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High precision study
of B*Bπ coupling
in unquenched QCD
Hiroshi Ohki, Tetsuya Onogi (YITP, Kyoto U.)
Hideo Matsufuru (KEK)
October 4,2007@Lattice2007
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Introduction
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Why
Coupling？
(1) The fundamental parameter in the effective
chiral lagrangian for heavy meson preserving
chiral and heavy quark symmetry.
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(2) Useful for phenomenological applications
in flavor physics
•
•
form factor (|Vub|)
Chiral behavior of
(|Vtd|)
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Previous results
can be obtained by
interpolating the results
in static limit and charm
region.
Figure from Abada et al. hep-lat/0310050
In full QCD we need significant improvement for
precision, given limited configurations.
Numerical techniques
for precision is crucial
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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 Morte et al. hep-lat/0307021
• All-to-all propagators with low mode averaging
J. Foley et al. hep-lat/0505023
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Simulation methods
Cf. Negishi et al hep-lat/0612029
(nf=0)
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How to obtain B*Bpi coupling
?
Compute the form factor at zero recoil
Light-light axial verctor current
In the static limit,
G.M.de Divitiis et al.JHEP 9810 (1998)010
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Analysis of
Simultaneous fit of 2pt and 3pt functions
(
: Const )
• As a result of the simultaneous fit for effective mass
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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
J.Foley et al.hep-lat/0505023
averaging,
T.A.DeGraand et al. hep-lat0202001
L.Giusti et al.hep-lat/0402002
- 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.
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2pt function
“lower”
Averaged over
Random noise
“higher”
for both lower and higher modes
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3pt function
“low-low”
“low-high”
“high-low”
“high-high”
Averaged over
for “low-low”,
“low-high”, “high-low”, “high-high”
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• Actions
Simulation setup
– 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:
Implicitly restarted Lanczos algorithm
This is based on the lesson from quenched study of Negishi et al.
• Computational resource :
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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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Results for 2pt function
All-to-all heavy-light propagator
Contributions to 2pt for all-to-all correlation functions
=0.1430,100 configs.
“low” becomes dominant
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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
=0.1430,100 configs.
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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
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Results for
3pt/2pt Ratio for all-to-all heavy-light
raw data
Z3/Z2 from the fit
=0.1430, 100 configs.
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Results for B*B pi at beta=1.80
CP-PACS, Phys.Rev.D65,054505
This does not contribute
after summing over space
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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.
(2,3: order estimation)
• Preliminary result
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Summary and
Future prospects
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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. 24
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
Previous work of quenched case.
Figure from Negishi et al hep-lat/0612029
(nf=0)
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Results for 2pt function
All-to-all heavy-light propagator
Effective mass plot for all-to-all heavy-light 2pt
=0.1430,100 configs.
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Results for
(1)
3pt/2pt Ratio for all-to-all heavy-light
Fit
=0.1409, 100 configs.
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Results for
(3)
3pt/2pt Ratio for all-to-all heavy-light
Fit
=0.1445, 100 configs.
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Results for
(4)
3pt/2pt Ratio for all-to-all heavy-light
Fit
=0.1464, 100 configs.
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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.
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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.
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 meson.
CKM fitter
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