  Assuming that neutrinos have non-vanishing magnetic moments, we discuss the
possibility of pair production through annihilation of charged fermions in
high-energy collisions. Adopting the Pauli interaction for photon-neutrino
coupling, we calculate the neutrino pair production cross section in the photon
channel and compare the result with the standard model in $ Z^{0} $ channel. we
demonstrated that the enhancement of the production rate for Majorana neutrino
pairs over the standard model rate can be possible at the center-of-mass energy
of $10 - 100$ TeV for the Large Hadron Collider or the ultra-high-energy cosmic
Ray when the transition magnetic moment is not smaller than $10^{-9} - 10^{-10}
\mu_B$.

High Energy Physics - Phenomenology