Influence of meson widths on Yukawa-like potentials and lattice correlation functions

Abstract

Euclidean point-to-point propagators or wall-to-wall correlators related to exchange by an unstable particle ($\ensuremath{\sigma},\ensuremath{\rho},\ensuremath{\omega}$ mesons) are modified by the presence of particle width. In particular, the usual method of deriving particle masses from logarithmic derivatives needs to be modified. Similarly, Yukawa-like potentials of nuclear physics due to the exchange of those mesons are significantly modified since the coupling to the decay products is strong. For example, the large-distance asymptotic changes, $~\mathrm{exp}(\ensuremath{-}{M}_{\mathrm{min}}r)$, where ${M}_{\mathrm{min}}$ is the sum of the decay product masses ($2{m}_{\ensuremath{\pi}},2{m}_{e},2{m}_{\ensuremath{\nu}}$). In the area ${M}_{\mathrm{min}}rl1,$ the potential has a long-range tail of \ensuremath{\sim}1/${r}^{3}$. Similar effects appear due to the virtual decays in the electroweak sector of the standard model. The $Z\text{\ensuremath{-}}\ensuremath{\gamma}$ mixing via electron loop gives the parity violation potential with the range $1/2{m}_{e}$, i.e., the range of the weak interaction increases ${10}^{5}$ times.