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 ……
….
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 ]
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!
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-
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）
Chiral: 5 ,D 0
NO fermion matrix D can satisfy all of the above 4 conditions
Chirality Becomes More Complicated on Lattices
Chiral properties of LQCD depend on
The type of lattice fermion being used
Quenched or unquenched
Variants of lattice fermions
Wilson fermion
Improved Wilson
Staggered (Kogut-Susskind) fermion
All boils down to not enough computers!
The trouble of being chiral
Chiral symmetry is crucial for QCD Nielsen-Ninomiya (no-go) theorem
Locality Hermitian Correct low-momentum limit
RBC & UKQCD conf.s:
DBW2 improved gauge 2 flavor domain wall fermion
Running parameters
Comparisons
NameΒιβλιοθήκη Current status
Wilson
Simple well-defined
No chiral symm.
running unquenched
unquenching costly
Staggered
Simple
Partial chiral symm.
Taste does NOT taste good!
running unquenched
Unquenching not so costly
Improved Staggered
Domain wall fermion Overlap fermion
Chiral fermions on the lattice
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.
悼念罗向前教授
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
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
perturbatively, etc.
Quenched vs. unquenched
Quenched
Ignore (apart from trivial renormalization effects) internal quark loops
Gauge field conf. generated via pure gauge