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B*Bpi coupling in unquenched QCD

Hiroshi Ohki (Kyoto Univ.)@BNM 2008

Outline 　　　　 Introduction Lattice calculation Results Summary and future prospects

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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.

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How to reduce the error?

(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.

unquenched lattice results

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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.

Dispersive bound tells us the dependencies of transfer momentum about form factors.

Our method: Dispersive bound

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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.

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Lattice calculation

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How to obtain B*Bpi coupling

The B*B pi coupling is defined by the matrix element

In the static limit

Light-light axial verctor current

G.M.de Divitiis et al.JHEP 9810 (1998)010

Lattice simulation

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Recent result

Becirevic et al.

Abada et al.

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

Figure from Abada et al. hep-lat/0310050

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First high precision study of static B*Bpi coupling

in unquenched QCD using improved techniques

The first step towards the determination of

Our strategy

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:

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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

Improved techniques

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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 :

Simulation setup

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RESULTS

Plots of 2,3-point functions Extraction of B*Bpi coupling Chiral extrapolation

Simulation point

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Effective mass plots for 2, 3 point

We get good plateau.

Ground state (B, B*) is successfully extracted.

B,B* state Binding energy

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Results for

fit

raw data

2pt/3pt ratio to extract B*Bpi coupling works very well.

3pt/2pt ratio

:Renormalization factor

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Chiral extrapolation

Fit by 3 points

Fit by 4 points

H.Y.Cheng et al. Phys.Rev.D49(1994)5857

We use three functions for fitting our numerical data

as follows

Mass dependence from chiral perturbation theory

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Chiral extrapolation

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Error estimation Systematic Error estimate 1.chiral extrap. 2.perturbative. 3.disc. Preliminary result (beta=1.95)

(2,3: order estimation)

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Summary and future prospects

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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.

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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.

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Future prospects

Towards precise determination of |Vub|

Our method: Dispersive bound

Experiment data of partial branching

fraction for B to pi l nu decay Lattice results of form factor

Next step

Ongoing project

Including the value of form factor

at B* pole using B*Bpi coupling

Input data

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Input data

Partial branching fraction spectrum for B to pi l nu decay in 12 bins of

BABAR Collab. B. Aubert et al., Phys.Rev.Lett.98,091801(2007),hep-ex/0612020

Lattice simulation

HPQCD collab. E. Gulez et al,Physical Review D 73,074502(2006)

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2 inputs

Result of |Vub| distribution

Preliminary results

3 inputs

Just for reference

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Consideration

Lattice theory Experiment

Our preliminary results

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.

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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.

Need improvements for experiment and theoretical inputs.

Moreover

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The End

Thank you