Production of heavy vector particles in interactions of leptons with the massless gauge bosons

The cross section for vector leptoquark production in electron--gluon collisions is calculated analytically using the Lagrangian with the minimal couplings between the leptoquarks and the gauge fields of the standard model. It is found that the cross section significantly exceeds the corresponding quantity previously presented in the literature. The cross section of exclusive $W$ boson production in neutrino--photon scattering emerges as a by-product of this letter. The obtained results can be used for studies at $ep$ colliders.