Unbreaking chiral symmetry

Abstract

In Quantum Chromodynamics (QCD) the eigenmodes of the Dirac operator with small absolute eigenvalues have a close relationship to the dynamical breaking of the chiral symmetry. In a simulation with two dynamical quarks, we study the behavior of meson propagators when removing increasingly more of those modes in the valence sector, thus partially removing effects of chiral symmetry breaking. We find that some of the symmetry aspects are restored (e.g., the masses of ρ and a1 approach each other) while confining properties persist.PACS numbers: 11.15.Ha, 12.38.Gc I. MOTIVATION AND INTRODUCTIONDynamical chiral symmetry breaking in QCD is associated with the low lying spectral modes of the Dirac operator D [1]. They affect the path integral weight of the gauge configurations through the determinant of D.As indicated by the Atiyah-Singer index theorem [2], the exact zero modes are related to topological excitations, the instantons. For Dirac operators violating chiral symmetry these are real eigenmodes. The nearby non-real modes are also thought to be related to composed structure of, e.g., overlapping instantons [3]. 1 In a series of papers [4][5][6] it was emphasized that low modes saturate the pseudoscalar and axial vector correlators at large distances and do not affect the part where high-lying states appear. In [6,7] low mode saturation and also effects of low mode removal for mesons were studied for quenched configurations with the overlap Dirac operator [8,9].Subsequently low modes were utilized to improve the convergence of the determination of hadron propagators [6,7,10,11] (see also the recent study [12,13] comparing the efficiency when using the low modes of the Dirac operator or the hermitian Dirac operator, where strong dependence on the parity of the hadron states was presented).Associating the low mode sector with the nonperturbative chiral symmetry breaking and the condensate [1], a complementary question is how important it is for confinement and mass generation of hadrons. Here we study what happens, if one removes up to 512 low lying modes from the valence quark sector. We compute propagators of the pion and other mesons and determine the effect of this removal on the mass spectrum. This way we want to shed light on the role of the condensate related to * christian.lang@uni-graz.at † mario.schroeck@uni-graz.at 1 Even when studying the low lying modes in quenched gauge ensembles one observes non-vanishing density and also the GellMann-Oakes-Renner relation works down to small values of the valence quark mass until quenched chiral logs destroy the leading chiral symmetry breaking behavior. the spectral part of the Dirac operator in confinement and chiral symmetry breaking. Our analysis is done for configurations generated for two light, mass degenerate dynamical quark flavors. The removal of the low lying modes is effective only in the valence quarks sector. However, as will be seen, this already has significant impact on the meson mass spectrum.In [14,15] it has been conjectured that chiral symmetr...

Analytical Formulae linking Quark Confinement and Chiral Symmetry Breaking

“…However, there are some contrary observations that chiral restoration does not immediately mean the quark deconfinement. For example, "hadrons" can be observed as bound states after removal of low-lying Dirac modes [8]. Also, it is shown that low-lying Dirac modes are not important for confinement properties such as the Polyakov loop and the linear confining potential of a quark-antiquark system [9].…”

Analytical relation between quark confinement and chiral symmetry breaking in odd-number lattice QCD

“…(Also, "hadrons" appear without low-lying Dirac modes [22], suggesting survival of confinement.) In our studies, we just consider the mathematical expansion by eigenmodes of the Dirac operator D = γ μ D μ .…”

Overlap Quark Propagator in Coulomb Gauge QCD

“…We use quenched Lüscher-Weisz gauge field configurations on a 20 4 lattice with β = 7.552, corresponding to the lattice spacing a = 0.2 fm, Ref. [13].…”

“…In this contribution we present our first results for the Overlap quark propagator in Coulomb gauge using quenched Lüscher-Weisz gauge field configurations on a 20 4 lattice. We also briefly discuss the effect of artificial chiral symmetry restoration on the quark propagator.…”

“…In recent years the effect of such an artificial symmetry restoration on the hadron spectrum has been analyzed, Refs. [4,5], and a study of the Landau gauge quark propagator has been given in Ref. [6], with using a fermion discretization, which only approximately fulfills the Ginsparg-Wilson equation.…”