Lattice QCD calculation of the subtraction function in forward Compton amplitude

Abstract

The subtraction function plays a pivotal role in calculations involving the forward Compton amplitude, which is crucial for predicting the Lamb shift in muonic atom, as well as the proton-neutron mass difference. In this work, we present a lattice QCD calculation of the subtraction function using two domain wall fermion gauge ensembles at the physical pion mass. We utilize a recently proposed subtraction point, demonstrating its advantage in mitigating statistical and systematic uncertainties by eliminating the need for ground-state subtraction. Our results reveal significant contributions from $N\ddot{I}€$ intermediate states to the subtraction function. Incorporating these contributions, we compute the proton, neutron and nucleon isovector subtraction functions at photon momentum transfer $Q^2\in [0,2]$ GeV${}^2$. For the proton subtraction function, we compare our lattice results with chiral perturbation theory prediction at low $Q^2$ and with the results from the perturbative operator-product expansion at high $Q^2$. Finally, using these subtraction functions as input, we determine their contribution to two-photon exchange effects in the Lamb shift and isovector nucleon electromagnetic self-energy.

10 pages, 10 figures; v2, accepted for publication in PRL