悼念罗向前教授

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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 ….

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物质场定义在 site上规范场定义在 link上

格点提供了自然的紫外、红外截断

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规范场部分夸克场部分

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）

How to do lattice QCD

Monte Carlo simulations

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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 tonot enough computers!

The trouble of being chiral

Chiral symmetry is crucial for QCD Nielsen-Ninomiya (no-go) theorem

Locality Hermitian Correct low-momentum limit Chiral:

NO fermion matrix D can satisfy all of the above 4 conditions

0,5 D

Chirality Becomes More Complicated on Lattices

Chiral properties of LQCD depend onThe type of lattice fermion be

ing usedQuenched or unquenched

Variants of lattice fermions

Wilson fermion Improved Wilson

Staggered (Kogut-Susskind) fermion Improved Staggered

Domain wall fermionOverlap fermion

Chiral fermions on the lattice

Chiral extrapolation (practical problem) All lattice simulations (quenched or unquenched) ar

e performed at a quark mass value higher than that of physical u&d quarks.

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-perturbativel

y, etc.

Quenched vs. unquenched Quenched

Ignore (apart from trivial renormalization effects) internal quark loops

Gauge field conf. generated via pure gauge

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!

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

RBC & UKQCD conf.s: DBW2 improved gauge 2 flavor domain wall fermion

Running parameters

Comparisons Name Current

status

Wilson Simplewell-defined

No chiral symm.unquenching costly

running unquenched

Staggered SimplePartial chiral symm.Unquenching not so costly

Taste does NOT taste good!

running unquenched

DW/Overlap chiral costly Mostly quenched

Finite density

Reweighting Taylor expansion Canonical ensemble

See: Lattice QCD at Finite Density

Christian SchmidtPoS (LAT2006) 021 hep-lat/06

10116

What about heavy quarks

Mass heavy, ma not much less than 1 Need improved action Better use anisotropic lattice Most difficult is heavy+light system Maybe DWF/overlap will help?

Fat resonances

格点计算中通常的谱计算给出哈密顿量的本征值

对于稳定的（或者足够苗条的）强子，格点计算的数值与强子的 pole mass接近

宽共振怎么办？

Some randomly (or not so randomly) selected results

Gold-plated quantities

Quark masses

Quenched light hadron spectrum

Unquenched results

2+1 flavor light hadron spectrum and quark masses with the $O(a)$ improved Wilson-clover quark formalismCP-PACS & JLQCD , PoS(LAT2006)181, hep-lat/0610050

非纯学术方面的进展对计算资源投入的加大

资金的投入机器的更新

合作组的形成格点资源的共享与交流

我国格点 QCD的现状

看来，咱也得搞互助组啊！

嗯那，以后还有初级社、高级社、…

China Lattice QCD Collaboration (CLQCD)

Faculty Members:Jian-Ping Ma ITP, CASChuan Liu Peking UniversityXiang-Qian Luo Zhongshan UniversityYubin Liu Nankai UniversityJianbo Zhang Zhejiang UniversityYing Chen IHEP, CAS

Graduate Students (not complete):Ming Gong, Xin Li, Guozhan Meng, Ji-Yuan Niu, Xu Feng, Song He(PKU), Xiang-Fei Meng (NKU), Gang Li, Yuan-Jiang Zhang (IHEP) , etc.

已经完成的一些工作 胶球谱 粲物理和其他强子谱 强子－强子相互作用 Overlap fermion 不对称格点上的 DWF/Overlap （主要应

用于含有粲夸克强子） 有限温度、有限密度

glueball

Glueball Spectrum and Matrix Elements on Anisotropic LatticesY. Chen, A. Alexandru, S.J. Dong, T. Draper, I. Horvath, F.X. Lee, K.F. Liu, N. Mathur, C. Morningstar, M. Peardon, S. Tamhankar, B.L. Young, J.B. Zhang Phys.Rev. D73 (2006) 014516, hep-lat/0510074

Monte Carlo study of glueball masses in the Hamiltonian limit of SU(3) lattice gauge theoryAuthors: Mushtaq Loan, Xiang-Qian Luo, Zhi-Huan Luo Int.J.Mod.Phys. A21 (2006) 2905 hep-lat/0503038

The First Calculation for the Mass of the Ground $4^{++}$ Glueball State on LatticeAuthors: Da Qing Liu, Ji Min Wu Mod.Phys.Lett. A17 (2002) 1419 hep-lat/0105019

Scalar and Tensor Glueballs on Asymmetric Coarse LatticesAuthors: C. Liu Nucl.Phys.Proc.Suppl. 94 (2001) 255 hep-lat/0010007

A Lattice Study of the Glueball SpectrumAuthors: Chuan Liu Chin.Phys.Lett. 18 (2001) 187 hep-lat/0004018

Finite density Phase structure of lattice QCD with Wilson and Neuberger quarks at finite temperature a

nd densityXiang-Qian Luo, He-Sheng Chen, Xiao-Lu Yu PoS LAT2005 (2005) 151, hep-lat/0510102

Phase diagram of QCD at finite temperature and chemical potential from lattice simulations with dynamical Wilson quarksHe-Sheng Chen, Xiang-Qian Luo Phys.Rev. D72 (2005) 034504 hep-lat/0411023

Chiral condensate of lattice QCD with massless quarks from the probability distribution function methodXiang-Qian Luo Phys.Rev. D69 (2004) 076012 hep-lat/0409032

Tricritical point of lattice QCD with Wilson quarks at finite temperature and densityXiang-Qian Luo Phys.Rev. D70 (2004) 091504, hep-lat/0405019

Hamiltonian lattice quantum chromodynamics at finite density with Wilson fermionsYi-Zhong Fang, Xiang-Qian Luo Phys.Rev. D69 (2004) 114501 hep-lat/0210031

Responses of quark condensates to the chemical potentialO. Miyamura, S. Choe, Y. Liu, T. Takaishi, A. NakamuraPhys.Rev. D66 (2002) 077502, hep-lat/0204013

Screening mass responses to the chemical potential at finite temperatureS. Choe, Ph. de Forcrand, M. García Pérez, S. Hioki, Y. Liu, H. Matsufuru, O. Miyamura, A. Nakamura, I.-O. Stamatescu, T. Takaishi, T. Umeda, Nucl.Phys.Proc.Suppl. 106 (2002) 462

Charm

Quenched charmonium spectrumS. Choe, Ph. de Forcrand, M. Garcia Perez, Y. Liu, A. Nakamura, I.-O. Stematescu, T. Takaishi, T. Umeda JHEP 0308 (2003) 022 hep-lat/0307004

Static Quark Potential and the Renormalized Anisotropy on Tadpole Improved Anisotropic LatticesWei Liu, Ying Chen, Ming Gong, Xin Li, Chuan Liu, Guozhan Meng Mod.Phys.Lett. A21 (2006) 2313 hep-lat/0603015

Gluonic excitation of non-exotic hybrid charmonium from lattice QCD Xiang-Qian Luo, Yan Liu Phys.Rev. D74 (2006) 034502; Erratum-ibid. D74 (2006) 039902 hep-lat/0512044

Estimate of the charmed 0-- hybrid meson spectrum from quenched lattice QCD Yan Liu, Xiang-Qian Luo Phys.Rev. D73 (2006) 014516 hep-lat/0511015

Charmonium Spectrum from Quenched QCD with Overlap FermionsS. Tamhankar, A. Alexandru, Y. Chen, S.J. Dong, T. Draper, I. Horvath, F.X. Lee, K.F. Liu, N. Mathur, J.B. Zhang Phys.Lett. B638 (2006) 55 hep-lat/0507027

Charm & others spectrum

Quenched Charmed Meson Spectra using Tadpole Improved Quark Action on Anisotropic LatticesLiuming Liu, Shiquan Su, Xin Li, Chuan Liu Chin.Phys.Lett. 22 (2005) 2198 hep-lat/0505006

A Numerical Study of Improved Quark Actions on Anisotropic LatticesShiquan Su, Liuming Liu, Xin Li, Chuan Liu Int.J.Mod.Phys. A21 (2006) 1015, hep-lat/0412034

A study of pentaquarks on the lattice with overlap fermionsN. Mathur, F.X. Lee, A. Alexandru, C. Bennhold, Y. Chen, S.J. Dong, T. Draper, I. Horvath, K.F. Liu, S. Tamhankar, J.B. Zhang Phys.Rev. D70 (2004) 074508, hep-ph/0406196

Roper Resonance and S_{11}(1535) from Lattice QCDN. Mathur, Y. Chen, S.J. Dong, T. Draper, I. Horváth, F.X. Lee, K.F. Liu, J.B. Zhang Phys.Lett. B605 (2005) 137 hep-ph/0306199

Domain wall/overlap Massive Domain Wall Fermions on Four-dimensional Anisotropic Lattices

Xu Feng, Xin Li, Wei Liu, Chuan Liu JHEP 0608 (2006) 060 Nonperturbative renormalization of composite operators with overlap fermions

J.B. Zhang, N. Mathur, S.J. Dong, T. Draper, I. Horváth, F.X. Lee, D.B.Leinweber, K.F. Liu, A.G. Williams Phys.Rev. D72 (2005) 114509 hep-lat/0507022

The Negativity of the Overlap-Based Topological Charge Density Correlator in Pure-Glue QCD and the Non-Integrable Nature of its Contact PartI. Horvath, A. Alexandru, J.B. Zhang, Y. Chen, S.J. Dong, T. Draper, K.F. Liu, N. Mathur, S. Tamhankar, H.B. Thacker Phys.Lett. B617 (2005) 49 hep-lat/0504005

Inherently Global Nature of Topological Charge Fluctuations in QCDI. Horvath, A. Alexandru, J.B. Zhang, Y. Chen, S.J. Dong, T. Draper, F.X. Lee, K.F. Liu, N. Mathur, S. Tamhankar, H.B. Thacker Phys.Lett. B612 (2005) 21 hep-lat/0501025

Chiral Logs in Quenched QCDY. Chen, S.J. Dong, T. Draper, I. Horváth, F.X. Lee, K.F. Liu, N. Mathur, J.B. Zhang Phys.Rev. D70 (2004) 034502 hep-lat/0304005

Low-Dimensional Long-Range Topological Charge Structure in the QCD VacuumI. Horvath, S.J. Dong, T. Draper, F.X. Lee, K.F. Liu, N. Mathur, H.B. Thacker, J.B. Zhang Phys.Rev. D68 (2003) 114505 hep-lat/0302009  

Chiral Properties of Pseudoscalar Mesons on a Quenched $20^4$ Lattice with Overlap FermionsS.J. Dong, T. Draper, I. Horvath, F.X. Lee, K.F. Liu, J.B. Zhang Phys.Rev. D65 (2002) 054507 hep-lat/010

8020

Hadron-hadron scattering

Two Particle States in a Box and the $s$-Matrix in Multi-Channel ScatteringChuan Liu, Xu Feng, Song He Int.J.Mod.Phys. A21 (2006) 847 hep-lat/0508022

Two Particle States and the $S$-matrix Elements in Multi-channel ScatteringSong He, Xu Feng, Chuan Liu JHEP 0507 (2005) 011 hep-lat/0504019

I=2 Pion scattering length with improved actions on anisotropic latticesXining Du, Guangwei Meng, Chuan Miao, Chuan Liu Int.J.Mod.Phys. A19 (2004) 5609 hep-lat/0404017

Two Particle States in an Asymmetric Box and the Elastic Scattering PhasesXu Feng, Xin Li, Chuan Liu Phys.Rev. D70 (2004) 014505 hep-lat/0404001

Lattice study on kaon pion scattering length in the $I=3/2$ channelChuan Miao, Xining Du, Guangwei Meng, Chuan Liu Phys.Lett. B595 (2004) 400 hep-lat/0403028

Two Particle States in an Asymmetric BoxXin Li, Chuan Liu Phys.Lett. B587 (2004) 100 hep-lat/0311035

Lattice study on kaon nucleon scattering length in the I=1 channelGuangwei Meng, Chuan Miao, Xining Du, Chuan Liu Int.J.Mod.Phys. A19 (2004) 4401 hep-lat/0309048

Calculating the I=2 Pion Scattering Length Using Tadpole Improved Clover Wilson Action on Coarse Anisotropic LatticesChuan Liu, Junhua Zhang, Ying Chen, J.P. Ma Nucl.Phys. B624 (2002) 360 hep-lat/0109020

几个正在进行的工作

Charmonium spectrum ( excited states, hybrids, etc.)

Pion-pion scattering phase shift Lattice QCD at finite temperature and fi

nite density Massive DWF applied to charmed hadr

ons

Charmonia spectra

Motivation A series of heavy meson states of open-charm and clos

ed-charm have been observed recently.

Y(4260) (likely a 1--,hybrid charmonium?)

X(3872) (most likely 1++, but refuses to fit into the 2P state predictions of non-relativistic quark models ).

Many model-dependent theoretical interpretation of th

e newly observed meson states.

Charmonia spectra

This figure and table on next page illustrate the results from the finest lattice.

X(3872)?

Summary to the charmonium spectrum study

1. With SEB, the masses of the excited states can be reliably derived from charmonium two-point functions.

2. The masses of 2S charmonium states agrees well with experimental data.

3. The masses of 2P charmonium states obtained in this work are 3.798( 70), 3.827(50), and 3.799(60) for 0++, 1++ and 1+- states, respectively. Given 1++ for X(3872), 2P(1++) is consistent with X(3872) in mass.

4. Masses of hybrid charmonia with exotic quantum numbers can be derived reliably. Howver for hybrid charmonia with non-exotic quantum numbers, it still a tough job.

5. In particular, we have not observed a clear hybrid states with mass around 4260 MeV.

Pion-Pion Scattering Phase Shift

The study of hadron-hadron scattering is helpful for understanding the low-energy structure of QCD.

Luscher’s formula relates the pion-pion phase shift in the continuum to the energy of two-pion system in a finite cubic box,

);1()(tan

200

2/3

qZ

qk

222 kmE kL

q2

can be calculated directly on lattice. )(kE

计算资源的情况Deepcomp 680

0Dawning 4000A NKStars

Speed 4.2Tflop

(Linpack)

10.2 Tflops(peak)

8 Tflops (Linpack)

4.7 Tflops (peak)

3.2 Tflops (Linpack)

Node Numbers 197 Compu,

4 I/O, 1 Console

512 Compu.,

16 I/O, 4 Console

384 Compu.

12 I/O, 4 Console

Processors 4 CPU/node

(1.3GHz Intel

Itanium, 8/16GB)

4 CPU/node

(2.4 GHz AMD Opereron, 8GB)

2 CPU/node

(IBM Xserver, 2GB)

Network Globus, MPI-G;

Oracle 10G

Myrinet 2000 Myrinet

Hard Disk 80TB 20TB 54TB

未来（近期）的计算资源 Supercomputing Center of CAS (SCCA

S) A 100 Tflops new computer is planned and expe

cted to be available in 2008.

Shanghai supercomputer Center (SSC) A 100 Tflops new computer is expected to be av

ailable in 2008.

Four things needed…

ppmm

Well-prepared project

sExperienced people Stable

machines

money

总结与展望

Summary & outlook

格点 QCD近年来在各个方面有相当迅速的发展（手征性质、 unquenched计算、有限密度等等）

随着对于格点 QCD的不断加大投入，随着大型合作组的形成以及国际交流、数据共享的发展，格点 QCD将会更迅速发展

我国目前的格点 QCD合作组刚刚起步，我们有了一个不错的开始，希望有一个更好的未来。

谢谢大家！