Higgs Decays to $Z\gamma$ and $\gamma\gamma$ in the Flavor-Gauged Two Higgs Doublet Model

Abstract

This work examines the $h\to Z\gamma$ and $h\to\gamma\gamma$ decays in the flavor-gauged two Higgs doublet model (FG2HDM), which augments the Standard Model (SM) with an additional scalar doublet, a singlet, and a $U(1)'$ flavor gauge symmetry. Beyond the SM spectrum, FG2HDM predicts five additional physical scalars and a new neutral gauge boson, $Z'$. We demonstrate that while both decay channels are sensitive to charged Higgs loops, $h \to Z\gamma$ is uniquely modified by fermion-antifermion-$Z$ ($f\bar{f}Z$) vertex corrections. These vertex corrections further impact top-quark observables and the flavor-changing neutral current (FCNC) process $b\to s\ell^+\ell^-$. Our analysis identifies a viable parameter space ($m_{H^\pm}>200$~GeV and $\lambda_{hH^+H^-}<0$) consistent with current $1\sigma$ experimental limits, where the signal strength $\mu_{\gamma\gamma}$ remains the primary constraint on scalar sector parameters. Regarding the $f\bar{f}Z$ couplings, we delineate the allowed regions in the $\mathcal{Q}_{tL}$-$\mathcal{Q}_{tR}$ plane by evaluating the leading top-quark contributions, revealing that $b\to s\ell^+\ell^-$ imposes the most stringent bounds. Finally, we highlight that the $14\%$ projected precision for $\mu_{Z\gamma}$ at the High-Luminosity LHC (HL-LHC) will significantly enhance sensitivity to the FG2HDM.