Quartic Higgs coupling at hadron colliders

The quartic Higgs self-coupling is the final measurement in the Higgs potential needed to fully understand electroweak symmetry breaking. None of the present or future colliders are known to be able to determine this parameter. We study the chances of measuring the quartic self-coupling at hadron colliders in general and at the very large hadron collider in particular. We find the prospects challenging.

Figure 1

Examples of Feynman diagrams contributing to the process $gg\to HHH$.

Figure 2

Total cross section for the production process $gg\to HHH$ at the 200 TeV VLHC in the standard model.

Figure 3

Total cross section ratios normalized to the standard model values for the production process $gg\to HHH$ at the LHC (left) and at the 200 TeV VLHC (right). The Higgs mass is fixed to 120 GeV, the absolute values of triple and quartic self-couplings are varied up to twice the standard model values. Contour lines are included every 0.25 steps on the $z$ axis. In the lower set of figures the triple Higgs self-coupling is fixed. The standard model values for the cross sections are $6.25\times {10}^{-2}\mathrm{fb}$ at the LHC and 9.45 fb at the VLHC.

Figure 4

Normalized partonic center-of-mass energy distributions for $gg\to HHH$ at the LHC (left) and at the 200 TeV VLHC (right). The Higgs mass is fixed to 120 GeV. The trilinear and quartic Higgs self-couplings are varied independently.