Lattice QCD 2007 - University of Glasgow

Lattice QCD2007Christine DaviesUniversity of Glasgow,HPQCD collaborationLepton-photon 2007Daegu, Korea

QCD is key part of SM but quark confinement trickyaLattice QCD enables calcn of QCDeffects “from first principles”. Doneby numerical evaln of Path Integral ina 4-d vol. of space-timeZdefined as alatticedA µ e −L QCDO(A µ )RECIPE• Generate sets of gluon fields thatcontribute most to the PI• Calculate averaged “hadroncorrelators” on these and fit to obtainmasses and simple matrix elements• Fix m q and determine a to getphysical results

Why is lattice QCD so hard?Handling light u,d, s quarks is a big headacheL q,QCD = ψ(γ · D + m)ψ ≡ ψMψQuarks must be ‘integrated out’by inverting Dirac matrix Mvalence quarks, calculate M −1sea quarks, includein importance samplinggluonsdet(M)Cost inc. as m q → 0a → 0and also asL → ∞

The story so far ....Early days (before 2000) - u, d, s sea quarks omitted orinc. with u/d masses 10-20x too big. (Quenched approx.)Systematic errors 10-20 % and theory not self-consistentNow (since 2000) - possible to inc. u/d sea quarks withmasses only 3-5x too large and extrapolate to real world.Improved staggered quark formalism first to do this sincenumerically very fast.2007 - improved staggered calculations have matured.Results using other formalisms now appearingFuture - looks good. Lots of analysis to be done ....see http://www.physik.uni-regensburg.de/lat07/

2007 resultsf &f Km $3m % - m Nm Dsm Dm D* - ms Dsm " - m #c"(1P-1S)2m Bs,av-m !m Bc!(3S-1S)!(2P-1S)!(1P-1S)!(1D-1S)lattexpt0.9 1 1.1n f =2+1Essential to check how latticeQCD is doing vs well-knowngold-plated experimentalquantitiesUpdate of 2003 results usingimp. stagg sea quarks.Fix QCD params fromϒ(2S − 1S),m π ,m K ,m ηc ,m ϒQA is dead!New (HPQCD): Highlyimproved staggered quarks(HISQ) - improves disc. errorsfurther over asqtad. Allowsuse for c quarks.

Kaon physics (Kl2) and VusΓ(K → µν)Γ(π → µν) → V 2us f 2 KV 2ud f 2 πRBC/UKQCD dw2007 results for calcswith u, d, s sea quarksVus competitive w. PDG1.31.25HPQCDvery coarsecoarsefineextrapolnPACS-CS clover1.2HPQCD HISQon asqtad seaMILC asqtadf K /f !1.151.11.05Kl30.22 0.225 0.23V usPDG 2006Error0.6%10 0.2 0.4 0.6 0.8 1m u,d / m ssee Jüttner, LAT07HPQCD: 0706.1726[hep-lat] , error budget

K semileptonic decay (Kl3) and VusV usWJ = V0, Vi, A0, AiBKπ|V us f Kπ+ (0)| = 0.21673(46)= f+(0)RBC/UKQCD,dw, 2+1, 2007V us0.23FlaviaNetKAON DECAY WGV ud(0 + → 0 + )0.225fit0.97 0.975fit withunitarityunitarityV us/V ud(K µ2)V us(K l3)V udExtrapoln gives f + (0) = 0.9609(51)V us = 0.2257(15)Lattice error 0.5%, need to check disc.errors + other calcs. See Jüttner, LAT07

K 0 mixing and CKM constraintV ∗K 0 B0 B0K 0 =isV idH WCalculate box in lattice QCD - needsgood chiral symmetryMixing throughbox givesindirect CP violn- measureε = K L → ππK s → ππ∝ fKB 2 K from ε and B K get constraint on UT2007 result - RBC/UKQCD dw 2+1B MSK (2GeV ) = 0.557(12)(29)(+0 − 28)hep-ph/0702042 on 16 3 , one aBoyle LAT07, biggervolume, 24 3 , result islowerSee also Van der Water, LAT07, dw on asqtad sea, 2 a values, big volumes, result shortly ...

Charm physics, new method, 2007HPQCD2Fix mcMass (GeV)1.9test Dmassesvs expt.Exp’t0.1 0.2 0.3 0.4 0.5m u/d /m sM DsM DKey issue is discretisation errors, because mca ~ 0.5HISQ - much improved control of disc. errorscan use for charmonium and D - more tests of lattice QCDpossible. Same action as for u,d,s.E.Follana et al, 0706.1726[hep-lat]

2007 New Results for D, Ds decay constants,for comparison to experimentD x → lνLattice inc u,d,s sea vs expt0.3GeVExp’tHPQCD, HISQBelleEPS2007BaBarhep-ex/06070940.25f DsCLEO0704.0437[hep-ex]0.25GeV0.2CLEONext two years: more latticeresults and improved semileptonicform factors also ...f D250 300 350f DsFNAL/MILC asqtadLAT07 prelim.HPQCD HISQon asqtad sea0706.1726[hep-lat]2 v. differentlattice calcs• expt uses Vcs = Vud• error will improve to few % in 2 yrs• not all em corrns calculated ..

physics - B 0 mixing and CKM constraintB0 B0 =V td V ∗tbParameterise withfBB 2 B where f B isdecay constant.H WΔM x = G2 F M2 W6π 2|V ∗txV tb | 2 η B 2S 0 (x t )M Bx f 2 B xˆB BxTake exptl ratio from oscillation rates for Bs and Bd√| V td ΔM d M| = ξBsV ts ΔM s M Bd,ξ = f B s√BBsf B√BBcalculatein latticeQCD,renormlncancels

ξ2007 New results for√MBs1.3 HPQCD (no 1/M correct.)MILC1.251.21.151.11.05M B10.1 0.2 0.3 0.4 0.5 0.6m d/ m sξ = f B s√BBsf B√BBHPQCDFNAL/MILCPRELIMINARYinc. u, d, s sea quarksNRQCD for bFNAL for bf Bs√HPQCDhep-lat/0610104ˆB Bs = 0.281(21)GeVone value of a so far,main error isrenormln of lattice 4-q operatorCan compare to easier lattice calc. of f Bs / f BHPQCD, hep-lat/0507015 1.20(3)FNAL/MILC, Simone, LAT07 1.26(4)Gamiz, LAT07

Discretization errorsB excl. semileptonic decay and CKM constraint10.980.96F(1)0.940.92hA1(1)FNAL/MILCV ub ,V cbWJ = V0, Vi, A0, AiB π,D,D ∗ ,...0.90.880.860 0.005 0.01 0.015 0.02 0.025 0.03a 2a 2 / f m 2B → D ∗ lν Laiho, LAT07rate at zero recoil∝ |VLat ‘07, August 2, 2007 – p.21/24cb F(1)| 2FNAL/MILC with u, d, s sea quarks, 3 values of aF(1) = 0.930(12)(19) HFAG V cb = 38.7(0.7)(0.9) × 10 −3stat syst expt lattFlynn+Nieves 0705.3553[hep-ph] combine lattice (HPQCD,B → πlν FNAL/MILC) with LCSR, getwork underway to extend lattice resultsV ub = 3.47(29) × 10 −3

Use lattice resultswith u, d, s sea quarks+ experimentfor constraints onunitarity triangle.Lattice inputs(2+1 sea quarks):B Kf K / f π , f + (K → πlν)F(B → D ∗ lν)f + (B → πlν)f Bs√BBsf B√BB"CKM 2007 LATTICE QCD10.80.60.40.20-0.2-0.4-0.6-0.8#V #ub#V #cbf Bsf BB BsB BB K-1-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1!%PDG06Errors on lattice results shouldhalve over next two yearsTo others using lattice results: QA is dead!$

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

Thanks to:Claude Bernard, Peter Boyle, Elvira Gamiz, AndreasJüttner, Jack Laiho, Peter Lepage, Craig McNeile,Matthew Moulson, Gerrit Schierholz, Junko Shigemitsu,Jim Simone, Doug Toussaint, Carsten Urbach, Ruth vander Water, Kit WongandConference organisers here in Korea