$gg\rightarrow HH$ amplitude induced by bottom quarks at two-loop level: planar master integrals

Abstract

We consider the two-loop amplitude of $gg\rightarrow HH$ mediated by bottom quarks, which provides a correction of percent level at leading order in the low invariant mass region. In order to compute the corresponding master integrals, we perform an expansion for the bottom quark mass, using the method of differential equations and fixing the boundary constants by a numerical approach. The results of 177 planar master integrals which are expressed in terms of multiple polylogarithms are provided.