Lattice QCD Christine Davies University of Glasgow, HPQCD collaboration. Lepton-photon 2007 Daegu, Korea

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1 Lattice QCD 2007 Christine Davies University of Glasgow, HPQCD collaboration Lepton-photon 2007 Daegu, Korea

2 QCD is key part of SM but quark confinement tricky a Lattice QCD enables calcn of QCD effects from first principles. Done by numerical evaln of Path Integral in a 4-d vol. of space-time Z defined as a lattice da µ e L QCD O(A µ ) RECIPE Generate sets of gluon fields that contribute most to the PI Calculate averaged hadron correlators on these and fit to obtain masses and simple matrix elements Fix m q and determine a to get physical results

3 Where can lattice QCD have most immediate impact? Precision calculations of electroweak decay rates for goldplated hadrons CKM physics V ub B W J = V0, Vi, A0, Ai expt=(ckm)x(lattice calc.) V ud V V cd V ub cb π V td V V cd V tb cb V ud V us V ub π lν K lν B πlν K πlν V cd V cs V cb D lν D s lν B Dlν D πlνd Klν V td V ts V tb B d B d B s B s Unitarity triangle - test this! 1 I will concentrate on results relevant to this programme...

4 Why is lattice QCD so hard? Handling light u,d, s quarks is a big headache L q,qcd = ψ(γ D + m)ψ ψmψ Quarks must be integrated out by inverting Dirac matrix M valence quarks, calculate M 1 sea quarks, include in importance sampling gluons det(m) Cost inc. as m q 0 a 0 and also as L

5 The story so far... Early days (before 2000) - u, d, s sea quarks omitted or inc. with u/d masses 10-20x too big. (Quenched approx.) Systematic errors % and theory not self-consistent Now (since 2000) - possible to inc. u/d sea quarks with masses only 3-5x too large and extrapolate to real world. Improved staggered quark formalism first to do this since numerically very fast improved staggered calculations have matured. Results using other formalisms now appearing Future - looks good. Lots of analysis to be done... see

6 Status of configs 2007 Choice of light quark formalism - issues are speed, disc. errors, chiral symmetry + technical issues. Can also mix e.g. dw valence on stagg. sea imp.stagg. (asqtad) domain wall clover twisted mass min / GeV2 m! 2 speed chiral symm. collab. fast slow fast fast OK good bad OK MILC/ HPQCD/ FNAL RBC/ UKQCD PACS-CS QCDSF CERN-TOV ETMC m 2 π,min/gev 2 mu/d MILC imp. staggered, 2+1 RBC/UKQCD DW, 2+1 PACS-CS, clover, 2+1 ETMC twisted mass, 2 CERN-TOV, clover, 2 QCDSF, clover, a 2 / fm 2 a 2 / f m 2 Extrapolate to physical point. Also need large L and good statistics. See Boyle, Urbach, Kuramashi, LAT07 no. of sea quarks

7 2007 results f & f K m $ 3m % - m N m Ds m D m D * - m s Ds m " - m #c "(1P-1S) 2m Bs,av -m! m Bc!(3S-1S)!(2P-1S)!(1P-1S)!(1D-1S) latt expt n f =2+1 Essential to check how lattice QCD is doing vs well-known gold-plated experimental quantities Update of 2003 results using imp. stagg sea quarks. Fix QCD params from ϒ(2S 1S),m π,m K,m ηc,m ϒ QA is dead! New (HPQCD): Highly improved staggered quarks (HISQ) - improves disc. errors further over asqtad. Allows use for c quarks.

8 ! Can compare results from different formalisms away from physical point if accurate enough. π leptonic decay quark formalisms with good chiral symmetry 0.3 f π 0.25 GeV HPQCD HISQ on asqtad sea 2+1 MILC asqtad 2+1 NPLQCD DW on asqtad sea 2+1 RBC/UKQCD DW 2+1 ETMC twsted mass 2 expt m! / GeV 2 McNeile, LAT07 no. of sea quarks m 2 π/gev 2 m u/d πb J=Aµ Br(π µν) Vud 2 fπ 2 Need multiple a and mu/d for chiral and contnm extrapoln for final result. Fitted lines from HISQ HPQCD [hep-lat] Need large volumes for accuracy - test vol. effects vs. chiral pert. th. (MILC, ETMC, QCDSF, RBC) W

9 Kaon physics (Kl2) and Vus Γ(K µν) Γ(π µν) V 2 us f 2 K V 2 ud f 2 π RBC/UKQCD dw 2007 results for calcs with u, d, s sea quarks Vus competitive w. PDG HPQCD very coarse coarse fine extrapoln PACS-CS clover 1.2 HPQCD HISQ on asqtad sea MILC asqtad f K /f! Kl V us PDG 2006 Error 0.6% m u,d / m s see Jüttner, LAT07 HPQCD: [hep-lat], error budget

10 K semileptonic decay (Kl3) and Vus V us W J = V0, Vi, A0, Ai BK π V us f Kπ + (0) = (46) = f+(0) RBC/UKQCD, dw, 2+1, 2007 V us 0.23 FlaviaNet KAON DECAY WG V ud ( ) fit fit with unitarity unitarity V us /V ud (K µ2 ) V us (K l3 ) V ud Extrapoln gives f + (0) = (51) V us = (15) Lattice error 0.5%, need to check disc. errors + other calcs. See Jüttner, LAT07

11 K 0 mixing and CKM constraint K 0 K 0 B0 B0 = V isv id H W Calculate box in lattice QCD - needs good chiral symmetry Mixing through box gives indirect CP violn - measure ε = K L ππ K s ππ fkb 2 K from ε and B K get constraint on UT 2007 result - RBC/UKQCD dw 2+1 B MS K (2GeV ) = 0.557(12)(29)(+0 28) hep-ph/ on 16 3, one a Boyle LAT07, bigger volume, 24 3, result is lower See also Van der Water, LAT07, dw on asqtad sea, 2 a values, big volumes, result shortly...

12 Charm physics, new method, 2007 HPQCD 2 Fix mc Mass (GeV) 1.9 test D masses vs expt. Exp t m u/d /m s M Ds M D Key issue is discretisation errors, because mca ~ 1 HISQ - much improved control of disc. errors can use for charmonium and D - more tests of lattice QCD possible E.Follana et al, [hep-lat]

13 2007 New Results for D, Ds decay constants, for comparison to experiment D x lν Lattice inc u,d,s sea vs expt 0.3 GeV Exp t HPQCD, HISQ Belle EPS2007 BaBar hep-ex/ f Ds CLEO [hep-ex] 0.25 GeV 0.2 CLEO Next two years: more lattice results and improved semileptonic form factors also... f D f Ds FNAL/MILC asqtad LAT07 prelim. HPQCD HISQ on asqtad sea [hep-lat] 2 v. different lattice calcs expt uses Vcs = Vud error will improve to few % in 2 yrs not all em corrns calculated..

14 b physics - B 0 mixing and CKM constraint B0 B0 = V td V tb Parameterise with fbb 2 B where f B is decay constant. H W ΔM x = G2 F M2 W 6π 2 V txv tb 2 η B 2S 0 (x t )M Bx f 2 B x ˆB Bx Take exptl ratio from oscillation rates for Bs and Bd V td ΔM d M = ξ Bs V ts ΔM s M Bd, ξ = f B s BBs f B BB calculate in lattice QCD, renormln cancels

15 2007 New results for MBs ξ = f B s BBs f B BB inc. u, d, s sea quarks ξ 1.3 HPQCD (no 1/M correct.) MILC 1.25 M B HPQCD FNAL/MILC PRELIMINARY HPQCD hep-lat/ f Bs ˆB Bs = 0.281(21)GeV one value of a so far, main error is renormln of lattice 4- q operator m d / m s Can compare to easier lattice calc. of f Bs / f B HPQCD, hep-lat/ (3) FNAL/MILC, Simone, LAT (4) Gamiz, LAT07

16 B excl. semileptonic decay and CKM constraint F(1) h A1 (1) FNAL/MILC V ub,v cb W J = V0, Vi, A0, Ai B π,d,d, a 2 a 2 / f m 2 B D lν Laiho, LAT07 rate at zero recoil V cb F(1) 2 FNAL/MILC with u, d, s sea quarks, 3 values of a F(1) = 0.930(12)(19) HFAG V cb = 38.7(0.7)(0.9) 10 3 stat syst expt latt Flynn+Nieves [hep-ph] combine lattice (HPQCD, B πlν FNAL/MILC) with LCSR, get work underway to extend lattice results V ub = 3.47(29) 10 3

17 Use lattice results with u, d, s sea quarks + experiment for constraints on unitarity triangle. Lattice inputs (2+1 sea quarks): B K f K / f π, f + (K πlν) F(B D lν) f + (B πlν) f Bs BBs f B BB " CKM 2007 LATTICE QCD #V # ub #V # cb f Bs f B B Bs B B B K ! % PDG06 Errors on lattice results should halve over next two years To others using lattice results: QA is dead! $

18 Conclusions Lattice calculations inc. sea quarks are in excellent shape. Calcs. with staggered quarks continue to improve and good results appearing now from other quark formalisms. Significant new results this year in s and c physics I have not mentioned hadron structure, harder meson and baryon spectrum calcs, phase structure at finite temp. etc etc. - see LAT07 website Future: In next two years, errors on CKM constraints should halve. More checks will be done against other gold-plated decays.

19 Thanks to: Claude Bernard, Peter Boyle, Elvira Gamiz, Andreas Jüttner, Jack Laiho, Peter Lepage, Craig McNeile, Matthew Moulson, Gerrit Schierholz, Junko Shigemitsu, Jim Simone, Doug Toussaint, Carsten Urbach, Ruth van der Water, Kit Wong and Conference organisers here in Korea