Higgs Decays to $Z{\hat{I}}^3$ and ${\hat{I}}^3{\hat{I}}^3$ in the Flavor-Gauged Two Higgs Doublet Model

Abstract

This work examines the $h\to Z{\hat{I}}^3$ and $h\to {\hat{I}}^3{\hat{I}}^3$ 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 $U(1{)}^{\prime }$ flavor gauge symmetry. Beyond the SM spectrum, FG2HDM predicts five additional physical scalars and a new neutral gauge boson, $Z^{\prime }$. We demonstrate that while both decay channels are sensitive to charged Higgs loops, $h\to Z{\hat{I}}^3$ 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 $\hat{I}{»}_{h{H}^{+}{H}^{-}}<0$) consistent with current $1\ddot{I}ƒ$ experimental limits, where the signal strength $\hat{I}{¼}_{{\hat{I}}^3{\hat{I}}^3}$ 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 $\hat{I}{¼}_{Z{\hat{I}}^3}$ at the High-Luminosity LHC (HL-LHC) will significantly enhance sensitivity to the FG2HDM.

27 pages, publised version