Two-flavor lattice QCD in the {epsilon} regime and chiral random matrix theory

Journal Article · Sat Sep 01 04:00:00 EDT 2007 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.76.054503· OSTI ID:21027696

Fukaya, H ^[1]; Aoki, S ^[2]; Chiu, T W; Ogawa, K ^[3]; Hashimoto, S; Kaneko, T; Yamada, N ^[4]; Matsufuru, H; Noaki, J ^[4]; Onogi, T ^[5]

---

1. Theoretical Physics Laboratory, RIKEN, Wako 351-0198 (Japan)
2. Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571 (Japan)
3. Physics Department and Center for Theoretical Sciences, National Taiwan University, Taipei, 10617, Taiwan (China)
4. High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801 (Japan)
5. Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)

The low-lying eigenvalue spectrum of the QCD Dirac operator in the {epsilon} regime is expected to match with that of chiral random matrix theory (ChRMT). We study this correspondence for the case including sea quarks by performing two-flavor QCD simulations on the lattice. Using the overlap fermion formulation, which preserves exact chiral symmetry at finite lattice spacings, we push the sea quark mass down to {approx}3 MeV on a 16{sup 3}x32 lattice at a lattice spacing a{approx_equal}0.11 fm. We compare the low-lying eigenvalue distributions and find a good agreement with the analytical predictions of ChRMT. By matching the lowest-lying eigenvalue we extract the chiral condensate, {sigma}{sup MS}(2 GeV)=(251{+-}7{+-}11 MeV){sup 3}, where errors represent statistical and higher order effects in the {epsilon} expansion. We also calculate the eigenvalue distributions on the lattices with heavier sea quarks at two lattice spacings. Although the {epsilon} expansion is not applied for those sea quarks, we find a reasonable agreement of the Dirac operator spectrum with ChRMT. The value of {sigma}, after extrapolating to the chiral limit, is consistent with the estimate in the {epsilon} regime.

• OSTI ID: 21027696
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 5 Vol. 76; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CHIRAL SYMMETRY
CHIRALITY
COMPARATIVE EVALUATIONS
DIRAC OPERATORS
DISTRIBUTION
EIGENVALUES
FLAVOR MODEL
GEV RANGE
LATTICE FIELD THEORY
MATRICES
MEV RANGE
QUANTUM CHROMODYNAMICS
QUARKS
RANDOMNESS
REST MASS