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

Euclidean point-to-point propagators or wall-to-wall correlators related to exchange by an unstable particle (σ,ρ,ω 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, ~exp(-Mminr), where Mmin is the sum of the decay product masses (2mπ,2me,2mν). In the area Mminr<1, the potential has a long-range tail of ∼1/r3. Similar effects appear due to the virtual decays in the electroweak sector of the standard model. The Z-γ mixing via electron loop gives the parity violation potential with the range 1/2me, i.e., the range of the weak interaction increases 105 times.