B*Bpi coupling in unquenched QCD

1. B*Bpi coupling in unquenched QCD Hiroshi Ohki (Kyoto Univ.) @BNM 2008 Outline • Introduction • Lattice calculation • Results • Summary and future prospects

2. Introduction • is very crucial parameter to test Standard Model. • Exclusive decay can play a important role, but it is consistent with unitarity and inclusive decay due to large error dominated by theory. We need more theoretical improvement for exclusive semileptonic decay.

3. How to reduce the error? unquenched lattice results (1) Alternative approach • Using soft pion theorem parameter • These parameters are very important for flavor physics. • In Particular decay constant is already studied widely. • B*Bpi coupling is determined almost 15% accuracy, crucial improvement is needed.

4. How to reduce the error? (2) Further study dependencies of form factor • We could improve the precision if we can use the experimental data for the whole range. Our method: Dispersive bound Dispersive bound tells us the dependencies of transfer momentum about form factors.

5. Plan of this work • 1. High precision study of B*Bpi coupling in unquenched lattice calculation • 2. Towards precise determination of |Vub| from dispersive bound We focus on the B*Bpi coupling in this talk.

6. Lattice calculation

7. How to obtain B*Bpi coupling The B*B pi coupling is defined by the matrix element Light-light axial verctor current In the static limit G.M.de Divitiis et al.JHEP 9810 (1998)010 Lattice simulation

8. Recent result Figure from Abada et al. hep-lat/0310050 In full QCD we need significant improvement for precision, given limited configurations. can be obtained by interpolating the results in static limit and charm region. Static results Abada et al. Becirevic et al.

9. Our strategy 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

10. Improved techniques • 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. 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) • Computational resource :

12. RESULTS Simulation point • Plots of 2,3-point functions • Extraction of B*Bpi coupling • Chiral extrapolation

13. Effective mass plots for 2, 3 point B,B* state Binding energy We get good plateau. Ground state (B, B*) is successfully extracted.

14. Results for 3pt/2pt ratio raw data fit :Renormalization factor 2pt/3pt ratio to extract B*Bpi coupling works very well.

15. Chiral extrapolation We use three functions for fitting our numerical data as follows Fit by 3 points Fit by 4 points Mass dependence from chiral perturbation theory H.Y.Cheng et al. Phys.Rev.D49(1994)5857

16. Chiral extrapolation

17. Error estimation • Systematic Error estimate 1.chiral extrap. 2.perturbative. 3.disc. • Preliminary result (beta=1.95) (2,3: order estimation)

18. Summary and future prospects

19. Summary • The stat. error remains tiny for all quark masses, giving ~2% even in the chiral limit. • The error is dominated by systematic errors 6% from pert, 6% from chiral extrap, 6% from disc.

20. Reduce the errors • Non perturbative matching of axial vector current  feasible using PCAC relation • Chiral extrapolation using unquenched configs. with light sea quark masses. (ex. JLQCD,PACS-CS) • Discretization error can reduced by simulating of finer lattices.

21. Future prospects Towards precise determination of |Vub| Our method: Dispersive bound Input data • Experiment data of partial branching fraction for B to pi l nu decay • Lattice results of form factor Ongoing project • Including the value of form factor at B* pole using B*Bpi coupling Next step

22. Input data Lattice simulation Partial branching fraction spectrum for B to pi l nu decay in 12 bins of HPQCD collab. E. Gulez et al, Physical Review D 73,074502(2006) BABAR Collab. B. Aubert et al., Phys.Rev.Lett.98,091801(2007),hep-ex/0612020

23. 3 inputs Preliminary results 2 inputs Result of |Vub| distribution Just for reference

24. Consideration Our preliminary results Lattice theory Experiment Dispersive Bound error • We made an exploratory study of |Vub| determination with dispersive bounds and obtained promising preliminary results using partial set of inputs. • It is also consistent by recent result by Flynn, Nieves 2007. • We made simplifications which could introduce systematic errors. We should either discard such simplification or study systematic errors, which can make the error larger.

25. Finally • To improve the accuracy • We can use the full range of data. • We can also use inputs from soft pion theorem with B*B pi coupling. Moreover Need improvements for experiment and theoretical inputs.

26. The End Thank you