Studies of nonresonant Higgs pair production at electron-proton colliders

Abstract

The measurement of the Higgs quartic coupling modifier between a Higgs boson pair and a vector boson pair, $κ_{2V}$, is expected to be achieved from vector-boson fusion (VBF) production of a Higgs boson pair. However, this process involves another unmeasured parameter, the trilinear Higgs self-coupling modifier $κ_{λ}$. A sensitivity analysis should target both parameters. Since the LHC cannot avoid the gluon fusion pollution, which becomes severe for non-SM $κ_{λ}$, an electron-proton collider is more appropriate for the comprehensive measurement. In this regard, we study the VBF production of a Higgs boson pair in the $b\bar{b}b\bar{b}$ final state at the LHeC and FCC-he. Performing detailed analysis using the simulated dataset, we devise the search strategy specialized at the LHeC and FCC-he and give a prediction for the sensitivity to both $κ_{2V}$ and $κ_{λ}$. We find that the two electron-proton colliders have high potential: the LHeC has similar exclusion prospects as the HL-LHC; the FCC-he is extremely efficient, excluding the parameter space outside $κ_{2V} \in [0.8, 1.2]$ and $κ_{λ}\in [1, 2.5]$ at 95% C.L. for the total luminosity of $10$ ab$^{-1}$ and 10% uncertainty on the background yields.