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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. Introduction. is very crucial parameter to test Standard Model. - PowerPoint PPT Presentation
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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
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