1. Recent Activities of CLQCD J.P. Ma ITP, Academia Sinica, Beijing Talk given at NTU, 0.1.06.2007

2. Outline 1. CLQCD 2. Selected Topics Charmonium Spectrum Pion-Pion Scattering Phase Shift 3. Future Interests

3. 1. CLQCD CLQCD: Chinese Lattice QCD Collaboration, exists since July, 2006, roughly. People: Faculty Members: Ying Chen Institute of High Energy Physics, CAS Chuan Liu Peking University Yubin Liu Nankai University Xiang-Qian Luo Sun Yat- Sen University Jian-Ping Ma Institute of Theoretical Physics, CAS Jianbo Zhang Zhejiang University Graduate Students (not complete): Ming Gong (PKU), Xin Li (PKU), Ji-Yuan Liu (PKU), Xiang-Fei Meng (NKU), Gang Li (IHEP), Yuan-Jiang Zhang (IHEP), …………….etc.

4. Deepcomp 6800Dawning 4000ANKStars Speed4.2Tflop (Linpack) 10.2 Tflops(peak) 8 Tflops (Linpack) 4.7 Tflops (peak) 3.2 Tflops (Linpack) Node Numbers197 Compu, 4 I/O, 1 Console 512 Compu., 16 I/O, 4 Console 384 Compu. 12 I/O, 4 Console Processors4 CPU/node (1.3GHzIntel Itanium, 8/16GB) 4 CPU/node (2.4 GHz AMD Opereron, 8GB) 2 CPU/node (IBM Xserver, 2GB) NetworkGlobus, MPI-G; Oracle 10G Myrinet 2000Myrinet Hard Disk80TB20TB54TB Machines: At present, Roughly 0.6-1.0 million CPUhours are allocated per year.

5. Forthcoming Machines Supercomputing Center of CAS (SCCAS) A 100 ~ 200Tflops new computer is planned and expected to be available in 2008. Shanghai supercomputer Center (SSC) A 100 Tflops new computer is expected to be available in 2008.

6. Current Activities: 1. Software for unquenching simulation 2. Charmonium spectrum and charmed hadrons 3. Scattering length and phase 4. ……………….

7. 2. Selected Topics Charmonium Spectrum Parts of results in the papers of CLQCD: hep-lat/0701021, hep-lat/0703015

8. Motivation A series of heavy meson states of open-charm and closed-charm have been observed recently(XYZ…) Y(4260) (likely a hybrid charmonium?) X(3872) (most likely, 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.

9. Lattice Formalism Anisotropic lattices: with finer lattice in time direction. It is very helpful to measure large energy of a system. Tadpole improved Symanzik’s gauge action. Tadpole improved Clover fermion action. (fm) #config 2.4 0.222(1) 1.78 200 2.6 0.176(1) 2.11 200 2.8 0.139(1) 2.22 200

10. Lattice interpolation field operators The operators are constructed by quark bilinears sandwiched with Gamma matrices and color fields. When calculating the two- point functions, the disconnected diagrams are neglected by assuming the OZI suppression.

11. Data analysis ---Sequential Empirical Bayes Method (Y. Chen et al., hep-lat/0405001) Bayes: constrained-curve fitting prior Empirical: priors are derived from part of data **(‘prior’ means the prior information of parameters) Sequential: states fitted one by one from low to high.

12. 0++ Three-mass-term fitting prodecure in 0++ channel Red points are data from the simulation, the blue curve is the plot of fit model with fitted parameters.

13. 1++ Three-mass-term fitting prodecure in 1++ channel Red points are data from the simulation, the blue curve is the plot of fit model with fitted parameters.

14. 1+- Three-mass-term fitting prodecure in 1+- channel Red points are data from the simulation, the blue curve is the plot of fit model with fitted parameters.

15. nS states and nP states

17. 2P states and X(3872) BGS represents the predictions of Swanson et al quark model. It is difficult to change quark model, as it can reproduce precisely the masses of almost all the known charmonium states (Swanson, hep- ph/0601110). For 2P states, earlier (quenched) lattice QCD predictions (CP-PACS and Chen) of their masses are roughly 100 MeV larger than QM prediction. This may be attributed to their two-mass-term fitting where the contamination of higher states to the first excited states cannot be neglected. Our result for 2P(1++) is consistent with X(3872) in mass.

18. Continuum limit extrapolation performed. The result is in agreement with previous (quenched) works Hyperfine splitting

19. hybrids (with exotic quantum numbers) hybrids (with exotic quantum numbers) These results are in agreement with previous quenched lattice QCD results.

20. Non-exotic hybrids and conventional charmonium Masses from the four-mass-term SEB fitting of hybrid-hybrid (HH) and meson- meson (MM) correlation functions in 1– and 0-+ channels. It is understandable that the masses of the ground states are almost the same and the masses of the first excited states are consistent with each other, because the operators with the same quantum numbers can overlap to the same hadron states. The masses of the second excited state of HH are very different from those of MM Still work on them….

21. A summary to the charmonium spectrum study A summary to the charmonium spectrum study 1.With SEB, the masses of the first excited states (even the second excited states in some channel) 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.

22. 4. Masses of hybrid charmonia with exotic quantum numbers can be derived more soundly, since there are no admixtures of conventional charmonia. Howver for hybrid charmonia with no-exotic quantum numbers, it still a tough task to separate them from conventional charmonia unambiguously in the present lattice study. 5.Specifically, we have not observed a clear hybrid states with mass around 4260 MeV in the vector channel. 6. We are still working on ……….

23. Pion-Pion Scattering Phase Shift Scattering is a powerful method to study hadron structure. Many data exist in the low energy range which can not be explained with perturbative QCD and QCD! Scattering amplitudes are determined by their scattering phase shifts (Quantum Scattering Theory) Lattice QCD provides a way to study them. How ? Finite Volume……

24. In a cubic box: A momentum is quantized: A two-pion system: one with another Define: The energy of the system, can be measured with lattice QCD

25. Luescher’s formula: The phase shift: If L is large enough, one can get the scattering length: Cubic box: degenerated momentum modes! Fewer data points in a given q^2 range.

26. More data points can be obtained if one uses asymmetrical box: the degeneration can be lifted and

27. Still, tadpole improved Symanzik’s gauge action. Tadpole improved Clover fermion action. Anisotropic lattices Chiral extrapolation, continuum limit…. Etc. Isospin = 2, J=0 channel

28. Results for scattering length: Previous results:

29. The phase shift: (“physical “ results)

30. 3. Future Interests Say “good bye” to QCD without dynamical fermions Numerical study of lattice QCD with dynamical fermions. How far we can go depends on our effort and the computing resource available !!

31. Thank You! 谢谢