Chiral symmetry breaking and the Banks-Casher relation in lattice QCD with Wilson quarks
By L. Giusti, M. Luscher. 2008
151 citations recorded by the source corpus.
The Banks-Casher relation links the spontaneous breaking of chiral symmetry in QCD to the presence of a non-zero density of quark modes at the low end of the spectrum of the Dirac operator. Spectral observables like the number of modes in a given energy interval are renormalizable and can therefore be computed using the Wilson formulation of lattice QCD even though the latter violates chiral symmetry at energies on the order of the inverse lattice spacing. Using numerical simulations, we find (in two-flavour QCD) that the low quark modes do condense in the expected way. In particular, the chiral condensate can be accurately calculated simply by counting the low modes on large lattices. Other spectral observables can be considered as well and have a potentially wide range of uses.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/8a7772610f89f47efbcbafc5fe37ddb6f394cf0a
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In Nuclear and High Energy Physics
Citations in the corpus
- Properties and uses of the Wilson flow in lattice QCD (2010, background): “Moreover, as shown in a forthcoming publication, the ratios of the fourth root of the second moments computed here and through a variant [18] of the universal formula proposed in [17] extrapolate to 1 in the continuum limit to within a statistical uncertainty of 3%.”
- Properties and uses of the Wilson flow in lattice QCD (2010, result): “ng a chiral lattice Dirac operator and the index theorem [15]. Moreover, as shown in a forthcoming publication, the ratios of the fourth root of the second moments computed here and through a variant [18] of the universal formula proposed in [17] extrapolate to 1 in the continuum limit to within a s”
- Review of lattice results concerning low-energy particle physics (2010, methodology): “the pion scalar radius to the experimental value. JLQCD/TWQCD 08A JLQCD 08A [95] [264] 2 290 NNLO SU(2) fit up to Mπ = 750 MeV. Estimate of systematic error due to truncation of chiral series. CERN 08 [215] 2 mq,min=13 MeV NLO SU(2) fit for the mode number of the Dirac operator. HHS 08 [247] 2 µ1 = mΣ”
- Hyperscaling relations in mass-deformed conformal gauge theories (2010, background): “[59], the mode number of the massive Dirac operator: ν(M,m) = ∫ +Λ”
- Transport properties of the quark-gluon plasma (2011, methodology): “This behavior is readily seen in simulations of QCD in large but finite volume [98].”