1
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
2
Introduction
3
(1) The fundamental parameter in the effective chiral lagrangian for heavy meson preserving chiral and heavy quark symmetry.
Why Coupling ?
4
• form factor (|Vub|)
• Chiral behavior of (|Vtd|)
(2) Useful for phenomenological applications in flavor physics
5
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
6
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:
7
Simulation methods
Cf. Negishi et al hep-lat/0612029 (nf=0)
8
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
9
Analysis of
Simultaneous fit of 2pt and 3pt functions
• As a result of the simultaneous fit for effective mass
( : Const )
10
• 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
11
“higher”“lower”
2pt function
Averaged over for both lower and higher modes
Random noise
12
“low-low” “low-high” “high-low” “high-high”
3pt function
Averaged over for “low-low”, “low-high”, “high-low”, “high-high”
13
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.
14
RESULTS• Low mode is dominant? and/or
Statistical noise is suppressed ? Plots of• Extraction of B*Bpi coupling • Chiral extrapolation
15
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.
16
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.
18
Results for
3pt/2pt Ratio for all-to-all heavy-light
=0.1430, 100 configs.
Z3/Z2 from the fit
raw data
19
Results for B*B pi at beta=1.80
This does not contribute after summing over spaceCP-PACS, Phys.Rev.D65,054505
20
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
21
Chiral extrapolation
Error of raw data is statistical only.
22
• Systematic Error estimate 1.chiral extrap. 2.perturbative. 3.disc. • Preliminary result
(2,3: order estimation)
23
Summary and Future prospects
24
• 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.
25
Comparison with other calculations
Pert. error
Stat. error
26
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
27
The End
Thank you.
28
Backup slides
29
N ev dependence of effective mass
Figure from Negishi et al hep-lat/0612029 (nf=0)
Previous work of quenched case.
30
31
All-to-all heavy-light propagator
Results for 2pt function
Effective mass plot for all-to-all heavy-light 2pt
=0.1430,100 configs.
32
Results for (1)
=0.1409, 100 configs.
Fit
3pt/2pt Ratio for all-to-all heavy-light
33
Results for (3)
=0.1445, 100 configs.
Fit
3pt/2pt Ratio for all-to-all heavy-light
34
Results for (4)
=0.1464, 100 configs.
Fit
3pt/2pt Ratio for all-to-all heavy-light
35
36
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.
37
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)
38
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.