Future Prospects from Lattice QCD Tetsuya Onogi (YITP, Kyoto) CKM2006, Nagoya Outline Introduction Systematic Errors New Developments Summary

1. Introduction Which parameters are more critical? What are the most reliable errors at present? chiral extraploation error perturbative and discretization errors (theoretical validity) What can we expect in the near future? New unquenched calculation Nonperturbative method for heavy quark All-to-all propagator for HQET

Unquenched lattice results . Using these results we can try three independent tests, given below. NOTE: FNAL/MILC and HPQCD use identical gauge configs. differences are purely systematic (no other excuse) , should be taken seriously

Two Unitarity tests Comparison of Do we exclude/find new physics? No, not enough precision

Test of charged Higgs effect from cancel SM prediction experiment Ratio of semileptonic and leptonic decay rates. A slight hint of deviation to opposite direction? Unlikely to have charged Higgs contribution ? Here again, we need more precision.

2. Systematic errors JLQCD: quenching error FNAL/MILC: HPQCD/MILC: Fermilab (heavy), Improved staggered (light) Matching = partially nonperturbative perturbative error Chiral extrapolation = staggered ChPT chiral extrap. error a=0.12fm, 0.09 fm discretization error HPQCD/MILC: NRQCD (heavy), Improved staggered (light) Matching = perturbative perturbative error Chiral extrapolation = staggered ChPT chiral extrap. error a=0.12fm , 0.09fm discretization error JLQCD: quenching error NRQCD (heavy), O(a)-improved Wilson (light) 　　Matching = perturbative perturbative error Chiral extrapolation = polynomial or polynomial + log chiral extrap. error a=0.12 fm discretization error

It is difficult to reduce the error further. Dominant error : perturbative error 10% for HPQCD, discretization error 6% for FNAL/MILC perturbative error 6% for JLQCD s-quark quenching error unknown for JLQCD nf=2 It is difficult to reduce the error further. Nonperturbative matching and continuum limit is needed.

It is also difficult to reduce the error further. Dominant error : perturbative error 9% for HPQCD, perturbative error 8% for JLQCD missing s-quark quenching error unknown for JLQCD nf=2 It is also difficult to reduce the error further. Nonperturbative matching and continuum limit is needed. by HPQCD (New!) has a smaller central value JLQCD after including 1/M correction (dim=7 operator) , which is NOT included in JLQCD’s calculation. Difficulty of operator mixing from wrong chirality in Wilson-type fermions.

Dominant error: Chiral extrap +disc. error 5% for FNAL/MILC, > 3% HPQCD/MILC Staggered ChPT, Aubin et al, recover the chiral log from the raw data removing O(a^2) suppressed chiral log is enhanced by factor about 16. HPQCD/MILC claim staggered ChPT is NOT essential. For FNAL/MILC, staggered ChPT is essential. Difference in chiral behavior ? HPQCD

Comparison of FNAL/MILC and HPQCD FNAL/MILC and HPQCD are consistent within errors. difficult to reduce the systematic errors further. Statistical error is also non-negligible

3. New Developments Developments in unquenched simulation Berlin’s Wall Ukawa (lattice2001@Berlin) Empirical law in the numerical Cost for 2-flavor O(a)-improved Wilson 24 years on Tflops machine

Fall-down of Berlin’s wall (Major breakthrough) Separate treatment for Low　(less frequently) and high modes　(more frequently) of the light quark determinant Domain decomposition (Luscher) 　 nf=2 dynamical Wilson 　　　separation in real space Del Debbio et al. Hasenbush trick ( energy space ) Only 0.5 year on PC cluster(64CPU)!

Dynamical overlap simulation from JLQCD Exact chiral symmetry New idea : Topology conserving action Hasenbusch trick is used. Okamoto’s data presented at Lattice 2006 Significantly light quark simulation is possible

projects of unquenched QCD simulations Many unquenched simulations are performed or starting now. In addition to rooted staggered by MILC collab., Wilson-type fermions and Ginsparg-Wilson fermions are in progress. Important for cross-check and theoretically clean

What do we expect in near future? Weak matrix elements for light hadrons (except for ): Chiral extrapolation will be under good control in many approaches. Nonperturbative renormalization is available. Continuum limit can be taken with Wilson-type fermions. Statistical error including fits and extrap. will be the dominant source. 2-3% accuracry will be feasible. What about ? Wilson fermion suffer from operator mixing with wrong chirality. Solutions : twisted mass QCD Overlap Domain-wall hybrid ( Wilson sea and Overlap valence) Slightly difficult but few % accuracy will be feasible.

What about heavy quark? Methods which allow the following are required. nonperturbative renormalization continuum limit Alpha method : HQET Nonpert. matching of HQET and QCD near continuum. Evolve the lattice HQET to coarser lattice by step scaling. For b-quark, match including 1/M term or interporate from HQET and from QCD. (b) Rome II method : step scaling using only relativistic QCD - decay const in small volume L0=0.4fm directly - finite vol. correction by extrapolations from smaller mQ.

quenched result 1/M dependence is in good control with static results. (c) Guazzini, Sommer, Tantalo quenched study of combination of two methods (a) and (b) Use static result to interpolate the finite vol. corr. Interpolation of finite size corrections slides from Guazzini’ at Lattice 2006. 1/M dependence is in good control with static results. quenched result

Technique for precision measurement: Static heavy-light was known to be very noisy, but all-to-all propagator for heavy-light system Low-mode averaging and noisy estimator (Trinlat collabollation.) quenched study of 2-,3-point function, Matsufuru, Negishi, T.O. Low mode averaging with100 eigenmodes Only a few ten configurations (32confs) is sufficient . Very clean plateau for heavy-light 2point function B*Bpi coupling is obtained with high accuracy 3%

4. Summary Experiment is confronting to new physics. Theoretical developments in lattice QCD are needed. Unquenched study with MILC configs are in progress. The systematic errors are controlled to 10%. Perturbative are discretization errors are getting serious. New developments unquenched simulation, step-scaling method(RomeII), nonperturbative HQET, all-to-all propagators are being developed which could reduce errors to few percent level.