Neutrino Radiative Decay in an External Electromagnetic Field via Vector Leptoquark

The massive neutrino radiative decay $\nu_i \rightarrow \nu_j \gamma$ ($i \ne j$) is investigated within the Minimal Quark-Lepton Symmetry of the Pati-Salam type based on the $SU(4)_V \times SU(2)_L \times G_R$ group in an external constant crossed field ($\vec {\cal E} \perp \vec H$, ${\cal E}=H$). The matrix element $\Delta M^{(X)}$ and the decay probability $W^{(X)}$ due to the leptoquark $X$ contribution are analysed. The effect of significant enhancement of the neutrino decay by the crossed field takes place. It is shown that the leptoquark contribution to the decay probability can dominate over the $W$-boson one in the case of strong suppression of the lepton mixing in the framework of the SM.