The renormalised $$\mathrm{O}(a)$$ improved vector current in three-flavour lattice QCD with Wilson quarks

We present the results of a non-perturbative determination of the improvement coefficient $$c_\mathrm{V}$$ c V and the renormalisation factor $$Z_\mathrm{V}$$ Z V , which define the renormalised vector current in three-flavour $$\mathrm{O}(a)$$ 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 $$0.04\,\mathrm{fm}\lesssim a\lesssim 0.1\,\mathrm{fm}$$ 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.

Infrared structure of SU(N) × U(1) gauge theory to three loops

We study the infrared (IR) structure of SU(N ) × U(1) (QCD × QED) gauge theory with nf quarks and nl leptons within the framework of perturbation theory. In particular, we unravel the IR structure of the form factors and inclusive real emission cross sections that contribute to inclusive production of color neutral states, such as a pair of leptons or single W/Z in Drell-Yan processes and a Higgs boson in bottom quark annihilation, in Large Hadron Collider (LHC) in the threshold limit. Explicit computation of the relevant form factors to third order and the use of Sudakov’s K + G equation in SU(N ) × U(1) gauge theory demonstrate the universality of the cusp anomalous dimensions (AI, I = q, b). The abelianization rules that relate AI of SU(N ) with those from U(1) and SU(N) × U(1) can be used to predict the soft distribution that results from the soft gluon emission subprocesses in the threshold limit. Using the latter and the third order form factors, we can obtain the collinear anomalous dimensions (BI) and the renormalisation constant Zb to third order in perturbation theory. The form factors, the process independent soft distribution functions can be used to predict fixed and resummed inclusive cross sections to third order in couplings and in leading logarithmic approximation respectively.