Lattice QCD calculation of the subtraction function in forward Compton amplitude

TL;DR

This paper presents a lattice QCD calculation of the subtraction function in the forward Compton amplitude, crucial for understanding the Lamb shift and nucleon mass differences, with improved methods reducing uncertainties and incorporating intermediate state contributions.

Contribution

The study introduces a novel lattice QCD approach using a new subtraction point that reduces uncertainties and accounts for $N ext{π}$ intermediate states in the subtraction function calculation.

Findings

Significant $N ext{π}$ contributions to the subtraction function.

Lattice results agree with chiral perturbation theory at low $Q^2$.

Results impact two-photon exchange calculations in the Lamb shift.

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 $N\pi$ 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.