Two-loop helicity amplitudes for gg → ZZ with full top-quark mass effects

Abstract

We calculate the two-loop QCD corrections to gg → ZZ involving a closed top-quark loop. We present a new method to systematically construct linear combinations of Feynman integrals with a convergent parametric representation, where we also allow for irreducible numerators, higher powers of propagators, dimensionally shifted integrals, and subsector integrals. The amplitude is expressed in terms of such finite integrals by employing syzygies derived with linear algebra and finite field techniques. Evaluating the amplitude using numerical integration, we find agreement with previous expansions in asymptotic limits and provide ab initio results also for intermediate partonic energies and non-central scattering at higher energies.

Off-shell Higgs production at the LHC as a probe of the trilinear Higgs coupling

“…We believe that these are conservative uncertainties -results for two additional more aggressive assumptions about the systematic uncertainties entering the HL-LHC off-shell Higgs analysis can be found in appendix B. In fact, given the steady progress in the calculation of massive higher-loop corrections to pp → ZZ → 4 (see [84,85] for the latest theoretical developments) and in view of the fact that it is theoretically known of how to achieve NLO accuracy for ME-based discriminants [72][73][74], it should be possible to put our naive estimates of theoretical uncertainties on more solid grounds. As can be seen from the left panel in figure 6, any improvement of our theoretical understanding of the D S distribution for D S −3.5 will notably increase the sensitive of off-shell Higgs measurements to modifications of the trilinear Higgs coupling.…”

Three-loop helicity amplitudes for diphoton production in gluon fusion

“…The next step is the actual IBP integral reduction. We did this using an in-house implementation of the Laporta algorithm [37], Finred [42], which exploits syzygy-based techniques [43][44][45][46][47][48] and finite-field arithmetics [42,[49][50][51]. We found in this way that the three loop helicity amplitudes can be expressed in terms of the 221 MIs computed in ref.…”

Probing Higgs portals with matrix-element based kinematic discriminants in $ZZ \to 4 \ell$ production

“…[51,63,64]) of the state-of-the-art SM predictions of pp → ZZ production for kinematic configurations above the two topquark threshold, achieving the assumed systematic uncertainties of ∆ = 8% and ∆ = 4% is certainly more challenging in the case of the m 4 distribution. The steady progress of perturbative QCD calculations, in particular the exact evaluations of the two-loop on-shell amplitudes for gg → ZZ involving top quarks [65,66] makes us, however, confident that systematic uncertainties in the ballpark of 10% or below are attainable till 3 ab −1 of data are collected at the HL-LHC.…”