opbasis -- a Python package to derive minimal operator bases

TL;DR

The paper introduces 'opbasis', a Python package designed to systematically derive minimal operator bases in lattice effective field theories, accommodating complex discrete symmetries and extensions for broader applications.

Contribution

It presents a new Python tool that simplifies the derivation of minimal operator bases for lattice EFTs with complex symmetries, extending beyond traditional continuum methods.

Findings

Successfully derives operator bases for Wilson QCD axial-vector

Constructs operator bases compatible with staggered quark symmetries

Demonstrates derivation of a pseudo-scalar operator with user-defined extensions

Abstract

Finding a complete and yet minimal on-shell basis of operators of a given mass-dimension that are compatible with a specific set of transformation properties is the first step in any Effective Field Theory description. This step is the main bottleneck for systematic studies of leading logarithmic corrections to integer-power lattice artifacts in Symanzik Effective Field Theory targeting various local fields and lattice actions. The focus on discrete symmetry transformations in lattice field theory, especially reduced hypercubic spacetime symmetry with Euclidean signature, complicates the use of standard continuum field theory tools. Here, a new Python package is being presented that targets the typical lattice field-theorist's use cases. While the main target lies on continuum EFTs describing 4D non-Abelian lattice gauge theories, the applicability can be extended beyond Effective Field Theories. New discrete symmetries, twisted masses, or the introduction of boosts are just a few examples of possible extensions that can be easily implemented by the user. This should allow for a wider range of theories and applications beyond the initial focus of this package. The general functionality of the package is explained along the lines of three examples: The $\mathrm{O}(a)$ operator basis of the axial-vector in Wilson QCD, operator bases compatible with the symmetries of unrooted Staggered quarks as well as a pedestrian derivation of a $B^*(\mathbf{p})\pi(-\mathbf{p})$ operator with pseudo-scalar quantum numbers. Each example makes use of an increasing range of features and requires user-defined extensions show-casing the versatility of the package.