Large neutrino magnetic moments in the light of recent experiments

The excess in electron recoil events reported recently by the XENON1T experiment may be interpreted as evidence for a sizable transition magnetic moment mu vev mu of Majorana neutrinos. We show the consistency of this scenario when a single component transition magnetic moment takes values mu vev mu is an element of (1.65-3.42) x10(-11)mu B. Such a large value typically leads to unacceptably large neutrino masses. In this paper we show that new leptonic symmetries can solve this problem and demonstrate this with several examples. We first revive and then propose a simplified model based on SU(2)(H) horizontal symmetry. Owing to the difference in their Lorentz structures, in the SU(2)(H) symmetric limit, m(nu) vanishes while mu vev mu is nonzero. Our simplified model is based on an approximate SU(2)(H), which we also generalize to a three family SU(3)(H)-symmetry. Collider and low energy tests of these models are analyzed. We have also analyzed implications of the XENON1T data for the Zee model and its extensions which naturally generate a large mu vev mu with suppressed m(nu) via a spin symmetry mechanism, but found that the induced mu vev mu is not large enough to explain recent data. Finally, we suggest a mechanism to evade stringent astrophysical limits on neutrino magnetic moments arising from stellar evolution by inducing a medium-dependent mass for the neutrino