Fully differential Higgs boson pair production in association with a $Z$ boson at next-to-next-to-leading order in QCD

We present a fully differential next-to-next-to-leading order QCD calculation of the Higgs pair production in association with a $Z$ boson at hadron colliders, which is important for probing the trilinear Higgs self-coupling. The next-to-next-to-leading-order corrections enhance the next-to-leading order total cross sections by a factor of 1.2–1.5, depending on the collider energy, and change the shape of next-to-leading order kinematic distributions. We discuss how to determine the trilinear Higgs self-coupling using our results.

Figure 1

Sample Feynman diagrams for $pp\to Zhh$ production.

Figure 2

The total cross sections of $pp\to Zhh$ production at NLO (left) and NNLO (right) without contribution from loop-induced $gg$ fusion channel. In the bottom panels, the deviation is defined as $\sigma (q_T^{\mathrm{cut}})/\sigma (q_T^{\mathrm{cut}}=10\mathrm{GeV})$. The curves are drawn using the linear interpolation method.

Figure 3

The total cross section of $pp\to Zhh$ production as a function of the collision energy. The bands denote the scale uncertainties when varying $\mu ={\mu }_F={\mu }_R$ by a factor of two. The NNLO total cross sections include the loop-induced $gg$ channel, and the contribution from this channel is also shown in the upper panel individually.

Figure 4

The kinematic distributions of $pp\to Zhh$ production at the 14 TeV LHC. $h1$ denotes the Higgs boson with larger transverse momentum.

Figure 5

The kinematic distributions of $pp\to Zhh$ production at a future 100 TeV hadron collider. $h1$ denotes the Higgs boson with larger transverse momentum.

Figure 6

The total cross section as a function of $\kappa$ at a hadron collider with $\sqrt{S}=100\mathrm{TeV}$.

Figure 7

Normalized NNLO $p_T$ distributions of the $Z$ boson with $\kappa =1$ and $-3.67$, which correspond to the same total cross section.