Influence of Meson's 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(sigma,rho,omega-mesons) are modified by presence of particle width. In particular, the usual method of deriving particle masses from logarithmic derivatives need to be modified. Similarly Yukawa-like potentials of nuclear physics due to exchange of those mesons are significantly modified since the coupling to the decay products is strong. For example, the large distance asymptotic changes, exp(-M_{min} r), where M_{min} is the sum of the decay product masses (2 m_{\pi}, 2 m_{e}, 2 m_{\nu}). In the area M_{min}r<1the potential has a long-range tail 1/r^3. Similar effects appear due to the virtual decays in the elecroweak sector of the Standard model. The $Z-\gamma$ 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.