We compute the next-to-leading virtual QCD corrections to the partonic cross section of the production of a Higgs boson in association with a Z boson in gluon fusion. The calculation is based on the recently introduced method of evaluating the amplitude via an expansion in terms of a small transverse momentum. We generalize the method to the case of different masses in the final state and of a process not symmetric in the forward-backward direction exchange. Our analytic approach gives a very good approximation (better than percent) of the partonic cross section in the center of mass energy region up to ∼ 750 GeV, where at the LHC ∼ 98% of the total hadronic cross section is concentrated.

The virtual corrections to gg → HH and gg → ZH are analytically evaluated combining an expansion in the small transverse momentum of the final particles with an expansion valid at high energies. The two expansion methods describe complementary regions of the phase space and we merge their results, extending the range of validity of both expansions using Padé approximants. We show that this approach can reproduce the available numerical results retaining the exact top quark mass dependence with an accuracy below the 1% level. Our results allow a fast and flexible evaluation of the virtual corrections of the considered processes. Furthermore, they are available in different renormalisation schemes of the top quark mass.

We compute the QCD corrections at next-to-leading order for the process gg → ZH, including both the virtual two-loop terms and real-emission contributions. The two-loop box diagrams in the virtual corrections are approximated analytically over the complete phase space, combining the results of an expansion in the limit of small transverse momentum and an expansion in the regime of high energy. We obtain both inclusive and differential results for the cross section. We find that the NLO QCD corrections are of the same size as the LO contribution up to ZH invariant masses close to 1 TeV, but they increase significantly when higher energies are considered, due to a class of real-emission diagrams in which the Z boson is radiated from an open quark line. Finally, we estimate the uncertainty due to the renormalization scheme used for the top-quark mass both on the total and differential cross section.

We compute the two-loop effects induced by an anomalous Higgs trilinear self-coupling in the partial decay width h → γZ. The computation is performed using the anomalous coupling approach working in the unitary gauge and in a theory in which the anomalous coupling is generated via the addition to the scalar potential part of the Standard Model Lagrangian of an (in)finite tower of (Φ † Φ) n terms. The former computation is automatically finite while the latter requires the renormalization of the lowest order contribution. We discuss the renormalization conditions that should be employed in order to obtain the same result in the two approaches. We find that the h → γZ process is one of the most sensitive mode to an anomalous trilinear Higgs self-coupling. As a by-product of this work we confirm one of two different results present in the literature concerning the contribution of an anomalous Higgs trilinear coupling in the h → γγ decay.

Associated 𝑍 𝐻 production plays a special role in the determination of Higgs properties at the LHC. An improved theoretical control over the 𝑔𝑔 → 𝑍 𝐻 subprocess is important to reduce the scale uncertainties in the SM prediction. We present the calculation of the virtual QCD corrections to 𝑔𝑔 → 𝑍 𝐻 using an analytic approximation, based on the expansion of the amplitude in terms of a small transverse momentum of the final particles. We also report on the combination of these results with those obtained from a complementary approach, based on the expansion of the amplitude in the high-energy limit. When the results of both expansions are improved using Padé approximants, their combination provides an accurate approximation over the whole phase space.