目前形势和我们的任务

Unquenched conf.s on the market (incomplete)
❖ MILC conf.s:
Symanzik improved gauge (2+1) flavor improved staggered (AsqTad)
❖ CP-PACS/JLQCD conf.s:
RG improved gauge (2+1) flavor Clover quark
How to do lattice QCD
❖ Monte Carlo simulations
Z D DDU exp SLQCD [ , ,U ] DU exp Sg [U ] det M [U ]
视为概率密度
Quench: 略去det
格点QCD近年进展
格点QCD的几个困难问题
❖ Chirality ❖ Quenched vs. unquenched ❖ Finite density ❖ Heavy quark ❖ Broad resonance ❖ ……
All boils down to not enough computers!
The trouble of being chiral
❖ RBC & UKQCD conf.s:
DBW2 improved gauge 2 flavor domain wall fermion
Running parameters
Name
Comparisons
Current status
Wilson
Simple well-defined
No chiral symm.
All lattice QCD calculations involving light quarks need chiral extrapolation
❖ Chiral fermions (more fundamental problem)
How to put chiral fermions on the lattice How to define chiral gauge theory non-perturbatively, etc.
S f [ , ,U ] x M [U ]x, y y
x, y
Z D DDU exp SLQCD [ , ,U ]
Why lattice QCD
❖ 强相互作用的非微扰特性 ❖ 格点QCD是系统处理QCD非微扰性质的
理论方法
非微扰的定义（path integral） 非微扰的计算（Monte Carlo）
❖ Wilson fermion
Improved Wilson
❖ Staggered (Kogut-Susskind) fermion
Improved Staggered
❖ Domain wall fermion ❖ Overlap fermion
Chiral fermions on the lattice
Chirality Becomes More Complicated on Lattices
❖Chiral properties of LQCD depend on
The type of lattice fermion being used
Quenched or unquLeabharlann Baidunched
Variants of lattice fermions
….
❖ 我国格点QCD 的情况
参加的人员
已经完成的工 作
正在进行的工 作
计算资源
❖ 总结与展望
格点QCD简介
What is lattice QCD
❖ QCD的场变量定义在四维格点上
夸克场 物质场定义在site上 部分 规范场定义在link上
规范场部分
❖ 格点提供了自然的紫外、红外截断
SLQCD [ , ,U ] S g [U ] S f [ , ,U ]
Quenched vs. unquenched
❖ Quenched
Ignore (apart from trivial renormalization effects) internal quark loops
Gauge field conf. generated via pure gauge
❖ Chiral extrapolation (practical problem)
All lattice simulations (quenched or unquenched) are performed at a quark mass value higher than that of physical u&d quarks.
running unquenched
unquenching costly
Staggered DW/Overlap
Simple Partial chiral symm. Unquenching not so costly
chiral
Taste does NOT taste good!
Back to physics …
目前形势和 我们的任务
－－近年格点QCD进展
北京大学物理学院理论物理所 刘川
Outline
❖ 格点QCD简介
What, Why & How
❖ 国际上的进展
Chiral Quenching Finite density Heavy quark Broad resonance
❖ Chiral symmetry is crucial for QCD
❖ Nielsen-Ninomiya (no-go) theorem
Locality
Hermitian
Correct Chiral:
low-momentum5 ,lDimit
0
NO fermion matrix D can satisfy all of the above 4 conditions
❖ Partially quenched
Gauge field conf. generated at some sea quark mass values Valance quark mass NOT equal to sea quark mass
❖ Unquenched
Just don’t quench!