Automation of a matching on-shell calculator

We introduce mosca , a 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. 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. PROGRAM SUMMARY Program Title: mosca CPC Library link to program files: https://doi.org/10.17632/xf8zs7hnhm.1 Developer’s repository link: https://gitlab.com/matchingonshell/mosca Licensing provisions: GPLv3 Programming language: Mathematica Nature of problem: Matching calculations in effective field theories are traditionally performed off-shell, involving complicated basis reductions through non-trivial field redefinitions to eliminate redundant operators. This process is algebraically intensive and prone to errors. Although on-shell matching, which focuses directly on physical observables, could simplify these steps by avoiding field redefinitions, it has been considered impractical due to the presence of apparent non-localities that must cancel precisely. Automating on-shell matching has therefore been a long-standing challenge. Solution method: Our approach is based on a numerical solution of the on-shell matching equations, which naturally and effortlessly enforces the delicate cancellation of non-local terms between the full theory and the effective theory. By employing rational on-shell kinematics, the method achieves an exact analytic solution despite using numerical techniques. This allows the matching to be performed entirely within a physical operator basis. Additional comments including restrictions and unusual features: The workflow for handling Lagrangians and Feynman diagrams in mosca is based on the integration of FeynArts and FeynCalc. Consequently, users need to provide specific FeynArts model files patched for compatibility with FeynCalc. Additionally, a specialized input format is required to define Wilson coefficients along with their corresponding EFT order (EFTOrder). These requirements ensure the correct processing of models and coefficients.