Nucleon Electric Polarizabilities and Nucleon-Pion Scattering at the Physical Pion Mass

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 $\sim 0.5\mathrm{GeV}$ 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.