Transition magnetic moments of Majorana neutrinos in supersymmetry without R-parity in light of neutrino oscillations

The transition magnetic moments of Majorana neutrinos ${\ensuremath{\mu}}_{{\ensuremath{\nu}}_{ij}}$ ($ij=e\ensuremath{\mu}$, $e\ensuremath{\tau}$, $\ensuremath{\mu}\ensuremath{\tau}$) are calculated in grand unified theory (GUT) constrained Minimal Supersymmetric Standard Model (MSSM) with explicit $R$-parity violation. It is assumed that neutrinos acquire masses via one-loop (quark-squark and lepton-slepton) radiative corrections. The mixing of squarks, sleptons, and quarks is considered explicitly. The connection between ${\ensuremath{\mu}}_{{\ensuremath{\nu}}_{ij}}$ and the entries of neutrino mass matrix is studied. The current upper limits on ${\ensuremath{\mu}}_{{\ensuremath{\nu}}_{ij}}$ are deduced from the elements of phenomenological neutrino mass matrix, which is reconstructed using the neutrino oscillation data and the lower bound on the neutrinoless double beta decay half-life. Further, the results for ${\ensuremath{\mu}}_{{\ensuremath{\nu}}_{e\ensuremath{\mu}}}$, ${\ensuremath{\mu}}_{{\ensuremath{\nu}}_{e\ensuremath{\tau}}}$ and ${\ensuremath{\mu}}_{{\ensuremath{\nu}}_{\ensuremath{\mu}\ensuremath{\tau}}}$ are presented for the cases of inverted and normal hierarchy of neutrino masses and different SUSY scenarios. The largest values are of the order of ${10}^{\ensuremath{-}17}$ in units of Bohr magneton.