Neutrino Trident Production: A Powerful Probe of New Physics with Neutrino Beams

The production of a ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ pair from the scattering of a muon neutrino off the Coulomb field of a nucleus, known as neutrino trident production, is a subweak process that has been observed in only a couple of experiments. As such, we show that it constitutes an exquisitely sensitive probe in the search for new neutral currents among leptons, putting the strongest constraints on well-motivated and well-hidden extensions of the standard model gauge group, including the one coupled to the difference of the lepton number between the muon and tau flavor, ${L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}}$. The new gauge boson ${Z}^{\ensuremath{'}}$, increases the rate of neutrino trident production by inducing additional $(\overline{\ensuremath{\mu}}{\ensuremath{\gamma}}_{\ensuremath{\alpha}}\ensuremath{\mu})(\overline{\ensuremath{\nu}}{\ensuremath{\gamma}}^{\ensuremath{\alpha}}\ensuremath{\nu})$ interactions, which interfere constructively with the standard model contribution. Existing experimental results put significant restrictions on the parameter space of any model coupled to muon number ${L}_{\ensuremath{\mu}}$, and disfavor a putative resolution to the muon $g\ensuremath{-}2$ discrepancy via the loop of ${Z}^{\ensuremath{'}}$ for any mass ${m}_{{Z}^{\ensuremath{'}}}\ensuremath{\gtrsim}400\text{ }\text{ }\mathrm{MeV}$. The reach to the models' parameter space can be widened with future searches of the trident production at high-intensity neutrino facilities such as the LBNE.

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