Download Lattice QCD in Mainland China: Status and Perspectives

Lattice QCD in China
Jianbo Zhang
Department of Physics, Zhejiang University
Sept. 20, 2006
Outline
1. China Lattice QCD Collaboration
2. Selected Topics
Charmonium Spectrum
Pion-Pion Scattering Phase Shift
3. Future Perspectives
1. China Lattice QCD Collaboration
An Introduction
• Members
Faculty Members:
Ying Chen
Chuan Liu
Yubin Liu
Xiang-Qian Luo
Jian-Ping Ma
Jianbo Zhang
Institute of High Energy Physics, CAS
Peking University
Nankai University
Zhongshan University
Institute of Theoretical Physics, CAS
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.
• Computers available
Deepcomp 6800
Dawning 4000A
NKStars
Speed
4.2Tflop
(Linpack)
10.2 Tflops(peak)
8 Tflops (Linpack)
4.7 Tflops (peak)
3.2 Tflops (Linpack)
Node Numbers
197 Comp. node
4 I/O, 1 Console
512 Comp. node
16 I/O, 4 Console
384 Compu. node
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
At present, Roughly 0.6-1.0 million CPUhours are allocated per year.
• Forthcoming Machines
Supercomputing Center of CAS (SCCAS)
A 100 Tflops 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.
•
Projects in progress
Charmonium spectrum ( excited states, hybrids, etc.)
Pion-pion scattering phase shift
Lattice QCD at finite temperature and finite density
2. Selected Topics
Charmonium Spectrum
• Motivation
A series of heavy meson states of open-charm and closed-charm
have been observed recently.

X(3872) (most likely
, but refuses to fit into the 2P
state predictions of non-relativistic quark models ).
1
Y(4260) (likely a
  hybrid charmonium?)
1
Many model-dependent theoretical interpretation of the newly
observed meson states.
( Review: Swanson, Phys. Rep. 429 (2006) 243-305 )
• Lattice Calculations (Quenched)
Tadpole improved Symanzik’s gauge action.
Tadpole improved Clover fermions action.
Anisotropic lattices.

as (fm)
L T
3
Las
(fm)
#config
2.4
0.222(1)
83  40
1.78
200
2.6
0.176(1)
123  64
2.11
200
2.8
0.139(1)
163  80
2.22
200
• Lattice interpolation field operators
The operators are
constructed by quark
bilinear sandwiched
with Gamma matrices
and color fields.
When calculating the
two-point functions,
the disconnected
diagrams are
neglected by
assuming the OZI
suppression.
• 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.
C (t )  Wi e  mit
i
An Example of SEB
•
Here is an example for the fitting
procedure in the vector channel (fourmass-term fit), where t_max =68, t_1=50,
t_2=30, t_3=15
•
Fit model
C (t )  Wi e  mit
i
•
The mass terms are fitted one by one from
low to high
1. Choose the t_max.
2. Varying t_1 towards small value, one-mass term fitting in the interval [t_1,t_max],
until the χ2/dof blows up ;
3. Add the second mass term at t_2=t_1-1.
Varying t_2, two-mass-term fitting in the
interval [t_2,t_max] with the first state
constrained by the fitted parameters in
Step 2.
4. When χ2/dof blows up again at the last t_2,
and add the third state at t_3=t_2-1.
5. Repeat.
6. The latest state is generally taken as a
garbage can and therefore not a realistic
state.
++
0
Three-mass-term fitting
procedure in 0++ channel
meff
1
C (t )
 ln
a C (t  1)
Red points are data from
the simulation, the blue
curve is the plot of fit
model with fitted
parameters.
1++
Three-mass-term fitting
procedure in 1++ channel
Red points are data from
the simulation, the blue
curve is the plot of fit
model with fitted
parameters.
1+Three-mass-term fitting
procedure in 1+- channel
Red points are data from
the simulation, the blue
curve is the plot of fit
model with fitted
parameters.
• 1S, 2S and 1P, 2P, 3P states
This figure and table on next page illustrate the results from the
finest lattice. The continuum extrapolation will be taken later
• 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.
• Hyperfine splitting
M  M ( J / )  M (c )
• Continuum limit
extrapolation performed.
M  83(3) MeV
• It is smaller than the
experiment value.
• The result is in agreement
with previous (quenched)
works
•
c cg
hybrids (with exotic quantum numbers)
M (1 )  4.30(7)GeV
M (0 )  4.67(17)GeV
•These results are in
agreement with
previous quenched
lattice QCD results.
M (0 )  5.88(15)GeV
• Non-exotic
c cg hybrids and conventional charmonium
• Masses from the four-mass-term SEB fitting of hybrid-hybrid (HH) and mesonmeson (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
• No convincing results of masses of non-exotic hybrids can be derived in our work.
• A summary to the charmonium spectrum study
1.
2.
3.
4.
5.
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.
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 more soundly, since there are no admixtures of
conventional charmonia. However for hybrid charmonia with noexotic quantum numbers, it still a tough task to separate them
from conventional charmonia unambiguously in the present lattice
study.
Specifically, we have not observed a clear hybrid states with
mass around 4260 MeV in the vector channel.
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,
tan  (k ) 
 3/ 2q
Z 00 (1; q 2 )
where Z 00 (1; q 2 )
is modified zeta-function and can be
numerically calculated. q and k are related to the two-pion
energy by
•
E (k )
q
L
k
2
and
E  2 m2  k 2
at different k can be calculated directly on lattice.
• We work on the spatially asymmetric lattices ,
so that there are more non-degenerate non-zero
three momentum modes.
. Luscher’s formula in a finite cubic box needs to be
( L Lxη
 L  L) LxL),
modified. For lattice of spatial size (η
1
2
with η1 and η2 equal or great than 1
1
2
(1L (21L  L)
 3/ 212 q
tan  (k ) 
Z 00 (1; q 2 ,1 ,2 )
. Z00(1, q2,η1,η2) represents the modified zeta
function for the asymmetric box, and can be calculated
numerically.
Here is the preliminary results obtained at two beta
values. More work is in progress
3. Future Perspectives
• Numerical study of lattice QCD with dynamical
fermions.
• Lattice QCD at finite temperature and finite
density.
How far we can go depends on the computing
resource available.
• A way out ---- International collaboration
Thank You!
谢谢!