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Hiroshi Ohki, Tetsuya Onogi Hiroshi Ohki, Tetsuya Onogi (YITP, Kyoto U.)(YITP, Kyoto U.)

Hideo Matsufuru Hideo Matsufuru (KEK)(KEK)

October 4,2007@Lattice2007 October 4,2007@Lattice2007

High precision study of B*Bπ coupling

in unquenched QCD

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Introduction

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

Why Coupling ？

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• 　　　　　　 form factor (|Vub|)

• Chiral behavior of (|Vtd|)

(2) Useful for phenomenological applications in flavor physics

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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

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Goal of this workFirst 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:

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Simulation methods

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

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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

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Analysis of

Simultaneous fit of 2pt and 3pt functions

• As a result of the simultaneous fit for effective mass

( : Const )

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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

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“higher”“lower”

2pt function

Averaged over for both lower and higher modes

Random noise

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“low-low” “low-high” “high-low” “high-high”

3pt function

Averaged over for “low-low”, “low-high”, “high-low”, “high-high”

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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.

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RESULTS• Low mode is dominant? and/or

Statistical noise is suppressed ? Plots of• Extraction of B*Bpi coupling • Chiral extrapolation

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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.

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Results for 3pt functionsWe 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.

17fit range: 2pt , 3pt

effective mass plots for 3pt and 2pt

fit of 2pt only

simultaneous fit for 2pt and 3pt

=0.1430,100 configs.

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Results for

3pt/2pt Ratio for all-to-all heavy-light

=0.1430, 100 configs.

Z3/Z2 from the fit

raw data

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Results for B*B pi at beta=1.80

This does not contribute after summing over spaceCP-PACS, Phys.Rev.D65,054505

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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

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Chiral extrapolation

Error of raw data is statistical only.

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• Systematic Error estimate 1.chiral extrap. 2.perturbative. 3.disc. • Preliminary result

(2,3: order estimation)

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Summary and Future prospects

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• 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.

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Comparison with other calculations

Pert. error

Stat. error

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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

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The End

Thank you.

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Backup slides

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N ev dependence of effective mass

Figure from Negishi et al hep-lat/0612029 (nf=0)

Previous work of quenched case.

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All-to-all heavy-light propagator

　　 Results for 2pt function 　　　　　　　　

Effective mass plot for all-to-all heavy-light 2pt

=0.1430,100 configs.

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Results for (1)

=0.1409, 100 configs.

Fit

3pt/2pt Ratio for all-to-all heavy-light

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Results for (3)

=0.1445, 100 configs.

Fit

3pt/2pt Ratio for all-to-all heavy-light

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Results for (4)

=0.1464, 100 configs.

Fit

3pt/2pt Ratio for all-to-all heavy-light

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Nonperturbative HQETHQET has a continuum limit and can be matched to QCDby 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.

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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)

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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 meso

n.