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Register a new userHigh precision renormalization of the flavour non-singlet Noether currents in lattice QCD with Wilson quarks
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We determine the non-perturbatively renormalized axial current for O($a$) improved lattice QCD with Wilson quarks. Our strategy is based on the chirally rotated Schrodinger functional and can be generalized to other finite (ratios of) renormalization constants which are traditionally obtained by imposing continuum chiral Ward identities as normalization conditions. Compared to the latter we achieve an error reduction up to one order of magnitude. Our results have already enabled the setting of the scale for the $N_{rm f}=2+1$ CLS ensembles [1] and are thus an essential ingredient for the recent $alpha_s$ determination by the ALPHA collaboration [2]. In this paper we shortly review the strategy and present our results for both $N_{rm f}=2$ and $N_{rm f}=3$ lattice QCD, where we match the $beta$-values of the CLS gauge configurations. In addition to the axial current renormalization, we also present precise results for the renormalized local vector current.
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We determine non-perturbatively the normalisation factor $r_mathrm{m}equiv Z_{rm S}/Z_{rm S}^{0}$, where $Z_{rm S}$ and $Z_{rm S}^{0}$ 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, $N_mathrm{f} = 3$ mass-degenerate $mathrm{O}(a)$ improved Wilson fermions and Schrodinger 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 $Z equiv Z_{rm P}/(Z_{rm S}Z_{rm A})$ in order to obtain $r_mathrm{m}$. 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 $N_mathrm{f} = 2+1$ QCD simulations in large volumes with the same lattice action are typically performed.
We present the results of a non-perturbative determination of the improvement coefficient $c_mathrm{V}$ and the renormalisation factor $Z_mathrm{V}$, which define the renormalised vector current in three-flavour $mathrm{O}(a)$ 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 Schrodinger 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 $0.04,mathrm{fm}lesssim alesssim 0.1,mathrm{fm}$ 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.
We apply spectral methods to compute the OZI-rule suppressed loop-loop correlators in the pseudoscalar meson flavour singlet channel. Using SESAM configurations (obtained with two degenerate sea quark flavours on 16x16x16x32 lattices at beta = 5.6 with standard Wilson action), we find for the first time clear evidence for mass plateau formation in the eta channel of this theory. As a consequence, we observe a clear signal of a mass gap persistent under chiral extrapolation. This sets the stage for a more realistic two-channel approach, where partially quenched strange quarks would be included, in addition to u, d sea quarks.
We present a study on the direct determination of the $eta $ mass on the full set of SESAM and T$chi$L QCD vacuum configurations with 2 active flavours of Wilson fermions, at $beta = 5.6$. We observe a definite dependency of the two-loop correlator on the topological charge sector.
We present preliminary results of the non-perturbative computation of the RI-MOM renormalisation constants in a mass-independent scheme for the action with Iwasaki glue and four dynamical Wilson quarks employed by ETMC. Our project requires dedicated gauge ensembles with four degenerate sea quark flavours at three lattice spacings and at several values of the standard and twisted quark mass parameters. The RI-MOM renormalisation constants are obtained from appropriate O(a) improved estimators extrapolated to the chiral limit.
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