LATTICE QCD AND FLAVOR PHYSICS Vittorio Lubicz OUTLINE OUTLINE 1. - PowerPoint PPT Presentation

LATTICE QCD AND FLAVOR PHYSICS Vittorio Lubicz OUTLINE OUTLINE 1. Motivations for flavor physics 1. Motivations for flavor physics 2. Lattice QCD and quark masses 2. Lattice QCD and quark masses 3. CKM matrix 3. CKM matrix a) The Cabibbo angle and the first row unitarity test a) The Cabibbo angle and the first row unitarity test b) The Unitarity Triangle Analysis and CP violation b) The Unitarity Triangle Analysis and CP violation INAUGURAL CONFERENCE September 19 - 21, 2005

1 MOTIVATIONS FOR FLAVOR PHYSICS 2

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

Flavor physics is an open window on New Physics: FCNC, CP asymmetries,… ˜ ˜ ˜ E.g. g s L d R K K K x x K K 0 -K 0 mixing: ˜ ˜ s L d R ˜ g New Physics can be conveniently described in terms of a low energy effective theory: E.g.: c c ∑ ∑ L L = + + (5) (6 ) i O i O + … Λ K0-K0 ~ 100 TeV eff SM i i Λ Λ 2 i i NP N P Λ NP >> Λ EWSB ~ O(1 TeV) The flavor problem: New Physics must be very special !! 4

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

2 LATTICE QCD AND QUARK MASSES 6

♦ QUARK MASSES CANNOT 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 THEORETICAL AND AN EXPERIMENTAL INPUT. E.G.: [M HAD ( Λ QCD ,m q )] TH. = [M HAD ] EXP. LATTICE QCD 7

LATTICE DETERMINATION OF QUARK MASSES ^ m q (µ) = m q (a) Z m (µa) ADJUSTED UNTIL PERTURBATION THEORY OR LATT = M H NON-PERTURBATIVE METHODS M H EXP Extrapolation to m = m s Extrapolation to m = m u,d 8

SYSTEMATIC ERRORS m q ( µ ) = m q (a) Z m ( µ a) ADJUSTED UNTIL PERTURBATION LATT = M H M H EXP THEORY O(a) O( α 2 ) NON-PERTURBATIVE IMPROVED ACTIONS: S LATT = S QCD + a S 1 + a 2 S 2 + … RENORMALIZATION TWO IMPORTANT THEORETICAL TOOLS 9

NON-PERTURBATIVE RENORMALIZATION NON-PERTURBATIVE RENORMALIZATION THE RI-MOM METHOD THE RI-MOM METHOD O = + + ... p p p p p p Γ O (p 2 ) The (non-perturbative) renormalization condition: Z O (aµ) Γ O (p 2 )| p 2 =µ 2 = Γ Tree-Level Several NPR techniques have been developed: Ward Identities, Schrodinger functional, X-space 10

THE STRANGE QUARK MASS UNQUENCHED The highest values obtained with NPR T.Izubuchi, plenary at Lattice 2005 V.Lubicz, plenary at Lattice 2000 m s (2 GeV ) = (105 ± 15 ± 20) MeV 2004 [PDG 2002 : m s = (120 ± 40) MeV ] 11

THE AVERAGE UP/DOWN QUARK MASS From S. Hashimoto ICHEP 2004 RATIOS OF LIGHT QUARK MASSES ARE PREDICTED ALSO BY CHIRAL PERTURBATION THEORY: m u = 0.553 ± 0.043 m d m s = 24.4 ± 1.5 (m u + m d )/2 2 m s /(m u +m d ) 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: |V ud | 2 + |V us | 2 + |V ub | 2 = 1 PDG 2004 quotes a 2 σ deviation from unitarity: |V ud | 2 + |V us | 2 + |V ub | 2 - 1 = - 0.0029 ± 0.0015 SFT and neutron β -decay |V ud | = 0.9740 ± 0.0005 |V us | = 0.2200 ± 0.0026 K →π l ν (BNL-E865 + old exps) b → u incl. and excl. ( |V ub | 2 ≈ 10 -5 ) |V ub | = 0.0037 ± 0.0005 BUT: the PDG average for |V us | is superseded by NEW experimental and theoretical results 14

Kl3: the NEW experimental results Kl3: the NEW experimental results V us f + ⋅ (0) - Summer 2004 BNL-E865 PRL 91, (2003) F.Mescia 261802 ICHEP ‘04 KTeV PRL 93, (2004) 181802 NA48 PLB 602, (2004) 41 KLOE hep-ex/0508027 15

K l 3 theory K l 3 theory l V us = λ v 2 5 G M s u Γ → π ν γ = ( K l ) ⋅ ( ) F K π 3 K 192 π − ⋅ | 0 π + δ | V | f (0) | 2 2 K 2 2 C I S (1 ) us + ew d K l l Ademollo- O(1%). But represents the f + (0) = 1 - O(m s -m u ) 2 Gatto: largest theoret. uncertainty ChPT f + (0) = 1 + f 2 + f 4 + O(p 8 ) “Standard” estimate: Leutwyler, Roos (1984) (QUARK MODEL) f 2 = − 0.023 f 4 = − 0.016 ± 0.008 Vector Current THE LARGEST Independent of L i Conservation UNCERTAINTY (Ademollo-Gatto) 16

f 4 : the ChPT calculation… 8 2 2 2 f 4 = ∆ loops ( µ ) − [C 12 ( µ ) + C 34 ( µ )] ( M K − M π ) Post and Schilcher, 4 F π Bijnens and Talavera C 12 ( µ ) and C 34 ( 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 ( µ = ???) LOC [Quark model ] Leutwyler and Roos, f 4 = -0.016 ± 0.008 LOC [Dispersive analysis] Jamin et al., f 4 = -0.018 ± 0.009 LOC [1/Nc+Low resonance] f 4 = -0.002 ± 0.008 Cirigliano et al., Lattice QCD: VERY CHALLENGING A PRECISION OF O(1%) MUST BE REACHED ON THE LATTICE !! 17

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 ] 2 1) Evaluation of f 0 (q MAX ) The basic ingredient is a double ratio of correlation functions: 1% 18

2 2) Extrapolation of f 0 (q MAX ) to f 0 (0) LQCD PREDICTION !! Comparison of polar fits: LQCD: λ + = ( 25 ± 2 ) 10 -3 λ 0 = ( 12 ± 2 ) 10 -3 KTeV: λ + = ( 24.11 ± 0.36 ) 10 -3 λ 0 = ( 13.62 ± 0.73 ) 10 -3 19

3) Extrapolation to the physical masses 3) Extrapolation to the physical masses Preliminary unquenched results have been also presented K 0 π - f + (0) = 0.960 ± 0.005 ± 0.007 C.Dawson, plenary at Lattice 2005 ( In agreement with LR !! ) 20

FIRST ROW UNITARITY FIRST ROW UNITARITY V us f + ⋅ (0) - Summer 2004 [V us ·f + (0)] EXP = = 0.2250 ± 0.0021 f + (0) = 0.960 ± 0.009 V us = 0.2250 ± 0.0021 |V ud | 2 + |V us | 2 + |V ub | 2 - 1 = - 0.0007 ± 0.0014 21

3 CKM MATRIX: b) THE UNITARITY TRIANGLE ANALYSIS AND CP VIOLATION 22

THE UNITARITY TRIANGLE ANALYSIS V ud V ub + V cd V cb + V td V tb = 0 * * * V CKM ≈ 1 - λ 2 λ A λ 3 ( ρ - i η ) - λ 1 - λ 2 /2 A λ 2 A λ 3 ( 1 - ρ - i η ) - A λ 2 1 CP violation 23

THE UNITARITY TRIANGLE ANALYSIS V ud V ub + V cd V cb + V td V tb = 0 * * * V CKM ≈ 1 - λ 2 λ A λ 3 ( ρ - i η ) - λ 1 - λ 2 /2 A λ 2 A λ 3 ( 1 - ρ - i η ) - A λ 2 1 CP violation 2 + (b → u)/(b → c) f + ,F(1),… ρ η 2 5 CONSTRAINTS Hadronic matrix elements from LATTICE QCD 24

THE UNITARITY TRIANGLE ANALYSIS V ud V ub + V cd V cb + V td V tb = 0 * * * V CKM ≈ 1 - λ 2 λ A λ 3 ( ρ - i η ) - λ 1 - λ 2 /2 A λ 2 A λ 3 ( 1 - ρ - i η ) - A λ 2 1 CP violation 2 + (b → u)/(b → c) f + ,F(1),… ρ η 2 5 CONSTRAINTS f B d B B d 2 ∆ m d ) 2 + ρ η (1– 2 Hadronic matrix ξ ∆ m d / ∆ m s ) 2 + (1– 2 ρ η elements from LATTICE QCD 25

THE UNITARITY TRIANGLE ANALYSIS V ud V ub + V cd V cb + V td V tb = 0 * * * V CKM ≈ 1 - λ 2 λ A λ 3 ( ρ - i η ) - λ 1 - λ 2 /2 A λ 2 A λ 3 ( 1 - ρ - i η ) - A λ 2 1 CP violation 2 + (b → u)/(b → c) f + ,F(1),… ρ η 2 5 CONSTRAINTS f B d B B d 2 ∆ m d ) 2 + ρ η (1– 2 Hadronic matrix ξ ∆ m d / ∆ m s ) 2 + (1– 2 ρ η elements from ε K [ ( 1– ) + P ] B K η ρ LATTICE QCD 26

THE UNITARITY TRIANGLE ANALYSIS V ud V ub + V cd V cb + V td V tb = 0 * * * V CKM ≈ 1 - λ 2 λ A λ 3 ( ρ - i η ) - λ 1 - λ 2 /2 A λ 2 A λ 3 ( 1 - ρ - i η ) - A λ 2 1 CP violation 2 + (b → u)/(b → c) f + ,F(1),… ρ η 2 5 CONSTRAINTS f B d B B d 2 ∆ m d ) 2 + ρ η (1– 2 Hadronic matrix ξ ∆ m d / ∆ m s ) 2 + (1– 2 ρ η elements from ε K [ ( 1– ) + P ] B K η ρ LATTICE QCD sin 2 β ( ρ , η ) A(J/ ψ K S ) 27

V ub and V cb from semileptonic decays 28

V ub and V cb from semileptonic decays l V ub v b u B π d G F 2 |V ub | 2 Γ (B → π lv) = ∫ dq 2 λ (q 2 ) 3/2 |f + ( q 2 ) | 2 192 π 3 QUENCHED UNQUENCHED 29

K–K mixing: ε K and B K 30

K–K mixing: ε K and B K From S. Hashimoto QUENCHED ICHEP 2004 K K ^ B K = 0.79 ± 0.04 ± 0.09 31

K–K mixing: ε K and B K From S. Hashimoto QUENCHED ICHEP 2004 K K ^ B K = 0.79 ± 0.04 ± 0.09 ^ LATTICE PREDICTION (!) B K = 0.90 ± 0.20 [Gavela et al., 1987] 32

B d and B s mixing: f B √ B B 33

B d and B s mixing: f B √ B B ICHEP 2004 From S. Hashimoto f Bs √ B Bs = 276 ± 38 MeV, ξ = 1.24 ± 0.04 ± 0.06 34

UT-FIT RESULTS UT-FIT RESULTS Collaboration [JHEP 0507 (2005) 028] ρ = 0.214 ± 0.047 η = 0.343 ± 0.028 α = (98.2 ± 7.7) o Sin2 β = 0.734 ± 0.024 γ = (57.9 ± 7.4) o 35

INDIRECT EVIDENCE OF CP A CRUCIAL TEST OF THE SM 3 FAMILIES: - Only 1 phase - Angles from the sides Sin2 β UT Sides = 0.793 ± 0.033 Sin2 β J / ψ K s = 0.687 ± 0.032 36