Electroweak Corrections to di-Higgs Boson Production considering the full Top-quark Mass Dependence

In this talk, I will present our detailed calculations of
two-loop electroweak (EW) corrections for Higgs boson pair production via
gluon fusion, taking into account the effects of the top-quark mass. Mixed
QCD-EW corrections are essential for reducing theoretical uncertainties in
predictions for the Large Hadron Collider (LHC) and its high-luminosity
upgrade (HL-LHC). The Higgs quartic coupling, which is a crucial quantity
defining the Higgs boson potential, only emerges at the NLO EW level.
Furthermore, NLO EW corrections calculated using the heavy top-quark mass
expansion have shown corrections as substantial as 65% when the partonic
center-of-mass energy is around 260 GeV. These findings emphasise the
urgent need for a thorough computation of the corrections to the process
gg → HH, similar to the one we are doing. The two-loop QCD-EW gg → HH 
process involves the following two broad categories of diagrams:

1) Box loops with top and bottom quarks and a scalar Higgs or goldstone
boson exchange.

2) Box loops with light quarks in addition to vector boson or goldstone
boson exchanges.

In my talk, I will outline the analytical and numerical methods we are
using to compute these diagrams and address the complex scale hierarchies
and divergences specific to this process. Given the significance and
complexity of these corrections, our work will provide new results at
higher orders in perturbation theory for highly relevant Higgs processes
at the LHC. In summary, understanding EW corrections can address
fundamental questions about our universe and directly impact experimental
physics, the potential for new discoveries, and collaboration within the
scientific community