Non-perturbative improvement of quark mass renormalization in two-flavour lattice QCD

Abstract

We non-perturbatively determine the renormalization constant and the improvement coefficients relating the renormalized current and subtracted quark mass of (quenched) valence quarks propagating in a sea of O(a) improved two massless quarks. We employ the Schrödinger functional scheme and fix the physical extent of the box by working at a constant value of the renormalized coupling. Our calculation yields results which cover two regions of bare parameter space. One is the weak-coupling region suitable for volumes of about half a fermi. By making simulations in this region, quarks as heavy as the bottom can be propagated with the full relativistic QCD action and renormalization problems in HQET can be solved non-perturbatively by a matching to QCD in finite volume. The other region refers to the common parameter range in large-volume simulations of two-flavour lattice QCD, where our results have particular relevance for charm physics applications.

Non-perturbative tests of continuum HQET through small-volume two-flavour QCD

“…This paper follows up our previous work [19] on the definition of a line of constant physics in N f = 2 lattice simulations. It allows us to non-perturbatively study the quark mass dependence of relativistic QCD meson observables in a finite box of extent L 1 ≈ 0.4 fm [20].…”

“…Equivalently, we will assign to them the dimensionless mass parameter z = L 1 M h from now on, where M h ≡ M denotes some fixed value of the renormalization group invariant (RGI) heavy quark mass. In [19] we have already shown that in such a small box the lattice spacing can be chosen small enough so that all heavy quarks up to a certain value can be simulated relativistically while keeping cutoff effects in the O(a) improved theory well under control. For any unexplained notation, the reader may consult [15,19].…”

“…How to non-perturbatively set up a line of constant physics in the envisaged small volume L 1 ≈ 0.4 fm has already been reported in [19]. In that volume we have four different ensembles with non-perturbatively O(a) improved dynamical Wilson fermions made of a doublet of massless quarks.…”

“…As yet we have not taken into account the error stemming from the tuning of the heavy quark mass (2.4) at finite lattice spacing. The uncertainty of the continuum heavy quark mass M = z/L 1 is ∆M/M = ∆z/z = 1.01% [19]. We add its error…”

“…The renormalization constants Z X , X = A, V, P, are known non-perturbatively in twoflavour QCD; as in our earlier work [19], Z A and Z V have been taken from [25], while Z P,RGI is available through the scale dependent renormalization factor Z P computed in refs. [9,38].…”