Fuensanta Vilches

We propose an efficient method to perform on-shell matching calculations in effective field theories. The standard off-shell approach to matching requires the use of a Green’s basis that includes redundant and evanescent operators. The reduction of such a basis to a physical one is often highly non-trivial, difficult to automate and error prone. Our proposal is based on a numerical solution of the corresponding on-shell matching equations, which automatically implements in a trivial way the delicate cancellation between the non-local terms in the full theory and those in the effective one. The use of rational on-shell kinematics ensures an exact analytic solution despite the numerical procedure. In this way we only need a physical basis to perform the matching. Our procedure can be used to reduce any Green’s basis to an arbitrary physical one, or to translate between physical bases; to renormalize arbitrary effective Lagrangians, directly in terms of a physical basis; and to perform finite matching, including evanescent contributions, as we discuss with explicit examples.

This is the third of a series of works [1, 2] aimed at renormalizing the Standard Model effective field theory at one loop and to order 1/Λ⁴, with Λ being the new physics cut-off. On this occasion, we concentrate on the running of two-fermion operators induced by pairs of dimension-six interactions. We work mostly off-shell, for which we obtain and provide a new and explicitly hermitian basis of dimension-eight Green’s functions. All our results can be accessed in https://github.com/SMEFT-Dimension8-RGEs.