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Hiroshi Ohki, Tetsuya Onogi (YITP, Kyoto U.) Hideo Matsufuru (KEK) October 4,2007@Lattice2007

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

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Hiroshi Ohki, Tetsuya Onogi (YITP, Kyoto U.) Hideo Matsufuru (KEK) October 4,2007@Lattice2007

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

  2. Introduction

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

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

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

  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 Improved techniques: • Link smearing, Della Morteet al. hep-lat/0307021 • All-to-all propagators with low mode averaging J. Foley et al. hep-lat/0505023

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

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

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

  10. Link smearing Della Morteet 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. “higher” “lower” 2pt function Random noise Averaged over for both lower and higher modes

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

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

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

  16. =0.1430,100 configs. 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

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

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

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

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

  23. Summary and Future prospects

  24. summary • 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 Discretization error dominates for our simulation on the coarsest lattice.

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

  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. The End Thank you.

  28. Backup slides

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

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

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

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

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

  34. 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.

  35. 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)

  36. 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. • Largest uncertainties arise from • Unquenching (common problem) • Chiral lmit (common problem) • Heavy quark • - discretization error • - pertubative error • HQET are free from these problems and • give a very good reference point for B meson. CKM fitter http://ckmfitter.in2p3.fr

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