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

Wilson Coefficients and Natural Zeros from the On-Shell Viewpoint