Renormalization Group Invariant Quark Mass Research Articles

Running quark mass in two flavor QCD

We present first results for the step scaling function σ P of the renormalization factor Z P of the pseudoscalar density. The simulations are performed within the framework of the Schro¨dinger functional with two flavors of O( a) improved Wilson fermions. The knowledge ofσ P is required to compute the renormalization group invariant quark masses. We also study the performance of a variant of the HMC algorithm using two pseudofermion fields.

The charm quark's mass in quenched QCD

We present our preliminary result for the charmed quark mass, which follows from taking the D s and K meson masses from exeriment and r 0 = 0.5 fm (or, equivalently F K = 160 MeV) to set the scale. For the renormalization group invariant quark mass we obtain M c = 1684(64) MeV, which translates to m c ( m c ) = 1314(40)(20)(7) MeV for the running mass in the MS scheme. Renormalization is treated non-perturbatively, and the continuum limit has been taken, so that the only uncontrolled systematic error consists in the use of the quenched approximation.

Chiral Symmetry, Quark Mass, and Scaling of the Overlap Fermions

The chiral symmetry relation and scaling of the overlap fermions are studied numerically on the quenched lattices at 3 couplings with about the same physical volume. We find that the generalized Gell-Mann-Oakes-Renner relation is satisfied to better than 1% down to the smallest quark mass at m(0)a = 0.006. We also obtain the quark mass from the PCAC relation and the pseudoscalar masses. The renormalization group invariant quark mass is shown to be fairly independent of scale. The pi and rho masses at a fixed m(pi)/m(rho) ratio indicate small O(a(2)) corrections. It is found that the critical slowing down sets in abruptly at a very small quark mass close to those of the physical u and d quarks.

Precision computation of the strange quark's mass in quenched QCD

We determine the renormalization group invariant quark mass corresponding to the sum of the strange and the average light quark mass in the quenched approximation of QCD, using as essential input the mass of the K-mesons. In the continuum limit we find (M s + M ̂ )/F K =0.874(29) , which includes systematic errors. Translating this non-perturbative result into the running quark masses in the MS scheme at μ=2 GeV and using the quark mass ratios from chiral perturbation theory, we obtain m s (2 GeV)=97(4) MeV . With the help of recent results by the CP-PACS Collaboration, we estimate that a 10% higher value would be obtained if one replaced F K by the nucleon mass to set the scale. This is a typical ambiguity in the quenched approximation.

Non-perturbative quark mass renormalization in quenched lattice QCD

The renormalization factor relating the bare to the renormalization group invariant quark masses is accurately calculated in quenched lattice QCD using a recursive finite-size technique. The result is presented in the form of a product of a universal factor times another factor, which depends on the details of the lattice theory but is easy to compute, since it does not involve any large scale differences. As a byproduct the A-parameter of the theory is obtained with a total error of 8%.

The running quark mass in the SF scheme and its two-loop anomalous dimension

The non-perturbatively defined running quark mass introduced by the ALPHA collaboration is based on the PCAC relation between correlation functions derived from the Schrödinger functional (SF). In order to complete its definition it remains to specify a number of parameters, including the ratio of time to spatial extent, T/ L, and the angle ø which appears in the spatial boundary conditions for the quark fields. We investigate the running mass in perturbation theory and propose a choice of parameters which attains two desired properties: firstly the two-loop anomalous dimension d 1 SF is reasonably small. This is needed in order to ease matching with the non-perturbative computations and to achieve a precise determination of the renormalization group invariant quark mass. Secondly, to one-loop order of perturbation theory, cut-off effects in the step-scaling function are small in O( a) improved lattice QCD.

Non-perturbative quark mass renormalization

We show that the renormalization factor relating the renormalization group invariant quark masses to the bare quark masses computed in lattice QCD can be determined non-perturbatively. The calculation is based on an extension of a finite-size technique previously employed to compute the running coupling in quenched QCD. As a by-product we obtain the Λ-parameter in this theory with completely controlled errors.