Lattice QCD Calculation of the Subtraction Function in Forward Compton Amplitude

The subtraction function plays a pivotal role in calculations involving the forward Compton amplitude, which is crucial for predicting the Lamb shift in muonic atoms, as well as the proton-neutron mass difference. In this Letter, we present a lattice QCD calculation of the subtraction function using two domain wall fermion gauge ensembles near 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 Nπ 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}∈[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.