Two-loop massless QCD corrections to the g + g → H + H four-point amplitude

Abstract

We compute the two-loop massless QCD corrections to the four-point amplitude g+g → H +H resulting from effective operator insertions that describe the interaction of a Higgs boson with gluons in the infinite top quark mass limit. This amplitude is an essential ingredient to the third-order QCD corrections to Higgs boson pair production. We have implemented our results in a numerical code that can be used for further phenomenological studies.

Higgs-pair production via gluon fusion at hadron colliders: NLO QCD corrections

“…Beyond these NNLO QCD corrections, the soft-gluon resummation (threshold resummation) has been performed at next-to-next-to-leading logarithmic (NNLL) accuracy for the total cross section and invariant mass distribution, modifying the total cross section further by a small amount if the central scales are chosen as µ R = µ F = Q/2 [56,57]. Very recently, the N 3 LO QCD corrections have been computed in the Born-improved HTL resulting in a small modification of the cross section beyond NNLO [31][32][33][34]. These N 3 LO QCD corrections in the HTL have been merged with the full top-mass effects of the NLO calculation [33].…”

“…We attribute additional Feynman parameters x 5 , x 6 to this residual propagator and the next one [(q − q 1 ) 2 ] and 1 − x 5 − x 6 for the last one (q 2 ) in Eq. (31). Performing the substitution 6…”

“…While the NLO corrections are large, the NNLO contributions are of more moderate size. Very recently, the next-to-next-to-next-to-leading order (N 3 LO) QCD corrections have been computed in the limit of heavy top quarks resulting in a small further modification of the cross section [31][32][33]. This calculation uses the N 3 LO corrections to the effective Higgs and Higgs-pair couplings to gluons in the heavy-top limit (HTL) [34].…”

The gluon-fusion production of Higgs boson pair: N3LO QCD corrections and top-quark mass effects

“…The prefactor i v 2 in the above equation is chosen in order to recycle the same notations used in ref. [126]. The amplitudes for Class-A and Class-B can be decomposed into two Lorentz covariant and gauge invariant terms [29] M A/B,µν ab…”

Fast-rolling relaxion

“…The simplest example of the new strong sector is given in [1], where we introduce new light fermions having the same SM charges as a right handed neutrino, N and N c , and new heavy fermions having the same Standard Model (SM) charges as a lepton doublet, L and L c . 3 They are charged under a new SU (3) group, whose field strength is denoted as G a µν . The relevant part of the Lagrangian is given by…”