Quenched QCD with fixed-point and chirally improved fermions

Abstract

In this contribution we present results from quenched QCD simulations with the parameterized fixed-point (FP) and the chirally improved (CI) Dirac operator. Both these operators are approximate solutions of the Ginsparg-Wilson equation and have good chiral properties. We focus our discussion on observables sensitive to chirality. In particular we explore pion masses down to 210 MeV in light hadron spectroscopy, quenched chiral logs, the pion decay constant and the pion scattering length. We discuss finite volume effects, scaling properties of the FP and CI operators and performance issues in their numerical implementation. * This contribution is based on parallel talks and posters presented

Low energy constants from the Chirally Improved Dirac operator D_CI

“…Several lattice sizes at different lattice spacings are studied, using pseudoscalar and axial vector correlators. We find consistent results for f π = 96(2) MeV, f K = 105(2) MeV, Σ = −(286(4) MeV) 3 , the average light quark massm = 4.1 (2.4) MeV and m s = 101(8) MeV.…”

“…Preliminary results for low energy constants in that context have been published in Ref. [3]. At that time the renormalization constants relating these to the continuum MS-scheme were not available.…”

Renormalization of bilinear quark operators for the chirally improved lattice Dirac operator

“…It is formulated as a truncated series of interaction terms with coefficients depending on the gauge coupling. Within the BGR collaboration it has been used to obtain the ground state hadrons in the quenched approximation [10] down to pion masses of 270 MeV, and it has been demonstrated to have good chiral properties [14]. The renormalization constants for quark bilinears determined in this work permit a more detailed analysis of the chiral properties of the CI operator.…”

Lattice calculation of low energy constants with Ginsparg-Wilson type fermions

“…Finite size dependence: In Fig. 3 we compare a 2 G (r) π /Z P determined from (26) for a m ≥ 0.01 for three volumes but at the same lattice scale. We find a strong volume dependence for the smallest lattice at bare quark masses below 0.06/a.…”

“…For the overlap action there have been several determinations of low energy parameters [13,14,15,16,17,18,19,20,21,22,23,24,25]. For the chirally improved Dirac operator D CI only preliminary results have been published [12,26]. The reason was, that the renormalization constants were not available.…”