Automatic generation of vertices for the Schroedinger functional

TL;DR

This paper introduces a recursive algorithm for automatically generating vertices in the Schroedinger functional framework, facilitating perturbative calculations across various lattice actions.

Contribution

The authors develop a novel recursive multiplication algorithm for vertices, enabling automated perturbative computations in the Schroedinger functional with diverse actions.

Findings

Derived ratios of lambda parameters between lattice and MS schemes.

Computed one-loop Schroedinger functional coupling for lattice T=L±a.

Algorithm supports automatic perturbative calculations.

Abstract

We present a multiplication algorithm to recursively construct vertices for the Schroedinger functional in the abelian background field case. The algorithm is suited for automatic perturbative calculations with a variety of actions. As first applications, we derive ratios of the lambda parameters between the lattice scheme (improved gauge actions including six link loops) and the $\bar{\rm MS}$ scheme, and one-loop results for the Schroedinger functional coupling with a lattice $T=L \pm a$, which is motivated by considering staggered fermions.