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We investigate forces induced by the exchange of two light neutrinos betweenStandard Model (SM) fermions in the presence of effective operatorsparametrising physics beyond the SM. We first set up a general framework inwhich we derive the long-range potential mediated by weakly interactingneutrinos in the SM, retaining both spin-independent and spin-dependent terms.We then derive neutrino-mediated potentials when there are vector, scalar andtensor non-standard interactions present as well as an exotic neutrino magneticmoment. Examining the phenomenology of such long-range potentials in atomicscale laboratory experiments, we derive upper bounds on the Wilson coefficientsof the effective operators and compare these to those from processes such ascharged lepton flavour violation.

Probing New Physics with Long-Range Neutrino Interactions: An Effective Field Theory Approach