Wilson Coefficients and Natural Zeros from the On-Shell Viewpoint

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.