THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS

1. Vittorio Lubicz THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS OUTLINE Flavour physics and its motivations Lattice QCD and the UTA input parameters UTA: results and perspectives Orsay, April 14-16 2004

2. 1 FLAVOUR PHYSICS AND ITS MOTIVATIONS

3. FLAVOUR PHYSICS • Why 3 families? • Why the hierarchy of masses? • Is the CKM mechanism and its explanation of CP violation correct? STANDARD MODEL AND FLAVOUR PHYSICS SU(2)L x U(1)Y x SU(3) Electromagnetic Symmetry breaking: Higgs (?) Strong Weak Flavour Only weak interactions can change flavour [CKM]

4. PHENOMENOLOGICAL INDICATIONS: • Unification of couplings (MGUT ≈ 1015-1016 GeV) • Dark matter (ΩM ≈ 0.35) • Neutrino masses • Matter/Anti-matter asymmetry (not enough CP in the SM) 2 2 2 2 THE “NATURAL” CUT-OFF: δmH= mtΛ≈ (0.3 Λ) 2 Λ = O(1 TeV) NEW PHYSICS MUST BE VERY “SPECIAL” 3GF √2π THE STANDARD MODEL: A LOW ENERGY EFFECTIVE THEORY • CONCEPTUAL PROBLEMSThe most obvious: • Gravity: MPlanck = (ħc/GN)1/2≈ 1019 GeV

5. QUANTUM EFFECTS THE FLAVOUR PROBLEM: ΛK0-K0≈O(100 TeV) PRECISION ERA OF FLAVOUR PHYSICS K We need to control the theoretical input parameters at a comparable level of accuracy !! εK= (2.271 ± 0.017) x 10-30.7% Δmd= (0.503 ± 0.006) ps-11% sin(2β)= 0.734 ± 0.054 7% NEW PHYSICS EFFECTS IN FLAVOUR PHYSICS K

6. Vub l W  b u Only 1 parameter for CP VIOLATION THE CKM MATRIX 3 FAMILIES: 3 angles and 1 phase

7. THE UNITARITY TRIANGLE

8. Hadronic Matrix Elements from LATTICE QCD (bu)/(bc) 2+2 , λ1 ,f+ ,… Λ ρ η K [(1–)+ P] BK η ρ md (1– )2 +2 fBd BBd ρ η 2 md/ ms (1– )2 +2 ξ ρ η A(J/ψ KS) sin2β(ρ, η) THE UNITARITY TRIANGLE ANALYSIS 5 CONSTRAINTS 2 PARAMETERS

9. 2 LATTICE QCD AND THE UTA INPUT PARAMETERS

10. Vub l Γ(B→ πlv) = ∫dq2λ(q2)3/2 |f+( q2)|2 GF2|Vub|2 192 π3 v b u B π NON-PERTURBATIVE PHYSICS d VubFROMB-MESONSEMILEPTONIC DECAYS EXPERIMENTS: CLEO, BaBar, Belle, … 15-20%

11. Vus = λ l Vcb = Aλ2 l v v s u b c D* K B π d d FB→D*(1) = ηA [1 - O(1/mb,1/mc)2] f+(0) = 1 - O(ms-mu)2 Luke theorem Ademollo-Gatto theorem + 0.024 - 0.017 APE - SPQCDR + 0.017 - 0.030 FNAL FB→D*(1)= 0.913 f+(0)= 0.960 ± 0.005 ± 0.007 PRECISION FLAVOUR PHYSICS ON THE LATTICE 1%

12. K K NON-PERTURBATIVE PHYSICS K K – K Mixing: εK and BK CP Violation

13. L.Giusti, EPS-HEP 2003 Quench. Appr. BK= 0.87 ± 0.06 ± 0.13 [ D. Becirevic, Plenary talk @ LATT03] LATTICE PREDICTION(!) BK = 0.90 ± 0.20 [Gavela et al., 1987] ^ Lattice Results for BK • High level of accuracy • Discretization effects not negligible • Estimate of quenching error from ChPT ≤ 15% (Sharpe) ^

14. BBd/s – BBd/s Mixing: fBd/s and BBd/s fDs /fDs = 1.08 ± 0.05 (CP-PACS,MILC) Nf=2 Nf=0 fDs= 265 ± 14 ± 13MeVLQCD Average [D.Becirevic] fDs= 285 ± 19 ± 40MeVEXP. PDG 2002 K – K Mixing: εK and BK THE Ds-MESON DECAY CONSTANT A long history of lattice calculations… QUENCHED New results expected from CLEO-c

15. J.Heitger, EPS-HEP 2003 JLQCD, 2003 Use , Becirevic et al. From fDsto fBd mQ « 1/a mπ» 1/L ● Extrapolations from mQ ~ mc to mb ● Extrapolations from mq to mu,d using ChPT as a guidance: ● Effective theories: HQET, NRQCD, “FNAL”, … ● Combine the two approaches Orsay ● Finite size approach ,APE-Tov

16. BBd/s – BBd/s Mixing: fBd/s and BBd/s fBs: the “world average” evolution QUENCHED fBs /fBs = 1.12 ± 0.05 (CP-PACS,MILC) Nf=2 Nf=0 In other quantities (fBs/ fBd, BBd, BBs/ BBd) quenching effects are smaller fBs√BBs= 276 ± 38 MeV, ξ= 1.24 ± 0.04 ± 0.06 LATTICE AVERAGES [ 1st Workshop on the CKM Unitarity Triangle, 2002 ] fBs√BBs= 254 ± 24 MeV, ξ= 1.21 ± 0.05 ± 0.01 [ D. Becirevic, 2nd Workshop on the CKM Unitarity Triangle, 2003]

17. Lattice QCD vs UT FITS

18. 3 THE UNITARITY TRIANGLE ANALISYS: RESULTS AND PERSPECTIVES

19. The Collaboration M.Bona, M.Ciuchini, E.Franco, V.L., G.Martinelli, F.Parodi, M.Pierini, P.Roudeau, C.Schiavi, L.Silvestrini, A.Stocchi Roma, Genova, Torino, Orsay THE CKM The WEB site www.utfit.org

20. ρ= 0.178 ± 0.046 η= 0.341 ± 0.028 FIT RESULTS Sin2α= – 0.19 ± 0.25 Sin2β= 0.710 ± 0.037 γ= (61.5± 7.0)o

21. INDIRECT EVIDENCE OF CP VIOLATION 3 FAMILIES - Only 1 phase - Angles from Sides Sin2βUTA= 0.685 ± 0.052 Sin2βJ/ψKs= 0.734 ± 0.054 Prediction (Ciuchini et al., 2000): Sin2βUTA= 0.698 ± 0.066

22. Δms NOT USED WITH ALL CONSTRAINTS Δms= (20.6 ± 3.5) ps-1 Δms= (18.3 ± 1.7) ps-1 Prediction for Δms A measurement is expected from Tevatron !

23. Experiments Other colors: Theory Sin2β AND Δms: HISTORY OF PREDICTIONS

24. THE “COMPATIBILITY” PLOTS “To whichextent improved determinations of the experimental constraints willbeable to detect New Physics?” Compatibility between direct and indirect determinations as a function of the measured value and its experimental uncertainty

25. 14 BK = 0.86 ± 0.06 ± 0.14 fBs√BBs = 276 ± 38 MeV 21 sin2β = 0.734 ± 0.054 ξ = 1.24 ± 0.04 ± 0.06 Δρ = 26% →15%Δη = 7.1% →4.6% IMPACT OF IMPROVED DETERMINATIONS TODAY NEXT YEARS

26. Δms= (20.6 ±3.5) ps-1 Δms= (20.6 ±1.8) ps-1 TODAY NEXT YEARS

27. An interesting case: New Physics in Bd–Bd mixing The New Physics mixing amplitudes can be parameterized in a simple general form: Δmd = Cd(Δmd)SM A(J/ψ KS)~ sin2(β+φd) Md = Cd e2i (Md)SM φd SEARCH FOR NEW PHYSICS “Given the present theoretical and experimental constraints, to which extent the UTA can still be affected by New Physics contributions?”

28. φd can be only determinedup to a trivial twofold ambiguity: β+φd → π–β–φd TWO SOLUTIONS: Standard Model solution: Cd = 1 φd = 0

29. Δms,η[KL→πνν], γ[B→DK], |Vtd| [B→ργ], … HOW CAN WE DISCRIMINATE BETWEEN THE TWO SOLUTIONS?

30. YEARS OF (ρ-η) DETERMINATIONS • (The “commercial” plot) Coming back to the Standard Model:

31. CONCLUSIONS • LATTICE QCD CALCULATIONS HAD A CRUCIAL IMPACT ON TESTING AND CONSTRAINING THE FLAVOUR SECTOR OF THE STANDARD MODEL • IN THE PRECISION ERA OF FLAVOUR PHYSICS, LATTICE SYSTEMATIC UNCERTAINTIES MUST (AND CAN) BE FURTHER REDUCED • IMPORTANT, BUT MORE DIFFICULT PROBLEMS (NON LEPTONIC DECAYS, RARE DECAYS, ...) ARE ALSO BEING ADDRESSED FOR ALL THAT, WE NEED T-FLOPS COMPUTERS!!