Non-perturbative quark mass renormalization in two-flavor QCD

Abstract

The running of renormalized quark masses is computed in lattice QCD with two flavors of massless O(a) improved Wilson quarks. The regularization and flavor independent factor that relates running quark masses to the renormalization group invariant ones is evaluated in the Schroedinger Functional scheme. Using existing data for the scale r_0 and the pseudoscalar meson masses, we define a reference quark mass in QCD with two degenerate quark flavors. We then compute the renormalization group invariant reference quark mass at three different lattice spacings. Our estimate for the continuum value is converted to the strange quark mass with the help of chiral perturbation theory.Comment: 25 pages, 6 figures; sections 1 and 4 rearranged, minor change to the summary plo

Non-perturbative renormalization of tensor currents: strategy and results for $$N_f=0$$ N f = 0 and $$N_

“…The purpose of this work is to set up the strategy for the application of finitesize scaling techniques based on the Schrödinger Functional (SF) [21], in order to obtain a fully non-perturbative determination of both current renormalization constants at hadronic energy scales, and the running of renormalized currents to the electroweak scale. This completes the ALPHA Collaboration non-perturbative renormalization programme for nonsinglet quark field bilinears [7][8][9][10][24][25][26] and four-quark operators [27][28][29][30][31][32][33].…”

“…μ = 1/L. To define suitable SF renormalization conditions we can follow the same strategy as in [7,8,55,56], which has been applied successfully also to several other composite operators both in QCD [25][26][27][28][29][30][31][57][58][59] and other theories. 3 We first introduce the two-point functions …”

“…They however do not constrain the tensor current, which runs with the only other independent anomalous dimension among quark bilinears. Controlling the current renormalization and running at the non-perturbative level, in the same fashion achieved for quark masses [7][8][9][10], is therefore necessary in order to control systematic uncertainties, and allow for solid conclusions in new physics searches. To make a specific example, the precision of the isovector nucleon tensor charge given by [5] is around 5%, to which renormalization and running is the largest contribution.…”

Estimating the unquenched strange quark mass from the lattice axial Ward identity

“…While there is a difference between the results, it is decreasing for β → ∞ and thus may be primarily due to remnant O(a 2 ) effects, which disappear in the continuum limit. That various determinations of Z RGĨ m have different numerical values can be seen from the results of [12] (open diamonds and triangles). In these results two different definitions of the axial renormalisation constant have been used, [53].…”

Trajectory length and autocorrelation times: Nf=2 simulations in the Schrodinger functional

“…Our present goal is to use the kaon decay constant F K as low-energy scale. This will also allow us to reduce the overall uncertainty on our recent determination of the strange quark mass [4].…”