Euclidean coordinate-space perturbation theory with a single mass scale

A

bstract

We develop elements of coordinate-space perturbation theory for massive quantum field theories in general d -dimensional Euclidean space. Using the expansion in Gegenbauer polynomials, we provide analytic expressions for several correlation functions in theories with one massive and one massless field. To this end, a class of antiderivatives of products of two Bessel functions multiplied by a power of their common argument are studied systematically. We expect these results to be useful in perturbative calculations at finite temperature and/or in finite volume, in quantum-field theories with high-degree vertices, as well as in auxiliary perturbative computations for a lattice QCD treatment of hadronic effects in precision observables. As an illustration, we compute the one-loop coordinate-space propagator of a massive particle coupled to a massless one, both in the vacuum and at finite temperature. We also provide a master formula for computing the electroweak triangle-diagram contribution to the muon ( g − 2) in lattice QCD.