Heavy flavour production in the presence of a weak magnetic field

We calculate analytic expression for the cross section up to order $(eB)^2$ for the production of a heavy quark $(Q)$ of mass $m_Q$ through the gluon $(g)$ fusion process $g+g\to Q+\bar{Q}$ in the presence of a constant weak external magnetic field $(B)$ with strength $eB \ll m_Q^2$. This is done us