Studies of nonresonant Higgs pair production at electron-proton colliders

The measurement of the Higgs quartic coupling modifier between a Higgs boson pair and a vector boson pair, $\kappa _{2V}$, 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 $\kappa _{\lambda }$. A sensitivity analysis should target both parameters. Since the LHC cannot avoid the gluon fusion pollution, which becomes severe for non-SM $\kappa _{\lambda }$, 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 $\kappa _{2V}$ and $\kappa _{\lambda }$. 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 $\kappa _{2V} \in [0.8, 1.2]$ and $\kappa _{\lambda }\in [1, 2.5]$ at 95% C.L. for the total luminosity of $10$ ab$^{-1}$ and 10% uncertainty on the background yields.