Recent results from lattice calculations Shoji Hashimoto (KEK) Aug. ICHEP 2004, Beijing

30 years of lattice QCD K. Wilson (1974) QCD potential QCD coupling const Flavor physics Hadron spectrum Phase transition Dynamical fermions

Lattice 2004 Jun Fermilab; 22 nd in the series 20 plenary talks; 216 parallel/posters Lattice talks at ICHEP 04 Kaneko, unquenched mini-review Hatsuda, review of hot and dense QCD Di Giacomo, chiral phase transition in Nf=2 Mescia, K l3 form factor for V us ; B K in Nf=2 Tomboulis, RG in SU(N) LGT Hari Dass, teraflop cluster in India

Topics to be covered Flavor physics related quantities, responsible for More fundamental questions: Requirements for unquenched lattice simulations Fundamental parameters of QCD Lattice QCD at the frontier of elementary particles

Plan of this talk 1.Issues in recent QCD simulations Chiral extrapolation, fermion formulations … 2.Fundamental parameters QCD coupling constant, quark masses 3.Kaon physics Form factors, kaon B parameter 4.Heavy quarks Decay constants, form factors …

1. Issues in recent lattice QCD simulations ― dynamical fermions, chiral extrapolation, fermion formulation

Lattice QCD Non-perturbative definition of QCD Monte Carlo simulation is possible. “ First principles ” calculation, but with approximations: –finite a –finite L –large m q need extrapolations; source of systematic errors. lattice spacing a lattice size L quark field gauge field ~ fm ~2-3 fm

Dynamical fermions Calculating the fermion determinant = numerically very hard. Quenched: neglect it Unquenched: include it How hard it is depends on the fermion formulation on the lattice.

Lattice fermions chiral symmetry flavor symmetry numerical simulation Wilson / O(a)- improved Wilson violated; will recover in the continuum okay expensive; harder at small quark masses twisted massviolated 2 flavors; a flavor mixing mass term less expensive at small quark masses staggered (Kogut-Susskind) exact U(1) out of U(4) 4 tastes; non- trivial mixing fast Ginsparg- Wilson (domain- wall, overlap) exact at finite a okay most expensive; still exploratory

Chiral extrapolation Lattice simulation is limited in a heavier quark mass region m q ~(0.5-1)m s. pion decay constant ChPT predicts the chiral log near the chiral limit. with a fixed coefficient. chiral log Staggered simulation can push the quark mass much lower. MILC (2004) Nf=2+1 JLQCD (2002) Nf=2

“ Lattice QCD confronts experiment ” HPQCD, MILC, UKQCD, Fermilab (2003) “ Gold-plated lattice observables agree with experiments within a few %. ” “ Only with 2+1 flavors. ” Is everything okay? PRL92, (2004)

Locality/Universality 4 tastes (unwanted) Fourth-root trick: no doubling Can it be written as a local field theory? Otherwise, there is no guarantee that the theory is renormalizable as a quantum field theory, i.e. continuum limit is the QCD. is non-local: Bunk et al, hep-lat/ ; Hart, Muller, hep-lat/ =?

Issue still controversial “We believe that existing staggered quark results make it unlikely that there are fundamental problems with the formalism we are using.” ― HPQCD, MILC, UKQCD Open question = project out a single taste from the staggered operator (possible?) and see if it is local. Positive indication from eigenvalue distribution: Follana et al, hep-lat/ ; Durr et al, hep-lat/ There are many other sensible people who cannot simply believe without a theoretical proof.

Major unquenched simulations Here, let us assume that the fourth-rooted staggered fermion is a correct (or at least effective) description of QCD. Current major unquenched simulations include Wilson, O(a)- improved Wilson –Nf=2: CP-PACS, JLQCD, QCDSF, UKQCD, qq+q, SPQcdR –Nf=2+1: CP-PACS/JLQCD Staggered – Nf=2 and 2+1: MILC Domain-wall – Nf=2: RBC Some recent results …

2. Fundamental parameters ― QCD coupling constant, quark masses

QCD coupling constant perturbation theory known to 2-loop From lattice simulation: scale q * from Upsilon spectrum (less sensitive to chiral extrap, volume effect, etc.) coupling constant α V from short distance observables; perturbative expansion. PDG 2004 HPQCD (2003) Nf=2+1

Updates at Lattice 2004 QCDSF-UKQCD (Horsley et al.) –O( a )-improved Wilson fermion –finer lattice added, aid the continuum limit. Result unchanged. HPQCD (Mason et al.) –improved staggered (MILC) –3-loop calculation! error reduced by a factor of 2. The disagreement with the Wilson-type fermion is not well understood. preliminary

Light quark masses One-loop perturbation, or partly non-perturvative Lattice simulation Input from m π and m K. is sensitive to chiral extrap. m s is less. PDG 2004 Some of these are from lattice.

Strange quark mass m s becomes lower by the sea quark effects (CP- PACS, JLQCD, N f =2) Systematic error due to perturbative matching could be larger: QCDSF- UKQCD (2004), VWI with non-perturbative renorm, error stat only Update in 2004: N f = 2+1 data –HPQCD-MILC-UKQCD –CP-PACS/JLQCD Lower end of the PDG band My average:

Quark mass ratio with EM corrections subtracted. : NLO ChPT Update 2004: HPQCD-MILC-UKQCD staggered Nf=2+1 consistent analysis including NLO ChPT higher order terms are also included. The result suggests significant NNLO contributions.

Charm quark mass Not too heavy = brute force continuum limit is possible. 2002~2003: Continuum limit with non-perturbative matching (quenched) Update 2004: UKQCD, Nf=2 at a fixed lattice spacing, preliminary result My recommendation: c.f. BaBar inclusive Vcb analysis:

Bottom quark mass Too heavy to proceed with the brute force. Use HQET, matching to continuum with non-perturbative or higher order PT Update 2004 Di Renzo-Scorzato NNNLO matching 1/m correction is missing ~ 30 MeV. My recommendation: c.f. BaBar inclusive Vcb analysis:

3. Kaon physics ― Kaon decay constant, form factors, B parameter

|V us | the Cabibbo angle Precisely determined through Theoretical input is the form factor which is 1 in the SU(3) limit. Previous estimate (Leutwyler-Roos 1984, 20 years ago!) includes model dependence at First lattice calculation: Becirevic et al., hep-lat/ quenched measures the SU(3) breaking using clever double ratios as in |V cb | by Fermilab Result consistent with Leutwyler- Roos 0.961(8)

Leptonic decay for |V us | can be used to determine | V us |, once f K is known from lattice (Marciano, hep-ph/ ) use the MILC result Nf=2+1 hep-lat/ The accuracy is now competing with the semi-leptonic determination.

Kaon B parameter Need chiral symmetry to avoid mixing of wrong chirality operators. Previous world average: Unchanged since 1997 (central value from JLQCD staggered) 2 nd error from quenching ~ 15% (Sharpe 1996)

Quenched B K : recent results Improved staggered: Lee-Sharpe (2003), Gamiz et al. at Lattice Domain wall: CP-PACS (2001), RBC (2002), RBC at Lattice Overlap: DeGrand (2003), Garron et al. (2003). Wilson, w/o subtraction: SPQcdR (2004). Chirally twisted mass: ALPHA at Lattice Much better scaling; non- perturbative renorm. My average (quenched):

Quenching effect on B K ? Dynamical quark effect was not clearly seen before (Ishizuka et al. (1993), Kilcup (1993), Lee-Klomfass (1996), Kilcup et al. (1996)) –Reduce by a few % (Soni, 1995) –Increase by 5±15% (Sharpe, 1998) Maybe, because the unimproved staggered quark has too large scaling violation. New results in 2004 Flynn et al. (UKQCD), O(a)- improved Wilson fermion, Nf=2, hep- lat/ RBC, dynamical domain-wall fermion, Nf=2, at Lattice 2004 Gamiz et al. (UKQCD), improved staggered, on MILC config, at Lattice 2004 (too early to quote numbers; expect results in near future)

Unquenched B K RBC (2004), preliminary Sea quark mass dependence is seen. B K is lower in the chiral limit. SU(3) breaking (m d ≠m s ) effect -3%. My average: Central value is from quenched, as the RBC work is still preliminary; second error represents quenching effect cf. the previous number 0.63(4)(9)

4. Heavy quarks ― Decay constants, B parameters, form factors

D (s) meson decays CLEO-c and BESIII promise to measure the D (s) decays at a few % accuracy. Provides a stringent check/calibration of lattice method for B physics Leptonic decays Semi-leptonic decays Decay constants; form factors Determination of | V cs |, | V cd | Provides input for the corresponding B meson form factor analysis.

D meson decay constants Recent developments Better control of systematic error in quenched QCD (ALPHA (2003), de Divitiis et al. (2003)) Nf=2+1 calculation –Wingate et al. (2003) –MILC at Lattice –Fermilab-MILC-HPQCD at Lattice preliminary c.f. new CLEO-c result:

Semi-leptonic D decays Form factors New Nf=2+1 calculation by Fermilab-MILC at Lattice –Staggered light, clover heavy –Dominant syst error from heavy quark discretization (~7%) preliminary SU(3) ratio c.f. new BES result: 0.93(19)(7) CLEO-c: 0.86(7)(+6-4)(1) c.f. new BES result: 0.78(4)(3)

Competing with CLEO-c in precision? Error estimates for f D : Simone (Fermilab) at Lattice 2004 Perturbative matching of heavy quark action Need 2-loop calc. Statistics + smaller sea quark mass Machine power Discretization error; finer lattice 5% accuracy is within reach in a few years; 1-2% is more challenging.

B meson mixing Lattice QCD is the prime tool to calculate them. Long history since ~ 1990 Heavy quark is involved; HQET is useful. Unquenching! Decay constant f B B parameter B B SU(3) breaking parameter ξ

Without chiral extrap: f Bs Improved precision in quenched QCD by continuum extrapolation (de Divitiis et al. (2003), ALPHA (2003)) JLQCD (2003), Nf=2, O( a )-improved, high statistics Wingate et al. (2003), Nf=2+1, staggered sea MILC at Lattice 2004, Nf=2+1, not shown 1.5σ disagreement: not yet understood; effect of +1 flavor is not likely (sea quark mass dependence is small). My estimate:

Chiral extrapolation: f B Need to include the effect of pion loops (chiral log) JLQCD (2003), Nf=2 HPQCD, Nf=2+1, staggered sea, at Lattice 2004 Chiral log is seen; consistent with the estimate of JLQCD My estimate:

Grinstein ratio More controlled chiral extrapolation for ratios Becirevic et al. (2003) Chiral log partially cancels. Unquenched analysis to be done.. JLQCD (2003), Nf=2, uses the Grinstein ratio. Chiral log cancels at LO Take advantage of expected CLEO-c data JLQCD preliminary (2003):

B parameter B B is less problematic. Coefficient of the chiral log term is small: (1-3g 2 ) ~ Lattice data are consistent with a constant. JLQCD (2003), Nf=2

B mixing summary Lellouch, ICHEP 2002 My average, ICHEP (27)(+0-20) 189(27) 238(31)230(30) 235(33)(+0-24) 214(38) 276(38)262(35) 1.18(4)(+12-0) 1.22(+5-6) 1.18(4)(+12-0) 1.23(6)

Semi-leptonic B decays for the |V ub | determination; form factors lattice calculation is feasible at the large q 2 region First Nf=2+1 calc this year both on the MILC conf, different heavy quark formulations Fermilab (2004) HPQCD (2004) No significant effect of quenching; chiral log not yet studied.

|V ub | determination CLEO analysis (2003): use the exp data above q 2 > 16 GeV 2 and input lattice form factor averaged over four quenched lattice calc. New Belle measurement (140 fb -1 ): CLEO (2003) with unquenched lattice calculation expect O(x10) statistics in near future

Heavy-to-heavy for |V cb | Zero recoil form factors of Precise calculation is possible using clever ratios Fermilab (1999,2001), Nf=0 Update by the Fermilab group at Lattice 2004, Nf=2+1 No significant effect of quenching preliminary

Implication for the CKM fit Change in the input parameters: B K : 0.86(6)(14) → 0.81(6)(+0-13) f Bs √B Bs (MeV): 276(38) → 262(35) ξ: 1.24(4)(6) → 1.22(+5-6) Plots provided by the UTfit collaboration (Pierini). ε K band becomes slightly narrower. Sea quark effect is being included.

Assuming the Unitarity … Put a constraint on these hadronic parameters from the UTfit with other inputs.

Topics not covered Spectrum, both light and heavy Exotics including pentaquarks decays: ΔI=1/2 rule, ε’/ε Hadronic decays including D sJ Nucleon decay matrix elements Details of the lattice methods; heavy quark formulation, etc. epsilon-regime of QCD; determination of low energy constants appearing in the ChPT. Other theoretical developments

Summary Many interesting physics results from the staggered Nf=2+1 simulation have appeared; chiral regime is reachable and the extrapolation is under good control. There is a risk of being irrelevant to QCD. (the fourth-root trick = locality?) Results with other (more robust) fermion formulations will follow especially using new generation machines. Previous quenching errors are now being eliminated by real simulations.

We are very close to the first- principles simulation of QCD. Through the flavor physics, lattice QCD can put constraints on the SM, and thus contribute to the search for new physics.

Thanks to I. Allison, Y. Aoki, C. Bernard, N. Christ, C. Dawson, J. Flynn, E. Gamiz, A. Gray, R. Horsley, T. Iijima, T. Izubuchi, T. Kaneko, Y. Kayaba, A. Kronfeld, J. Laiho, C.-J. D. Lin, Q. Mason, C. Maynard, F. Mescia, J. Noaki, M. Okamoto, T. Onogi, C. Pena, M. Pierini, G. Schierholz, J. Shigemitsu, J. Simone, A. Soni, A. Stocchi, S. Tamhankar, Y. Taniguchi, N. Tsutsui, M. Wingate, H. Wittig, N. Yamada. members of the CP-PACS/JLQCD collaborations the organizers and the audience!

Backup slides Machines, …

Machines for lattice QCD QCDOC –10 TFlops (RBRC) + 10 TFlops (UKQCD) in Sep –another 10 TFlops in Mar apeNEXT –10 TFlops (INFN) in late PC clusters at many institutes