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Euclidean point-to-point propagators or wall-to-wall correlators related toexchange by an unstable particle(sigma,rho,omega-mesons) are modified bypresence of particle width. In particular, the usual method of derivingparticle masses from logarithmic derivatives need to be modified. SimilarlyYukawa-like potentials of nuclear physics due to exchange of those mesons aresignificantly modified since the coupling to the decay products is strong. Forexample, 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 along-range tail 1/r^3. Similar effects appear due to the virtual decays in theelecroweak sector of the Standard model. The $Z-\gamma$ mixing via electronloop gives the parity violation potential with the range $1/2 m_{e}$, i.e. therange of the weak interaction increases $10^{5}$ times

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