悼念罗向前教授

1. 悼念罗向前教授

2. Back to physics …

3. 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

4. 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 Outline

5. 格点QCD简介

6. 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 夸克场部分 规范场部分

7. 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）

8. How to do lattice QCD • Monte Carlo simulations 视为概率密度 Quench: 略去det

9. 格点QCD近年进展

10. 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!

11. 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

12. Chirality Becomes More Complicated on Lattices • Chiral properties of LQCD depend on • The type of lattice fermion being used • Quenched or unquenched

13. Variants of lattice fermions • Wilson fermion • Improved Wilson • Staggered (Kogut-Susskind) fermion • Improved Staggered • Domain wall fermion • Overlap fermion

14. 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. • 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.

15. 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!

16. 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

17. Running parameters

18. Comparisons

19. Finite density • Reweighting • Taylor expansion • Canonical ensemble See: Lattice QCD at Finite DensityChristian Schmidt PoS (LAT2006) 021 hep-lat/0610116

20. 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?

21. 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？

22. Some randomly (or not so randomly) selected results

23. Gold-plated quantities

24. Quark masses

25. Quenched light hadron spectrum

26. 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

27. 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

28. 我国格点QCD的现状

29. 嗯那，以后还有初级社、高级社、… 看来，咱也得搞互助组啊！

30. China Lattice QCD Collaboration (CLQCD) Faculty Members: Jian-Ping Ma ITP, CAS Chuan Liu Peking University Xiang-Qian Luo Zhongshan University Yubin Liu Nankai University Jianbo Zhang Zhejiang University Ying 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.

31. 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

32. 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

33. Finite density • Phase structure of lattice QCD with Wilson and Neuberger quarks at finite temperature and 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

34. 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

35. 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. ZhangPhys.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

36. Domain wall/overlap • Massive Domain Wall Fermions on Four-dimensional Anisotropic LatticesXu Feng, Xin Li, Wei Liu, Chuan LiuJHEP 0608 (2006) 060 • Nonperturbative renormalization of composite operators with overlap fermionsJ.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. ZhangPhys.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/0108020

37. 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

38. 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 finite density • Massive DWF applied to charmed hadrons

39. Charmonia spectra • Motivation A series of heavy meson states of open-charm and closed-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 the newly observed meson states.

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

41. X(3872)?

42. Summary to the charmonium spectrum study • With SEB, the masses of the excited states can be reliably derived from charmonium two-point functions. • The masses of 2S charmonium states agrees well with experimental data. • 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. • 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. • In particular, we have not observed a clear hybrid states with mass around 4260 MeV.

43. 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, can be calculated directly on lattice.

44. 计算资源的情况

45. 未来（近期）的计算资源 • Supercomputing Center of CAS (SCCAS) • A 100 Tflopsnew computer is planned and expected to be available in 2008. • Shanghai supercomputer Center (SSC) • A 100 Tflopsnew computer is expected to be available in 2008.

46. Four things needed… ppmm Well-prepared projects money Experiencedpeople Stable machines

47. 总结与展望

48. 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。

49. 谢谢大家！