Helicity amplitude for the process $q\text{Bar}q\to q\text{Bar}qg$

Precision calculations in hadronic processes at high energy colliders are crucial for improving the understanding of the standard phenomena as well as for the discovery of new physics. Spinor-helicity formalism serves as one of the most efficient ways to simplify the calculations of $S$ matrix elements. In this article, we compute the $S$ matrix elements for the process $q\text{Bar}q\to q\text{Bar}qg$ mediated by photon and gluon. Ignoring the contribution of $Z$ boson exchange, we show that the calculation of $S$ matrix elements for this process simplifies to a great extent by using spinor-helicity formalism.