Gluon fusion production at NLO: merging the transverse momentum and the high-energy expansions

Abstract

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.

On the NLO QCD corrections to gluon-initiated ZH production

“…Instead, the two-loop box integrals associated to A (1, ) i were evaluated combining two analytic approximations corresponding to different kinematical regimes, and here we briefly recall the main features of this approach, described in detail in ref. [36].…”

“…In ref. [36] it has been shown that, in the forward kinematic regime 6 defined by | t| ≤ |û|, the results of the p T expansion are accurate in the phase-space region | t| 4m 2 t , while the HE expansion is accurate in the complementary region | t| 4m 2 t . If the convergence of both expansions is improved using Padé approximants, then the combination of the results allows to approximate the exact cross section with an accuracy of 1% or below over the whole phase space.…”

“…(14,15) in ref. [36]. This shift is applied to the form factors before the construction of the relative Padé approximants.…”

“…In ref. [36] it has been shown that this approach can provide a fast evaluation of the virtual corrections with an accuracy of 1% or below. In this paper, we present a complete assessment of the NLO QCD corrections to gg → ZH by including the real-emission contributions, which are related to one-loop diagrams with an additional parton in the final state.…”

ZH production in gluon fusion at NLO in QCD

“…Recently, the virtual corrections to both gg → HH and gg → ZH, based on a combination of transverse-momentum expansion and high-energy expansion, have been presented in ref. [33]. The total cross section and invariant-mass distribution for gg → ZH at NLO QCD has been calculated in ref.…”