1. 1 Hiroshi Ohki, Tetsuya Onogi (YITP, Kyoto U.) Hideo Matsufuru (KEK) October 4,2007@Lattice2007 High precision study of B*Bπ coupling in unquenched QCD

2. 2 Introduction

3. 3 (1)The fundamental parameter in the effective chiral lagrangian for heavy meson preserving chiral and heavy quark symmetry. Why Coupling ？

4. 4 form factor (|Vub|) Chiral behavior of (|Vtd|) (2) Useful for phenomenological applications in flavor physics

5. 5 Previous results In full QCD we need significant improvement for precision, given limited configurations. Numerical techniques for precision is crucial can be obtained by interpolating the results in static limit and charm region. Figure from Abada et al. hep-lat/0310050

6. 6 Goal of this work First high precision study of static B*Bpi coupling in unquenched QCD using improved techniques The first step towards the determination of Link smearing, Della Morte et al. hep-lat/0307021 All-to-all propagators with low mode averaging J. Foley et al. hep-lat/0505023 Improved techniques:

7. 7 Simulation methods Cf. Negishi et al hep-lat/0612029 (nf=0)

8. 8 Compute the form factor at zero recoil In the static limit, How to obtain B*Bpi coupling ? Light-light axial verctor current G.M.de Divitiis et al.JHEP 9810 (1998)010

9. 9 Analysis of Simultaneous fit of 2pt and 3pt functions As a result of the simultaneous fit for effective mass ( : Const )

10. 10 Link smearing Della Morte et al. hep-lat/0307021 A new HQET action using HYP(APE) smeared links. Suppress the short distance fluctuation of the gauge field. All-to-all propagators with low mode averaging, -divide the light quark propagator into low and high mode -Low mode : low eigenmodes of the Dirac Hamiltonian. -High mode: using the standard random noise methods. J.Foley et al.hep-lat/0505023 T.A.DeGraand et al. hep-lat0202001 L.Giusti et al.hep-lat/0402002

11. 11 “higher” “lower” 2pt function Averaged over for both lower and higher modes Random noise

12. 12 “low-low” “low-high” “high-low” “high-high” 3pt function Averaged over for “ low-low ”, “ low-high ”, “ high-low ”, “ high-high ”

13. 13 Simulation setup Actions –Gauge: Nf=2 unquenched configurations by CP-PACS http://www.jldg.org/lqa/CPPACSconfig.html –Light: O(a)-improved Wilson –Heavy: Static quark with HYP1 link V(x,0) Operator: light source, sink smeared Parameters for all-to-all: Computational resource : Implicitly restarted Lanczos algorithm This is based on the lesson from quenched study of Negishi et al.

14. 14 RESULTS Low mode is dominant? and/or Statistical noise is suppressed ?  Plots of Extraction of B*Bpi coupling Chiral extrapolation

15. 15 All-to-all heavy-light propagator Results for 2pt function “low” becomes dominant Contributions to 2pt for all-to-all correlation functions =0.1430,100 configs.

16. 16 Results for 3pt functions We fix time difference between current and the source as “ low-low ” is the dominant Contributions to 3pt for all-to-all correlation functions =0.1430,100 configs.

17. 17 fit range: 2pt, 3pt effective mass plots for 3pt and 2pt fit of 2pt only simultaneous fit for 2pt and 3pt =0.1430,100 configs.

18. 18 Results for 3pt/2pt Ratio for all-to-all heavy-light =0.1430, 100 configs. Z3/Z2 from the fit raw data

19. 19 Results for B*B pi at beta=1.80 This does not contribute after summing over space CP-PACS, Phys.Rev.D65,054505

20. 20 Analysis our results of numerical data Chiral extrapolation We use three functions for fitting our numerical data as follows Fit by 3 points Fit by 4 points H.Y.Cheng et al. Phys.Rev.D49(1994)5857

21. 21 Chiral extrapolation Error of raw data is statistical only.

22. 22 Systematic Error estimate 1.chiral extrap. 2.perturbative. 3.disc. Preliminary result (2,3: order estimation)

23. 23 Summary and Future prospects

24. 24 All-to-all propagator and HYP smearing are useful for static heavy-light simulations in unquenced QCD. The stat. error remains tiny for all quark masses, giving ~5% in the chiral limit. Our preliminary result for nf=2 at beta=1.80 summary Discretization error dominates for our simulation on the coarsest lattice.

25. 25 Comparison with other calculations Pert. error Stat. error

26. 26 Future prospects Non perturbative matching -> feasible using PCAC relation Continuum limit -> Need to simulate on finer lattices from CP-PACS Extending to simulations from studying 1/M dependence of -> calculation of with all-to-all propagator

27. 27 The End Thank you.

28. 28 Backup slides

29. 29 N ev dependence of effective mass Figure from Negishi et al hep-lat/0612029 (nf=0) Previous work of quenched case.

30. 30

31. 31 All-to-all heavy-light propagator Results for 2pt function Effective mass plot for all-to-all heavy-light 2pt =0.1430,100 configs.

32. 32 Results for (1) =0.1409, 100 configs. Fit 3pt/2pt Ratio for all-to-all heavy-light

33. 33 Results for (3) =0.1445, 100 configs. Fit 3pt/2pt Ratio for all-to-all heavy-light

34. 34 Results for (4) =0.1464, 100 configs. Fit 3pt/2pt Ratio for all-to-all heavy-light

35. 35

36. 36 Nonperturbative HQET HQET has a continuum limit and can be matched to QCD by appropriate nonperturbative renormalization schemes. Successful for determination of A lot of other applications should be possible and deadly needed for flavor physics In this work we focus on coupling.

37. 37 Need for all-to-all propagator HQET propagators are very noisy. Link smearing with HYP, APE,.. (Alpha) All-to-all propagators with low-mode averaging and noise method for high-mode (Trinlat)

38. 38 Why HQET ? SM with CKM describes flavor physics unexpectedly well. At 10-20% level we see no deviation. We do need much better precision for weak matrix elements. CKM fitter http://ckmfitter.in2p3.fr Largest uncertainties arise from 1. Unquenching (common problem) 2. Chiral lmit (common problem) 3.Heavy quark - discretization error - pertubative error HQET are free from these problems and give a very good reference point for B meson.