1. Heavy-light weak matrix elements using all-to-all propagators
Shunsuke Negishi, Tetsuya Onogi (YITP, Kyoto U.)
Hideo Matsufuru (KEK)
October meeting of
pacific region physics community meetings

2. The goal of this work coupling with all-to-all propagators with HQET
Fundamental parameter in heavy meson effective theory
Important for and determination
Improve the accuracy compared to previous calculations
A step towards the study full QCD and 1/M correction.

3. CKM fitter http://ckmfitter.in2p3.fr
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
Unquenching (common problem)
Chiral lmit (common problem)
Heavy quark
- discretization error
- pertubative error
HQET are free from these problems and
give a very good reference point for B meson.
CKM fitter

4. In this work we focus on coupling.
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.

5. Why coupling is important?
Effective chiral lagrangian for heavy meson
preserving chiral and heavy quark symmetry.
If term included,
fundamental low energy constant
controls the chiral log
also appears in form factors

6. Chiral behavior of
Soft pion relation for form factor through
Precise determination of is very useful
in precise determination of

7. How to obtain coupling? Compute the form factor at zero recoil
From ChPT, one can relate it to the coupling
In the static limit it simplifies to
Light-light axial verctor current

8. Previous results Becirevic et al.
In full QCD we need significant improvement for precision, given limited configurations.
Particularly, for more serious if we study 1/M dependence.
Numerical techniques for precision is crucial

9. 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)

10. Simulation Methods This is important for low-mode dominance
Gauge: plaquette
Light: O(a)-improved Wilson
Heavy: Static quark with HYP link V(x,0)
Operator: light source, sink smeared
Parameters:
This is important for low-mode dominance

11. 2pt function Averaged over for both lower and higher modes “lower”
Random noise
“lower”
“higher”
Averaged over for both lower and higher modes

12. Results for 2pt function
All-to-all heavy-light propagator with 32 configs.
(preliminary)
M. Della Morte et al. JHEP08(2005)051
“low” becomes dominant

13. 3pt function “low-low” “low-high” “high-low” “high-high”
Averaged over for “low-low”
Not averaged over for other three

14. Results for 3pt functions
“low-low” is the dominant,
“low-high” is the subdominant contribution

15. Results for

16. Results for B*B pi
This does not contribute after summing over space

17. Our result Comparison with Becirevic et al. JHEP02(2004)016
Our result with 32 confs. is consistent with Becirevic et al.
Our result

18. Summary and future prospects
All-to-all propagator enables
high precision determination of
Further improvement should be achieved with
average for high modes, optimization of smearing function.
chiral limit, full QCD,1/M correction should be studied.
Application to flavor physics