Research Activities

The group’s major activities and goals are to carry out first principles calculation of the nucleon and vacuum structure. These calculations are based on the lattice version of the fundamental theory of the strong interaction of quarks and gluons – Quantum Chromodynamics (Lattice QCD). The quantities to be calculated for the nucleon structure include strangeness and charmness, quark and glue momenta and angular momenta, quark spin, strangeness electromagnetic form factors, axial form factor, electromagnetic form factors of proton and neutron, and neutron electric dipole moment from the theta term. The vacuum structure study entails the calculation of the chiral polarization properties of quarks in the context of thermal QCD transition and QCD with many light flavors (low energy conformality).

We use the overlap fermion, which has chiral symmetry, as the valence quarks on the 2+1 flavor domain wall fermion gauge configurations that we borrow from the Riken-Brookhaven-Columbia (RBC) Collaboration. There are 5 lattices with different lattice spacing and sea quark masses to calculate the above observables in order to carry out continuum and physical pion extrapolations with finite volume corrections in order to make predictions for the quark orbital angular momentum and glue angular momentum for future experiments, as well as to facilitate and constrain dark matter search with precise calculation of the quark contents in the nucleon.

During the last three years, quite a bit of effort has been spent on improving the inversion code which calculates the quark propagator. We have implemented smearing of the gauge field via the Hypercube Blocking (HYP)-smearing procedure which has been shown to map the gauge field closer to that of the continuum and with renormalization constants much closer to unity. This lifts up the smallest eigenvalues of the Wilson fermion in the inner do loop of the overlap fermion inversion and reduces the conjugate gradient steps by a factor of ∼ 3. We have also developed eigenvalue and eigenvector code for the overlap fermion and have been able to calculate 400 complex conjugate pairs of eigenmodes in addition to the zero modes. We have done deflation for the outer loop of the overlap inversion with these eigenmodes by projecting these eigenmodes out from the source and solving the matrix equation which is orthogonal to this low-frequency part of the Hilbert space. After this is done, we can add back the low-frequency part of the propagator with the original source since we have both the eigenvalues and eigenvectors. This is done on the fly when the quark propagators are generated. The detailed study of our approach and its speedup with the overlap valence on DWF sea is published in Phys. Rev. D 82, 114501 (2010) arXiv:1005.5424. The improvement of the nucleon correlator with low-mode substitution and the loop with low-mode average and its application in the calculation of strangeness and charmness in the nucleon has been published in Phys. Rev. D88, 014503 (2013).

Projects on DLX

Nucleon Structure and Hadron Spectroscopy

Over the past several years, we have initiated a long-term project to study nucleon form factors, hadron spectroscopy, and decay constants with valence overlap fermion on 2+1-flavor dynamical gauge configurations with domain-wall fermions produced by the the Riken-Brookhaven-Columbia (RBC) Collaboration, the UKQCD Collaboration of the United Kingdom, and the Lattice Hadron Physics Collaboration (LHPC). Both the overlap fermion and the domain-wall fermions satisfy chiral symmetry via the Ginsparg-Wilson relation. There are 5 sets of domain-wall fermion gauge lattices available with 3 lattice spacings and the physical size ranges from 2.8 fm to 5.5 fm. The lowest pion mass has reached the physical mass of 140 MeV for the two large lattices with 5.5 fm size. We are currently working on the three smaller lattices with the physical size at 2.8 fm and 4.5 fm and the lowest pion mass at 170 MeV. There is a good deal of theoretical and experimental interest in strangeness and charmness which are related to dark matter searches. The composition of the proton spin in terms of quark spin, quark orbital angular momentum, and the glue spin are being actively pursued experimentally at JLab, STAR at Brookhaven, and COMPASS at CERN. The strangeness electric and magnetic form factors are studied by G0 and HAPPEX Collaborations at JLab. We are calculating these quantities on the above-mentioned lattices to carry out continuum and physical pion extrapolations with finite volume corrections so that we can compare with existing experiments and make predictions for future experiments and quantities which are not readily observable experimentally, such as strangeness and charmness.

We have succeeded in completing the world's first calculation (M. Deka et al., arXiv:1312:4816 hep-lat, submitted to Physical Review D) of the quark and glue momentum and angular momentum in the nucleon in the so called quenched approximation. We find the quark spin, the quark orbital angular momentum, and the glue angular momentum contribute 25%, 50%, and 25% to the proton spin respectively. Since we have demonstrated that we can do the complete calculation with this approximation, we have moved aggressively ahead to carry out the realistic calculation with the physical quark mass, large volume and with extrapolation to the continuum limit.

We have calculated the strangeness and charmness contents in the nucleon which are needed for estimating the cross section for the dark matter search with the neutralino as the popular candidate which couples to the target nuclei via Higgs exchange. The improvement of the nucleon correlator with low-mode substitution and of the loop with low-mode averaging and the application to our calculation of strangeness and charmness in the nucleon has been published in Phys. Rev. D88, 014503 (2013).

Yibo Yang has led the project to decompose the hadron masses (meson and nucleon) into their components - quark mass, quark kinetic and potential energy, glue field energy, and glue anomaly contribution (Y.-B. Yang et al., arXiv: 1405:4440 hep-ph). This has been submitted for publication in Physical Review D.

Yibo Yang and our chi-QCD Collaboration have finished a multi-year project to find the strange and charm quark masses with two lattice spacings and 3 sets of sea quark masses each to extrapolate to the continuum and physical pion mass limits. The preliminary results were published in the lattice proceedings (Y. Yang at al., PoS LATTICE 2013, 500 (2013)) and the full-length manuscript is being written up for publication. The quark masses, the charmonium hyperfine splitting, the charmonium P-wave states and the Ds decay constant all agree with experiments. This is an ab initio calculation which has only the quark masses as parameters.

The bulk part of this project is being carried out with resources provided by ALCC (ASCR on OLCF), NERSC, NICS, and USQCD. However, we do some of our extensive data analysis and code testing on DLX.

Participants:

PI: Keh-Fei Liu
CoPI: Terrence Draper
Postdocs: Ming Gong, Michael Glatzmaier, Yibo Yang
Staff: Shao-Jing Dong
Students: Raza Suffian, Mingyang Sun, Gen Wang

Non-UK collaborators:

Faculty: Andrei Alexander (George Washington University), Takumi Doi (RIKEN, Japan), Ying Chen (Institute of High Energy Physics, China)
Postdocs: Mridupawan Deka (Dubna, Russia)

Computation method:

Linear algebra for eigenvalue problems and large sparse matrix inversion with Krylov space algorithms, Monte Carlo simulations.

Software:

No commercial software are needed.

Dynamical Chirality: Novel Characterization of Strongly Coupled Dynamics

The goal of the project is to investigate chiral polarization properties of quarks using dynamical chiral polarization methods. This is studied mainly in the context of thermal QCD transition and in the context of QCD with many light flavors (low energy conformality). The study is expected to provide a non-trivial new insight into the dynamics of strongly coupled theories.

Participants:

Dr. Ivan Horvath (UK faculty)

Collaborator

Prof. Andrei Alexandru (non-UK faculty, George Washington University)

Computation method:

The computational tools employed are the Krylov space methods applied to various versions of lattice Dirac operator. These methods are currently available at UK (our own implemen¬tation).

Software:

No external software will be used.

Testing of GPU

DLX is used for debugging and testing GPUs codes, like QUDA.
QUDA is an generic inverter for various fermion actions. It is an open source software. GPU is used to do most of the calculation and to exchange data through MPI on CPU. Most of the fermion actions are done and currently, the project is working on the overlap fermion action.

Participant:

Postdoc - Yibo Yang
Postdoc - Ming Gong

Computation method:

Large matrix inversion with GPUs

Software:

QUDA and MPI are both available on DLX.

Collaborators

Ming Gong - Institute of High Energy Physics, China

Grants

1. Liu, Keh FeiDE-FG02-84ER40154 Lattice QCD Study of Hadron Spectrum, Nucleon Structure, and Finite Density Department of Energy 2/1/1998 - 1/31/2015 $777,000
2. Liu, Keh Fei Lattice QCD Calculation of Nucleon Structure and Excited States U.S. Department of Energy, DE-FG05-84ER40154, 02/13–01/16, $606K, K.F. Liu (PI), T. Draper (co-PI)

Inactive Grants:

1. “Lattice QCD Calculation of Hadronic Spectrum, Nucleon Structure, and Finite Density” U.S. Department of Energy, DE-FG05-84ER40154, 02/10–01/13, $579K, K.F. Liu (PI), T. Draper (co-PI)

2. “Research in Theoretical Nuclear Physics” U.S. Department of Energy, DE-FG05-84ER40154, 02/07–01/10, $540K, K.F. Liu (PI), T. Draper (co-PI)

3. "Lattice QCD Calculation of Nucleon Structure and Excited States", U.S. Department of Energy, DE-FG05-84ER40154, 02/13-01/15, $391K, K.F. Liu (PI), T. Draper (co-PI)

ASCR Award

We have been awarded 69 million processor-hours from the 2014 ASCR Leadership Computing Challenge (ALCC) which is a competitive award from DOE to perform Advanced Scientific Computing Research (ASCR) on Oak Ridge Leadership Computing Facility (OLCF). In 2013, 39 awards were made with a total of 1.8 billion processor hours for an average of 46 million processor hours per award.

According to the ASCR website (http://science.energy.gov/ascr/facilities/alcc/), ``The mission of the ASCR Leadership Computing Challenge (ALCC) is to provide an allocation program for projects of interest to the Department of Energy (DOE) with an emphasis on high-risk, high-payoff simulations in areas directly related to the DOE mission and for broadening the community of researchers capable of using leadership computing resources.''

Protons and neutrons (collectively known as nucleons) found in the nuclei of atoms are made of quarks and gluons. Therefore, studying and understanding the quark-gluon structure of the nucleons and their interactions are of fundamental importance to understanding the building blocks of our universe and life. Quantum Chromodynamics (QCD) is the fundamental theory of quarks and gluons. The aim of this project is to determine how a basic property of a proton, namely its spin, is made up from its constituent quarks and gluons. It will investigate the quark and gluon compositions of the proton spin with a numerical approach called ``Lattice QCD.'' The outcome of this work will be an improved and first-principle-based understanding of the quark-gluon structure of the nucleon which can be compared with experiments being conducted in high energy and nuclear physics laboratories around the world.

This proposal was submitted by K.F. Liu as PI with co-PI's T. Draper of UK, and A. Alexandru and F.X. Lee of George Washington University on behalf the `chi QCD' Collaboration which consists of 23 members from institutions based in the US, China, India, and Japan.

Collaborators

chi QCD Collaboration Membership:
Senior Researchers:
Keh-Fei Liu, Terrence Draper, Shao-Jing Dong, Ivan Horvath (University of Kentucky)
Andrei Alexandru, Frank Lee (George Washington University)
Ying Chen, Ming Gong, Zhaofeng Liu (Inst. of High Energy Physics, Beijing)
Takumi Doi (RIKEN, Japan)
Huey-Wen Lin (University of Washington)
Nilmani Mathur (Tata Institute, Mumbai)
Hank Thacker (University of Virginia)
Jianbo Zhang (Zhejiang University)

Students

Postdocs:
Mridupawan Deka (JINR, Dubna, Russia)
Walter Freeman (George Washington University)
Michael Glatzmaier, Yibo Yang (University of Kentucky)
Anyi Li (INT, University of Washington)

Graduate Students:
Michael Lujan (George Washington University)
Raza Sufian, Mingyang Sun, Geng Wang (University of Kentucky)

Thesis - Gen Wang

DLX account needed to do lattice QCD calculations

Publications

1. Meson Mass Decomposition from Lattice QCD.
By Yi-Bo Yang, Ying Chen, Terrence Draper, Ming Gong, Keh-Fei Liu, Zhaofeng Liu, Jian-Ping Ma. [arXiv:1405.4440 hep-ph].
2. Chiral Symmetry Breaking and Chiral Polarization: Tests for Finite Temperature and Many Flavors. By Andrei Alexandru, Ivan Horváth. [arXiv:1405.2968 hep-lat].
3. From Nuclear Structure to Nucleon Structure. By Keh-Fei Liu. [arXiv:1404.3754 hep-ph].
4. Perturbative Renormalization and Mixing of Quark and Glue Energy-Momentum Tensors on the Lattice. By Michael Glatzmaier, Keh-Fei Liu. [arXiv:1403.7211 hep-lat].
5. The Roper Puzzle. By Keh-Fei Liu, Ying Chen, Ming Gong, Raza Sufian, Mingyang Sun, Anyi Li. [arXiv:1403.6847 hep-ph]. PoS LATTICE2013 (2014) 507.
6. The Flavor Structure of the Nucleon Sea. By J.C. Peng, W.C. Chang, H.Y. Cheng, K.F. Liu. [arXiv:1402.1236 hep-ph].
7. On the Momentum Dependence of the Flavor Structure of the Nucleon Sea. By Jen-Chieh Peng, Wen-Chen Chang, Hai-Yang Cheng, Tie-Jiun Hou, Keh-Fei Liu, Jian-Wei Qiu. [arXiv:1401.1705 hep-ph].
8. Charmonium, $D_s$ and $D_s^*$ from overlap fermion on DWF configurations. By Y.B. Yang, Y. Chen, A. Alexandru, S.J. Dong, T. Draper, M. Gong, F.X. Lee, A. Li et al.. [arXiv:1401.1487 hep-lat].
9. Non-perturbative renormalization of overlap quark bilinears on 2+1-flavor domain wall fermion configurations. By chiQCD Collaboration (Zhaofeng Liu et al.). [arXiv:1312.7628 hep-lat].
10. A Lattice Study of Quark and Glue Momenta and Angular omenta in the Nucleon. By M. Deka, T. Doi, Y.B. Yang, B. Chakraborty, S.J. Dong, T. Draper, M. Glatzmaier, M. Gong et al.. [arXiv:1312.4816 hep-lat].
11. Non-perturbative renormalization of overlap quark bilinears on domain wall fermion configurations. By chiQCD Collaboration (Zhaofeng Liu et al.). [arXiv:1312.0375 hep-lat]. PoS LATTICE2013 (2013) 307.
12. Oscillatory behavior of the domain wall fermions revisited.
By Jian Liang, Ying Chen, Ming Gong, Long-Cheng Gui, Keh-Fei Liu, Zhaofeng Liu, Yi-Bo Yang. [arXiv:1310.3532 hep-lat].
10.1103/PhysRevD.89.094507. Phys.Rev. D89 (2014) 094507.
13. “Chiral polarization scale of QCD vacuum and spontaneous chiral symmetry breaking” A. Alexandru and I. Horvath. 10.1088/1742-6596/432/1/012034 J. Phys. Conf. Ser. 432, 012034 (2013).
14. “Strangeness and charmness content of nucleon from overlap fermions on 2+1¬flavor domain-wall fermion configurations” M. Gong, A. Alexandru, Y. Chen, T. Doi, S. J. Dong, T. Draper, W. Freeman and M. Glatz¬maier et al.. arXiv:1304.1194 hep-ph Phys. Rev. D 88, 014503 (2013).
15. “Dynamical Local Chirality and Chiral Symmetry Breaking”
A. Alexandru and I. Horvath. arXiv:1302.0905 hep-lat PoS ConfinementX , 079 (2012)
16. “Chiral polarization scale of QCD vacuum and spontaneous chiral symmetry breaking” A. Alexandru and I. Horvath. arXiv:1211.3728 hep-lat
17. “Chiral Polarization Scale at Finite Temperature”
A. Alexandru and I. Horvath. arXiv:1211.2601 hep-lat PoS LATTICE 2012, 210 (2012)
18. “Spontaneous Chiral Symmetry Breaking as Condensation of Dynamical Chiral¬ity” A. Alexandru and I. Horvath. arXiv:1210.7849 hep-lat 10.1016/j.physletb.2013.03.041 Phys. Lett. B 722, 160 (2013)
19. “Connected-Sea Partons”
K. -F. Liu, W. -C. Chang, H. -Y. Cheng and J. -C. Peng. arXiv:1206.4339 hep-ph 10.1103/PhysRevLett.109.252002 Phys. Rev. Lett. 109, 252002 (2012)
20. “The Δmix parameter in the overlap on domain-wall mixed action” M. Lujan, A. Alexandru, Y. Chen, T. Draper, W. Freeman, M. Gong, F. X. Lee and A. Li et al.. arXiv:1204.6256 hep-lat 10.1103/PhysRevD.86.014501 Phys. Rev. D 86, 014501 (2012)
21. “The Strangeness and Charmness of Nucleon from Overlap Fermions” M. Gong et al. xQCD Collaboration. arXiv:1204.0685 hep-lat PoS LATTICE 2011, 156 (2011)
22. “Quark and Glue Momenta and Angular Momenta in the Proton — a Lattice Calculation” K. F. Liu, M. Deka, T. Doi, Y. B. Yang, B. Chakraborty, Y. Chen, S. J. Dong and T. Draper et al.. arXiv:1203.6388 hep-ph PoS LATTICE 2011, 164 (2011)
23. “Is 1−+ Meson a Hybrid?” Y. -B. Yang, Y. Chen, G. Li and K. -F. Liu. arXiv:1202.2205 hep-ph 10.1103/PhysRevD.86.094511 Phys. Rev. D 86, 094511 (2012)
24. “Absolute X-distribution and self-duality” A. Alexandru and I. Horvath. arXiv:1111.3897 hep-lat PoS LATTICE 2011, 268 (2011)
25. “Comment on ‘Controversy concerning the definition of quark and gluon angular momentum’ by Elliot Leader (PRD 83, 096012 (2011))” H. -W. Lin and K. -F. Liu. arXiv:1111.0678 hep-ph 10.1103/PhysRevD.85.058901 Phys. Rev. D 85, 058901 (2012)
26. “How Self-Dual is QCD?” A. Alexandru and I. Horvath. arXiv:1110.2762 hep-lat 10.1016/j.physletb.2011.11.034 Phys. Lett. B 706, 436 (2012)
27. “Charge-dependent Azimuthal Correlations in Relativistic Heavy-ion Collisions and Electromagnetic Effects”
K. F. Liu. arXiv:1109.4883 nucl-th 10.1103/PhysRevC.85.014909 Phys. Rev. C 85, 014909 (2012)
28. “Critical point of Nf =3 QCD from lattice simulations in the canonical ensemble” A. Li, A. Alexandru and K. -F. Liu. arXiv:1103.3045 hep-ph 10.1103/PhysRevD.84.071503 Phys. Rev. D 84, 071503 (2011)
29. “Study of the scalar charmed-strange meson Ds∗ 0(2317) with chiral fermions” M. Gong, A. Li, A. Alexandru, Y. Chen, T. Draper and K. F. Liu. arXiv:1103.0589 hep-lat PoS LATTICE 2010, 106 (2010)
30. “Chiral extrapolation beyond the power-counting regime”
J. M. M. Hall, F. X. Lee, D. B. Leinweber, K. F. Liu, N. Mathur, R. D. Young and J. B. Zhang. arXiv:1101.4411 hep-lat 10.1103/PhysRevD.84.114011 Phys. Rev. D 84, 114011 (2011)
31. “Meson spectra from overlap fermion on domain wall gauge configurations” N. Mathur et al. xQCD Collaboration. arXiv:1011.4378 hep-lat PoS LATTICE 2010, 114 (2010)
32. “Absolute Measure of Local Chirality and the Chiral Polarization Scale of the QCD Vacuum” A. Alexandru, T. Draper, I. Horvath and T. Streuer. arXiv:1010.5474 hep-lat PoS LATTICE 2010, 082 (2010)
33. “Nucleon strangeness form factors and moments of PDF”
T. Doi, M. Deka, S. -J. Dong, T. Draper, K. -F. Liu, D. Mankame, N. Mathur and T. Streuer. arXiv:1010.2834 hep-lat 10.1063/1.3647212 AIP Conf. Proc. 1374, 598 (2011)
34. “The Analysis of Space-Time Structure in QCD Vacuum II: Dynamics of Polar¬ization and Absolute X-Distribution”
A. Alexandru, T. Draper, I. Horvath and T. Streuer.
arXiv:1009.4451 hep-lat 10.1016/j.aop.2011.04.007 Annals Phys. 326, 1941 (2011)
35. “Overlap Valence on 2+1 Flavor Domain Wall Fermion Configurations with De¬flation and Low-mode Substitution”
A. Li et al. xQCD Collaboration. arXiv:1005.5424 hep-lat 10.1103/PhysRevD.82.114501 Phys. Rev. D 82, 114501 (2010)
36. “Finite density phase transition of QCD with Nf =4 and Nf =2 using canonical ensemble method” A. Li, A. Alexandru, K. -F. Liu and X. Meng. arXiv:1005.4158 hep-lat 10.1103/PhysRevD.82.054502 Phys. Rev. D 82, 054502 (2010)
37. “Lattice study of light scalar tetraquarks with I=0,2,1/2,3/2: Are σ and κ tetraquarks?”
S. Prelovsek, T. Draper, C. B. Lang, M. Limmer, K. -F. Liu, N. Mathur and D. Mohler. arXiv:1005.0948 hep-lat 10.1103/PhysRevD.82.094507 Phys. Rev. D 82, 094507 (2010)
38. “Searching for tetraquarks on the lattice”
S. Prelovsek, T. Draper, C. B. Lang, M. Limmer, K. F. Liu, N. Mathur and D. Mohler. arXiv:1002.0193 hep-ph 10.3204/DESY-PROC-2010-04/P37 Conf. Proc. C 0908171, 508 (2009)
39. “The Charmed-strange meson spectrum from overlap fermions on domain wall dynamical fermion configurations”
S. J. Dong et al. QCD Collaboration. arXiv:0911.0868 hep-ph PoS LAT 2009, 090 (2009)
40. “Spectroscopy of light tetraquark states” S. Prelovsek, C. B. Lang, M. Limmer, D. Mohler, T. Draper, K. -F. Liu and N. Mathur. arXiv:0910.2749 hep-lat PoS LAT 2009, 103 (2009)
41. “The Calculation of nucleon strangeness form factors from N(f) = 2+1 clover fermion lattice QCD” T. Doi, M. Deka, S. -J. Dong, T. Draper, K. -F. Liu, D. Mankame, N. Mathur and T. Streuer. arXiv:0910.2687 hep-lat PoS LAT 2009, 134 (2009)
42. “Study of QCD critical point using canonical ensemble method” A. Li et al. chi QCD Collaboration. arXiv:0908.1155 hep-lat 10.1016/j.nuclphysa.2009.10.113 Nucl. Phys. A 830, 633C (2009)
43. “Nucleon strangeness form factors from N(f) = 2+1 clover fermion lattice QCD” T. Doi, M. Deka, S. -J. Dong, T. Draper, K. -F. Liu, D. Mankame, N. Mathur and T. Streuer. arXiv:0903.3232 hep-ph 10.1103/PhysRevD.80.094503 Phys. Rev. D 80, 094503 (2009)
44. “Panel discussion on scalar mesons: Plenary session”
F. Buccella, D. V. Bugg, Y. .S. Kalashnikova, K. F. Liu, F. Llanes-Estrada, T. Matsuki,
J. A. Oller and J. L. Rosner et al.. 10.1063/1.2973536 AIP Conf. Proc. 1030, 387 (2008).
45. “Panel discussion on scalar mesons” K. -F. Liu. 10.1063/1.2973534 AIP Conf. Proc. 1030, 383 (2008).
46. “Pseudoscalar glueball mass from eta -eta-prime -G mixing”
H. -Y. Cheng, H. -n. Li and K. -F. Liu. arXiv:0811.2577 hep-ph 10.1103/PhysRevD.79.014024 Phys. Rev. D 79, 014024 (2009)
47. “Winding number expansion for the canonical approach to finite density simula¬tions” X. -f. Meng, A. Li, A. Alexandru and K. -F. Liu. arXiv:0811.2112 hep-lat PoS LATTICE 2008, 032 (2008)
48. “Moments of Nucleon’s Parton Distribution for the Sea and Valence Quarks from Lattice QCD” M. Deka, T. Streuer, T. Doi, S. J. Dong, T. Draper, K. F. Liu, N. Mathur and A. W. Thomas. arXiv:0811.1779 hep-ph 10.1103/PhysRevD.79.094502 Phys. Rev. D 79, 094502 (2009)
49. “Light scalar mesons in 2+1 flavor full QCD” T. Draper, T. Doi, K. -F. Liu, D. Mankame, N. Mathur and X. -f. Meng. arXiv:0810.5512 hep-lat PoS LATTICE 2008, 108 (2008)
50. “2+1 flavor QCD calculation of ¡x¿ and ¡x**2¿”
D. Mankame, T. Doi, T. Draper, K. -F. Liu and T. Streuer. arXiv:0810.3241 hep-lat PoS LATTICE 2008, 142 (2008)
51. “Charmed Strange mesons from Lattice QCD with Overlap Fermions” S. J. Dong et al. chi QCD Collaboration. arXiv:0810.2993 hep-lat PoS LATTICE 2008, 117 (2008)
52. “Strangeness and glue in the nucleon from lattice QCD”
T. Doi et al. QCD Collaboration. arXiv:0810.2482 hep-lat PoS LATTICE 2008, 163 (2008)
53. “Finite Density Simulations with Canonical Ensemble”
A. Li, X. Meng, A. Alexandru and K. -F. Liu. arXiv:0810.2349 hep-lat PoS LATTICE 2008, 178 (2008)
54. “Dominance of Sign Geometry and the Homogeneity of the Fundamental Topo¬logical Structure”
I. Horvath, A. Alexandru and T. Streuer. arXiv:0809.2834 hep-lat PoS LATTICE 2008, 261 (2008)
55. “Neutron Electric Dipole Moment at Fixed Topology”
K. -F. Liu. arXiv:0807.1365 hep-ph 10.1142/S0217732309031375 Mod. Phys. Lett. A 24, 1971 (2009)
56. “Challenges of Lattice Calculation of Scalar Mesons”
K. -F. Liu. arXiv:0805.3364 hep-lat
57. “Classical Limits of Scalar and Tensor Gauge Operators Based on the Overlap Dirac Matrix” A. Alexandru, I. Horvath and K. -F. Liu. arXiv:0803.2744 hep-lat 10.1103/PhysRevD.78.085002 Phys. Rev. D 78, 085002 (2008)
58. “Gauge field strength tensor from the overlap Dirac operator” K. F. Liu, A. Alexandru and I. Horvath. hep-lat/0703010 HEP-LAT 10.1016/j.physletb.2007.11.010 Phys. Lett. B 659, 773 (2008)