非等方格子上での クォーク作用の非摂動繰り込み

Presentation on theme: "非等方格子上での クォーク作用の非摂動繰り込み"— Presentation transcript:

1 非等方格子上での クォーク作用の非摂動繰り込み
非等方格子上での 　クォーク作用の非摂動繰り込み　　 梅田貴士、大野木哲也、深谷英則（京大基研） 根岸俊輔（京大理）　松古栄夫（KEK) 　　　　 ２００５年3月２７日　 日本物理学会（東京理科大学野田キャンパス） 日本物理学会　２００５年３月２７日

2 Motivation Hadronic matrix elements with high precision
Relativistic quark Fermilab approach, AKT NRQCD Nonperturbtive HQET (Alpha collab.) Our motivation: 　　study the heavy quark action on anisotropic lattice 日本物理学会　２００５年３月２７日

3 Why anisotropic lattice ?
( anisotropy: ) Our expectation: for ,( not necessarily ) mass dep. of parameters in the action are so small. Nonperturbative renormalization techniqe (based on the PCAC relation) is possible. 日本物理学会　２００５年３月２７日

4 Parameters we have to tune
Quark action on the anisotropic lattice: ( , , ) should be determined. is to control the O(ma) error. 日本物理学会　２００５年３月２７日

5 Is mass dependence really small ?
One-loop calc. for , Harada et al. Phys. Rev. D64 (2001) Nonperturbative calc. for Matsufuru et al., Phys. Rev. D64(2001)114503 Harada et al., Phys. Rev. D66(2002)014509 Application to Heavy-light decay constant Matsufuru et al., hep-lat/ Encouraging result for fully O(a) improvement ! 日本物理学会　２００５年３月２７日

6 Fully nonperturb. O(a) improvement
We have to tune ( ) simultaneously. tuning fixed Using Physical isotropic condition (spatial meson mass) (temporal meson mass) vs (=4) with tree-level & Well determined ! 日本物理学会　２００５年３月２７日

7 Fully nonperturb. O(a) improvement
tuning We have to tune ( ) simultaneously. fixed Schrödinger Functional method (PCAC relation) 日本物理学会　２００５年３月２７日

8 Fully nonperturb. O(a) improvement
Schrödinger Functional method (PCAC relation) boundary C’ Constant Chromo-Electric background field Improvement cond. for boundary C 日本物理学会　２００５年３月２７日

9 Fully nonperturb. O(a) improvement
Schrödinger Functional method (PCAC relation) at high beta consistent with (mean-field) tree-level dependence is weak ( only chromo-elect. field is induced ) Well determined ! 日本物理学会　２００５年３月２７日

10 Fully nonperturb. O(a) improvement
We have to tune ( ) simultaneously. fixed tuning (1) Self-dual background field ?? 日本物理学会　２００５年３月２７日

11 Fully nonperturb. O(a) improvement
We have to tune ( ) simultaneously. fixed tuning (2) Constant Chromo-Magnetic background field causes oscillating modes from doublers 日本物理学会　２００５年３月２７日

12 Fully nonperturb. O(a) improvement
We have to tune ( ) simultaneously. fixed tuning (2) Constant Chromo-Magnetic background field causes oscillating modes from doublers 日本物理学会　２００５年３月２７日

13 Fully nonperturb. O(a) improvement
(2) Constant Chromo-Magnetic background field (Dirichlet) (Neumann) (Neumann) (Dirichlet) 日本物理学会　２００５年３月２７日

14 Summary Outlook Anisotropic lattice is efficient
for heavy quark physics in practical. , can be determined. could be determined. Outlook Application to heavy-light matrix elements.  High precision comp. actually possible ? Extension to dynamical QCD. 日本物理学会　２００５年３月２７日

15 Contents Nonperturbative improvement
for anisotropic lattice quark action Motivation tree-level improved results Nonperturbative improvement Summary & Outlook 日本物理学会　２００５年３月２７日

16 Is mass dependence really small ?
Application to Heavy-light decay constant Matsufuru et al., hep-lat/ Our result vs ALPHA’s result Scaling violation is small ↓ is under control Encouraging result for fully O(a) improvement ! 日本物理学会　２００５年３月２７日