Automation of a Matching On-Shell Calculator

Abstract: We introduce $\texttt{mosca}$, a $\texttt{Mathematica}$ package designed to facilitate on-shell calculations in effective field theories (EFTs). This initial release focuses on the reduction of Green's bases to physical bases, as well as transformations between arbitrary operator bases. The core of the package is based on a diagrammatic on-shell matching procedure, grounded in the equivalence of physical observables derived from both redundant and non-redundant Lagrangians. $\texttt{mosca}$ offers a complete set of tools for performing basis transformations, diagram isomorphism detection, numerical substitution of kinematic configurations, and symbolic manipulation of algebraic expressions. Planned future developments include extension to one-loop computations, thus providing support for EFT renormalization directly in a physical basis and automated computation of one-loop finite matching, including contributions from evanescent operators. The package, along with example notebooks and documentation, is available at: https://gitlab.com/matchingonshell/mosca.