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We determine non-perturbatively the normalisation factor r m ≡ Z S / Z S 0 , where Z S and Z S 0 are the renormalisation parameters of the flavour non-singlet and singlet scalar densities, respectively. This quantity is required in the computation of quark masses with Wilson fermions and for instance the renormalisation of nucleon matrix elements of scalar densities. Our calculation involves simulations of finite-volume lattice QCD with the tree-level Symanzik-improved gauge action, N f = 3 mass-degenerate O (a) improved Wilson fermions and Schrödinger functional boundary conditions. The slope of the current quark mass, as a function of the subtracted Wilson quark mass is extracted both in a unitary setup (where nearly chiral valence and sea quark masses are degenerate) and in a non-unitary setup (where all valence flavours are chiral and the sea quark masses are small). These slopes are then combined with Z ≡ Z P / (Z S Z A) in order to obtain r m . A novel chiral Ward identity is employed for the calculation of the normalisation factor Z. Our results cover the range of gauge couplings corresponding to lattice spacings below 0.1 fm, for which N f = 2 + 1 QCD simulations in large volumes with the same lattice action are typically performed. [ABSTRACT FROM AUTHOR]

We present a determination of the charm quark mass in lattice QCD with three active quark flavours. The calculation is based on PCAC masses extracted from Nf = 2 + 1 flavour gauge field ensembles at five different lattice spacings in a range from 0.087 fm down to 0.039 fm. The lattice action consists of the O(a) improved Wilson-clover action and a tree-level improved Symanzik gauge action. Quark masses are non-perturbatively O(a) improved employing the Symanzik-counterterms available for this discretisation of QCD. To relate the bare mass at a specified low-energy scale with the renormalisation group invariant mass in the continuum limit, we use the non-pertubatively known factors that account for the running of the quark masses as well as for their renormalisation at hadronic scales. We obtain the renormalisation group invariant charm quark mass at the physical point of the three-flavour theory to be Mc = 1486(21) MeV. Combining this result with five-loop perturbation theory and the corresponding decoupling relations in the MS ¯ scheme, one arrives at a result for the renormalisation group invariant charm quark mass in the four-flavour theory of Mc(Nf = 4) = 1548(23) MeV, where effects associated with the absence of a charmed, sea quark in the non-perturbative evaluation of the QCD path integral are not accounted for. In the MS ¯ scheme, and at finite energy scales conventional in phenomenology, we quote m c MS ¯ ( m c MS ¯ ; Nf = 4) = 1296(19) MeV and m c MS ¯ (3 GeV; Nf = 4) = 1007(16) MeV for the renormalised charm quark mass. [ABSTRACT FROM AUTHOR]

We present the results of a non-perturbative determination of the improvement coefficient c V and the renormalisation factor Z V , which define the renormalised vector current in three-flavour O (a) improved lattice QCD with Wilson quarks and tree-level Symanzik-improved gauge action. In case of the improvement coefficient, we consider both lattice descriptions of the vector current, the local as well as the conserved (i.e., point-split) one. Our improvement and normalisation conditions are based on massive chiral Ward identities and numerically evaluated in the Schrödinger functional setup, which allows to eliminate finite quark mass effects in a controlled way. In order to ensure a smooth dependence of the renormalisation constant and improvement coefficients on the bare gauge coupling, our computation proceeds along a line of constant physics, covering the typical range of lattice spacings 0.04 fm ≲ a ≲ 0.1 fm that is useful for phenomenological applications. Especially for the improvement coefficient of the local vector current, we report significant differences between the one-loop perturbative estimates and our non-perturbative results. [ABSTRACT FROM AUTHOR]

We derive chiral Ward identities for lattice QCD with Wilson quarks and N f ≥ 3 flavours, on small lattices with Schrödinger functional boundary conditions and vanishingly small quark masses. These identities relate the axial variation of the non-singlet pseudoscalar density to the scalar one, thus enabling the non-perturbative determination of the scale-independent ratio Z S / Z P of the renormalisation parameters of these operators. We obtain results for N f = 3 QCD with tree-level Symanzik-improved gluons and Wilson-Clover quarks, for bare gauge couplings which cover the typical range of large-volume N f = 2 + 1 simulations with Wilson fermions at lattice spacings below 0.1 fm. The precision of our results varies from 0.3 to 1%, except for the coarsest lattice, where it is 2%. We discuss how the Z S / Z P ratio can be used in the non-perturbative calculations of O (a) improved renormalised quark masses. [ABSTRACT FROM AUTHOR]

Hadronic matrix elements involving tensor currents play an important rôle in decays that allow to probe the consistency of the Standard Model via precision lattice QCD calculations. The non-singlet tensor current is a scale-dependent (anomalous) quantity. We fully resolve its renormalisation group (RG) running in the continuum by carrying out a recursive finite-size scaling technique. In this way ambiguities due to a perturbative RG running and matching to lattice data at low energies are eliminated. We provide the total renormalisation factor at a hadronic scale of 233 MeV, which converts the bare current into its RG-invariant form. Our calculation features three flavours of O(a) improved Wilson fermions and tree-level Symanzik-improved gauge action. We employ the (massless) Schrödinger functional renormalisation scheme throughout and present the first non-perturbative determination of the Symanzik counterterm cT derived from an axial Ward identity. We elaborate on various details of our calculations, including two different renormalisation conditions. [ABSTRACT FROM AUTHOR]

The original article can be found online at https://doi.org/10.1140/epjc/s10052-021-09387-z. J. Heitger, F. Joswig, A. Vladikas, C.Wittemeier, Non-perturbative determination of cv, ZV and ZS/ZP in HT ht lattice QCD. [Extracted from the article]

A lattice computation of the B-meson decay constant and the mass of the b-quark to leading order in the heavy quark effective theory is presented. The involved renormalization problems are solved non-perturbatively, and the continuum limit is taken. In the quenched approximation the results reported here already offer an interesting numerical precision, which will be further improved in the near future. [ABSTRACT FROM AUTHOR]

We present results for the leptonic decay constants of the D and Ds mesons from Nf = 2 + 1 lattice QCD. We employ a set of 49 high statistics gauge ensembles generated by the Coordinated Lattice Simulations (CLS) effort utilising non-perturbatively improved Wilson fermions and the tree-level Symanzik improved gauge action at six values of the lattice spacing in the range a = 0.098 fm down to a = 0.039 fm, with pion masses varying from around 420 MeV down to below the physical point. The ensembles lie on three trajectories in the quark mass plane, two trajectories intersecting close to the physical quark mass point and the third one approaching the SU(3) chiral limit, enabling tight control of the light and strange quark mass dependence. We obtain f D s = 246.8(1.3) MeV, fD = 208.4(1.5) MeV and f D s /fD = 1.1842(36), where the precision of our results is mostly limited by the determination of the scale. [ABSTRACT FROM AUTHOR]

We determine non-perturbatively the normalisation parameter Z m Z P / Z A as well as the Symanzik coefficients b m and b A - b P , required in O (a) improved quark mass renormalisation with Wilson fermions. The strategy underlying their computation involves simulations in N f = 3 QCD with O (a) improved massless sea and non-degenerate valence quarks in the finite-volume Schrödinger functional scheme. Our results, which cover the typical gauge coupling range of large-volume N f = 2 + 1 QCD simulations with Wilson fermions at lattice spacings below 0.1 fm , are of particular use for the non-perturbative calculation of O (a) improved renormalised quark masses. [ABSTRACT FROM AUTHOR]

Abstract: We report our final estimate of the b-quark mass from lattice QCD simulations using Heavy Quark Effective Theory non-perturbatively matched to QCD at . Treating systematic and statistical errors in a conservative manner, we obtain after an extrapolation to the physical point. [Copyright &y& Elsevier]