Nucleon electric polarizabilities and nucleon-pion scattering at physical pion mass

TL;DR

This study uses lattice QCD to accurately compute nucleon electric polarizabilities at the physical pion mass, emphasizing the importance of including $N ext{-} ext{pi}$ state contributions for agreement with experimental data.

Contribution

It introduces a method to incorporate dynamic $N ext{-} ext{pi}$ contributions in lattice QCD calculations of nucleon polarizabilities, improving their accuracy.

Findings

$N ext{-} ext{pi}$ states significantly affect polarizability calculations.

Including $N ext{-} ext{pi}$ contributions aligns lattice results with experimental values.

Methodology enables future studies of other nucleon polarizabilities.

Abstract

We present a lattice QCD calculation of the nucleon electric polarizabilities at the physical pion mass. Our findings reveal the substantial contributions of the $N\pi$ states to these polarizabilities. Without considering these contributions, the lattice results fall significantly below the experimental values, consistent with previous lattice studies. This observation has motivated us to compute both the parity-negative $N\pi$ scattering up to a nucleon momentum of $\sim0.5$ GeV in the center-of-mass frame and corresponding $N\gamma^*\to N\pi$ matrix elements using lattice QCD. Our results confirm that incorporating dynamic $N\pi$ contributions is crucial for a reliable determination of the polarizabilities from lattice QCD. This methodology lays the groundwork for future lattice QCD investigations into various other polarizabilities.