calculation D.Becirevic, G.Isidori, V.L., G.Martinelli, F.Mescia, S.Simula, C.Tarantino, G.Villadoro. [NPB 705,339,2005] The basic ingredient is a double ratio of correlation functions:

  18. 2) Extrapolation off0(qMAX) to f0(0) 2 LQCD PREDICTION !! Comparison of polar fits: LQCD:λ+=(25±2)10-3λ0=(12±2)10-3 KTeV:λ+=(24.11±0.36)10-3λ0=(13.62±0.73)10-3

  19. f+ (0) = 0.960 ± 0.005 ± 0.007 K0π- C.Dawson, plenary at Lattice 2005 ( In agreement with LR !! ) 3) Extrapolation to the physical masses Preliminary unquenched results have been also presented

  20. FIRST ROW UNITARITY [Vus∙f+(0)]EXP = = 0.2250±0.0021 f+(0) =0.960±0.009 Vus =0.2250±0.0021 |Vud|2+|Vus|2+|Vub|2- 1 = -0.0007±0.0014

  21. 3 CKM MATRIX: b) THE UNITARITY TRIANGLE ANALYSIS AND CP VIOLATION

  22. VudVub + VcdVcb + VtdVtb = 0 * * * VCKM 1-2  A 3(-i) - 1- 2/2A 2 A3(1- -i) -A 2 1 CP violation ρ η (bu)/(bc) 2+2 f+,F(1),… 5 CONSTRAINTS η ρ K [(1–)+ P] BK ρ η md (1– )2 +2 fBd BBd Hadronic matrix elements from LATTICE QCD 2 md/ ms (1– )2 +2 ξ ρ η A(J/ψ KS) sin2β(ρ, η) THE UNITARITY TRIANGLE ANALYSIS

  23. Vuband Vcbfrom semileptonic decays Vub l v b u B π d Γ(B→ πlv) = ∫dq2λ(q2)3/2 |f+( q2)|2 GF2|Vub|2 192 π3 QUENCHED UNQUENCHED (preliminary)

  24. K–K mixing: εK and BK From S. Hashimoto ICHEP 2004 K K QUENCHED ^ BK= 0.79 ± 0.04 ± 0.09 LATTICE PREDICTION(!) BK = 0.90 ± 0.20 [Gavela et al., 1987] ^

  25. BdandBs mixing: fB√BB From S. Hashimoto ICHEP 2004 fBs√BBs= 276 ± 38 MeV, ξ= 1.24 ± 0.04 ± 0.06

  26. ρ= 0.214 ± 0.047 η= 0.343 ± 0.028 UT-FIT RESULTS Collaboration [JHEP 0507 (2005) 028] Sin2β= 0.734 ± 0.024 α= (98.2± 7.7)o γ= (57.9± 7.4)o

  27. INDIRECT EVIDENCE OF CP A CRUCIAL TEST OF THE SM 3 FAMILIES: - Only 1 phase - Angles from the sides Sin2βUTSides= 0.793 ± 0.033 Sin2βJ/ψKs= 0.687 ± 0.032 Prediction (Ciuchini et al., 2000): Sin2βUTA= 0.698 ± 0.066

  28. PREDICTION FORΔms Δms= (22.2 ± 3.1) ps-1 DIRECT MEASUREMENT:Δms> 14.5 ps-1@ 95% C.L.

  29. ^ BK Lattice QCD UT Fits 0.79 ± 0.04 ± 0.09 0.69 ± 0.10 fBs√BBs 276 ± 38 MeV 265 ± 13 MeV ξ 1.24 ± 0.04 ± 0.06 1.15 ± 0.11 LATTICE QCD vs UT FITS

  30. YEARS OF (ρ-η) DETERMINATIONS Such a progress would have not been possible without LATTICE QCD calculations !!

  31. Backup slides

  32. PROGRESS OF THE UT ANALYSIS No angles: |Vub/Vcb|, Δmd, Δms, εK Angles only: sin2β, cos2β,sin2α,γ All constraints

  33. Helicity distrib. Δu- Δd Unpolarized distrib. u-d LATTICE QCD CALCULATIONS OF PDFs From Detmold et al., hep-lat/0206001 Lattice data from QCDSF, MIT, MIT-SESAM, MIT-SCRI, KEK

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