Spinor-helicity calculation of the $g^{\ast }{g}^{\ast }\to q\bar{q}{V}^{\ast }$ amplitude at the tree level

We compute amplitudes for the process $g^{\ast }{g}^{\ast }\to q\bar{q}{V}^{\ast }$ (two virtual gluons into a quark, antiquark and a boson) at the tree level using the spinor-helicity formalism. The resulting analytic expressions are much shorter than squared amplitudes obtained using trace methods. Our results can be used to expedite numerical calculations in phenomenological studies of the Drell-Yan process in high energy factorization framework.