Higgs Boson Pair Production in Gluon Fusion at Next-to-Leading Order with Full Top-Quark Mass Dependence

We present the calculation of the cross section and invariant mass distribution for Higgs boson pair production in gluon fusion at next-to-leading order (NLO) in QCD. Top-quark masses are fully taken into account throughout the calculation. The virtual two-loop amplitude has been generated using an extension of the program GoSam supplemented with an interface to Reduze for the integral reduction. The occurring integrals have been calculated numerically using the program SecDec. Our results, including the full top-quark mass dependence for the first time, allow us to assess the validity of various approximations proposed in the literature, which we also recalculate. We find substantial deviations between the NLO result and the different approximations, which emphasizes the importance of including the full top-quark mass dependence at NLO.

Figure 1

Comparison of the full calculation to various approximations for the Higgs pair invariant mass distribution at $\sqrt{s}=13\mathrm{TeV}$. NLO HEFT denotes the effective field theory result, i.e., approximation (i) above, while ${\mathrm{FT}}_{\text{approx}}$ stands for approximation (ii), where the top-quark mass is taken into account in the real radiation part only. The band results from scale variations by a factor of 2 around the central scale $\mu =m_{hh}/2$.

Figure 2

Comparison of the virtual amplitude with full top-quark mass dependence to various orders in a $1/m_t^2$ expansion. $V_N^{\prime }$ denotes the Born-improved HEFT result to order $N$ in the $1/m_t^2$ expansion, i.e., $V_N^{\prime }=V_{N}B/B_N$.