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The two-Higgs-doublet model with a $U(1)_H$ gauge symmetry (N2HDM-$U(1)$) hasseveral advantages compared to the ``standard'' $Z_2$ version (N2HDM-$Z_2$): Itis purely based on gauge symmetries, involves only spontaneous symmetrybreaking, and is more predictive because it contains one parameter less in theHiggs potential, which further ensures $CP$ conservation, i.e., avoiding thestringent bounds from electric dipole moments. After pointing out that asecond, so far unknown version of the N2HDM-$U(1)$ exists, we examine thephenomenological consequences for the Large Hadron Collider (LHC) of thedifferences in the scalar potentials. In particular, we find that while theN2HDM-$Z_2$ predicts suppressed branching ratios for decays into differentHiggs bosons for the case of the small scalar mixing (as suggested by Higgscoupling measurements), both versions of the N2HDM-$U(1)$ allow for sizablerates. This is particularly relevant in light of the CMS excess in resonantHiggs-pair production at around $650\,$GeV of a Standard Model Higgs bosonsubsequently decaying to photons and a new scalar with a mass of$\approx90\,$GeV subsequently decaying to bottom quarks (i.e., compatible withthe CMS and ATLAS $\gamma\gamma$ excesses at $95\,$GeV and $\approx 670\,$GeV).As we will show, this excess can be addressed within the N2HDM-$U(1)$ in caseof a nonminimal Yukawa sector, predicting an interesting and unavoidable $Z+b\bar b$ signal and motivating further asymmetric di-Higgs searches at the LHC.

Asymmetric di-Higgs signals of the next-to-minimal 2HDM with a $U(1)$ symmetry