Long-Range Forces from Neutrino-Pair Exchange

The long-range forces arising from neutrino-pair exchange between elementary systems are studied with the use of dispersion-theoretic techniques previously applied to the study of multiphoton exchange. It is shown that the potential decreases as $r^{-5\mathrm{}}$ for large separation $r$, independently of the particles or systems under consideration. The weak lepton-lepton force does not seem to be observable at present in laboratory experiments. The long-range forces on neutrinos are also studied. For the case of two neutral molecules, a numerical comparison is made of the three types of long-range forces: gravitational, electromagnetic, and weak.