High-precision lattice determination of the interaction potential of an SU(2) solitonic dipole and comparison with perturbative QED

Abstract

We determine the interaction potential of a solitonic dipole in the singlet state, modeled as an SU(2) field, using improved lattice simulations of two stationary solitons at varying separations. The potential is extracted from the energy of two-soliton configurations as a function of distance. At large separations, the interaction reproduces the classical Coulomb potential quantitatively up to an energy shift $\delta E_\infty\approx 9\;\text{keV}$ of the fitted asymptotic constant relative to $2m_ec_0^2$, assumed to be related to limited numerical precision on the lattice. At shorter distances, deviations from the Coloumb potential of point-like charges appear, that are in qualitative agreement with the asymptotic formula of perturbative Quantum Electrodynamics, reflecting the running of the fine-structure constant, with the inverse fine-structure constant ($\alpha^{-1} \approx 137$) reproduced.