Wilson Coefficients and Natural Zeros from the On-Shell Viewpoint

TL;DR

This paper introduces an on-shell method to efficiently compute finite contributions to EFT Wilson coefficients from heavy particles, revealing natural zeros and simplifying calculations for processes like g-2 and Hγγ.

Contribution

It presents a novel on-shell approach to calculate Wilson coefficients, enabling easier identification of natural zeros and non-zero contributions in effective field theories.

Findings

Finite contributions can be derived from tree-level amplitude products.

Natural zeros occur due to parity symmetry in certain cases.

The method simplifies calculations of loop effects in EFTs.

Abstract

We show how to simplify the calculation of the finite contributions from heavy particles to EFT Wilson coefficients by using on-shell methods. We apply the technique to the one-loop calculation of $g-2$ and $H\gamma\gamma$, showing how finite contributions can be obtained from the product of tree-level amplitudes. In certain cases, due to a parity symmetry of these amplitudes, the total contribution adds up to zero, as previously found in the literature. Our method allows to search for new natural zeros, as well as to obtain non-zero contributions in a straightforward way.