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

2. 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

3. 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

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

5. 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.

6. 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

7. It is difficult to reduce the error further.
Dominant error :
perturbative error % for HPQCD,
discretization error % for FNAL/MILC
perturbative error % 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.

8. It is also difficult to reduce the error further.
Dominant error :
perturbative error % for HPQCD,
perturbative error % 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.

9. 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

10. 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

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

12. 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)!

13. 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

14. 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

15. 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.

16. 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.

17. 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

18. 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%

19. 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.