Measurements of the SUSY Higgs self-couplings and the reconstruction of the Higgs potential

TL;DR

This work analyzes reconstructing the SUSY Higgs potential within a CP-conserving two-Higgs-doublet framework relevant to the MSSM, arguing that full reconstruction at dim-4 requires access to some quartic self-couplings beyond the trilinears. By expressing self-couplings in the mass basis and exploring the decoupling limit, it shows that most dependence on the underlying λ_i is screened, leaving the light-Higgs mass M_h and the mixing factor s_{β-α} as primary determinants of the hhh coupling. Radiative corrections are shown to be largely absorbed into the corrected Higgs mass, reinforcing the decoupling intuition, while higher-order (dim-6) operators can modify couplings but are suppressed by Λ^2 and remain difficult to detect. The phenomenological analysis across staged lepton colliders demonstrates that, even with measurements of masses and couplings, reconstructing the full dim-4 potential—and especially accessing λ_a, λ_b, λ_c via quartic interactions—appears infeasible within expected experimental precision, though collider data can still constrain the parameter space and hint at hard (beyond-dim-4) contributions.

Abstract

We address the issue of the reconstruction of the scalar potential of a two-Higgs doublet model having in mind that of the MSSM. We first consider the general CP conserving dim-4 effective potential. To fully reconstruct this potential, we show that even if all the Higgs masses and their couplings to the standard model particles are measured one needs not only to measure certain trilinear Higgs self-couplings but some of the quartic couplings as well. We also advocate expressing the Higgs self couplings in the mass basis. We show explicitly, that in the so-called decoupling limit, the most easily accessible Higgs self-couplings are given in terms of the Higgs mass while all other dependencies on the parameters of the general effective potential are screened. This helps also easily explain how, in the MSSM, the largest radiative corrections which affect these self couplings are reabsorbed by using the corrected Higgs mass. We also extend our analysis to higher order operators in the effective Higgs potential. While the above screening properties do not hold, we argue that these effects must be small and may not be measured considering the foreseen poor experimental precision in the extraction of the SUSY Higgs self-couplings.

Figures (3)

• Figure 1: Higgs mass spectrum without "hard" terms but with $A_t=1000$GeV, $M_S=800$GeV, $\mu=-300$GeV and $\tan \beta=10$ (left) and with the inclusion of additional terms with $\lambda_{1-5}^{\rm new}=-\lambda_{6,7}^{\rm new}=.1$(right). All masses are in GeV.
• Figure 2: $s_{\beta-\alpha}^2$ as a function of $M_A$. MSSM refers to $\lambda_i=0$ with $A_t=1000$GeV, $M_S=800$GeV,$\mu=-300$GeV while "new" has $\lambda_{1-5}^{\rm new}=-\lambda_{6,7}^{\rm new}=.1$. tb stands for $\tan \beta$.
• Figure 3: $g_{H^i H^j H^k}/\tilde{g}_{hhh}^{\rm SM}$ with $\tilde{g}_{hhh}^{\rm SM}=-3M_h^2/2v^2$. The SM Higgs mass is identified with $M_h$ (and thus varies with $M_A$). The curve in the first panel is the usual MSSM where the one in the second panel is defined with the same parameters as in Fig. \ref{['figsmasses']}.