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Recent results from lattice calculations

Recent results from lattice calculations. Shoji Hashimoto (KEK) Aug. 20 @ ICHEP 2004, Beijing. 30 years of lattice QCD. K. Wilson (1974). QCD potential. QCD coupling const. Phase transition. Flavor physics. Hadron spectrum. Dynamical fermions. Lattice 2004.

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Recent results from lattice calculations

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  1. Recent results from lattice calculations Shoji Hashimoto (KEK) Aug. 20 @ ICHEP 2004, Beijing

  2. 30 years of lattice QCD K. Wilson (1974) QCD potential QCD coupling const Phase transition Flavor physics Hadron spectrum Dynamical fermions

  3. Lattice 2004 • Jun 21-26 @ Fermilab; 22nd 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, Kl3 form factor for Vus; B_K in Nf=2 • Tomboulis, RG in SU(N) LGT • Hari Dass, teraflop cluster in India

  4. 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

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

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

  7. Non-perturbative definition of QCD Monte Carlo simulation is possible. “First principles” calculation, but with approximations: finite a finite L large mq need extrapolations; source of systematic errors. Lattice QCD lattice size L ~2-3 fm gauge field quark field lattice spacing a ~ 0.1-0.2 fm

  8. 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.

  9. Lattice fermions

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

  11. “Lattice QCD confronts experiment” HPQCD, MILC, UKQCD, Fermilab (2003) “Gold-plated lattice observables agree with experiments within a few %.” “Only with 2+1 flavors.” PRL92, 022001 (2004) Is everything okay?

  12. Locality/Universality Fourth-root trick: 4 tastes (unwanted) 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/0403022; Hart, Muller, hep-lat/0406030.

  13. 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 There are many other sensible people who cannot simply believe without a theoretical proof. 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/0406010; Durr et al, hep-lat/0406027

  14. 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 …

  15. 2. Fundamental parameters ― QCD coupling constant, quark masses

  16. QCD coupling constant PDG 2004 perturbation theory known to 3-loop • From lattice simulation: • scale q* from Upsilon spectrum (less sensitive to chiral extrap, volume effect, etc.) • coupling constant αV from short distance observables; perturbative expansion. HPQCD (2003) Nf=2+1

  17. 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. preliminary The disagreement with the Wilson-type fermion is not well understood.

  18. Light quark masses PDG 2004 One-loop perturbation, or partly non-perturvative Lattice simulation Input from mπ and mK. is sensitive to chiral extrap. ms is less. Some of these are from lattice.

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

  20. Quark mass ratio : NLO ChPT with EM corrections subtracted. • 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.

  21. 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 Charm quark mass My recommendation: c.f. BaBar inclusive Vcb analysis:

  22. 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:

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

  24. |Vus| 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/0403217 • quenched • measures the SU(3) breaking using clever double ratios as in |Vcb| by Fermilab • Result • consistent with Leutwyler-Roos0.961(8)

  25. Leptonic decay for |Vus| • can be used to determine |Vus|, once fK is known from lattice (Marciano, hep-ph/0402299) • use the MILC result Nf=2+1 hep-lat/0407028 The accuracy is now competing with the semi-leptonic determination.

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

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

  28. Dynamical quark effect was not clearly seenbefore (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/0406013 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) Quenching effect on BK?

  29. RBC (2004), preliminary Sea quark mass dependence is seen. BK is lower in the chiral limit. SU(3) breaking (md≠ms) effect -3%. Unquenched BK 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)

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

  31. 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 |Vcs|, |Vcd| • Provides input for the corresponding B meson form factor analysis.

  32. 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 2004. • Fermilab-MILC-HPQCD at Lattice 2004. preliminary

  33. Semi-leptonic D decays Form factors New Nf=2+1 calculation by Fermilab-MILC at Lattice 2004. • Staggered light, clover heavy • Dominant syst error from heavy quark discretization (~7%) preliminary

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

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

  36. 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 Without chiral extrap: fBs 1.5σ disagreement: not yet understood; effect of +1 flavor is not likely (sea quark mass dependence is small). My estimate:

  37. Need to include the effect of pion loops (chiral log) Chiral extrapolation: fB 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:

  38. 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. JLQCD preliminary (2003): • Chiral log cancels at LO • Take advantage of expected CLEO-c data

  39. BB is less problematic. B parameter • Coefficient of the chiral log term is small: • (1-3g2) ~ -0.05. • Lattice data are consistent with a constant. JLQCD (2003), Nf=2

  40. B mixing summary

  41. Semi-leptonic B decays • for the |Vub| determination; form factors • lattice calculation is feasible at the large q2 region • First Nf=2+1 calc this year both on the MILC conf, different heavy quark formulations No significant effect of quenching; chiral log not yet studied. Fermilab (2004) HPQCD (2004)

  42. CLEO analysis (2003): use the exp data above q2 > 16 GeV2 and input lattice form factor averaged over four quenched lattice calc. |Vub| determination CLEO (2003) New Belle measurement (140 fb-1): expect O(x10) statistics in near future with unquenched lattice calculation

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

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

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

  46. Spectrum, both light and heavy Exotics including pentaquarks decays: ΔI=1/2 rule, ε’/ε Hadronic decays including DsJ 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 Topics not covered

  47. Summary Previous quenching errors are now being eliminated by real simulations. • 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.

  48. 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.

  49. 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!

  50. Backup slides Machines, …

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