We study the $h \to Z\gamma$ decay within the flavor gauged two Higgs doublet model (FG2HDM). This model extends the Standard Model (SM) to include a scalar doublet and a scalar singlet, under the imposition of a $U(1)'$ flavor gauge symmetry. Compared to the SM, the FG2HDM predicts five additional physical scalars and a neutral gauge boson, $Z'$. The $h \to Z\gamma$ decay can be influenced in this model through contributions from either charged Higgs loops or corrections to the fermion-antifermion-$Z$ ($f\bar{ f}Z$) vertex. For the charged Higgs contribution, combining the $\mu_{ Z\gamma}$ measurement with the more stringent result from $\mu_{ \gamma\gamma}$, we identify a parameter region (with $m_{ H^\pm}>200$~GeV and $\lambda_{ hH^+H^-}<0$) that satisfies both constraints at the $1\sigma$ level. However, due to the larger uncertainty in $\mu_{ Z\gamma}$, this region is primarily constrained by $\mu_{ \gamma\gamma}$. Regarding the vertex corrections, we consider the dominant contribution from the top quark. We find an allowed region in the $\mathcal{ Q}_{ tL}$-$\mathcal{ Q}_{ tR}$ plane that can simultaneously accommodate $\mu_{ Z\gamma}$, top quark observables, and $b \to s\ell^+\ell^-$ data. Similarly, the most stringent constraint in this case originates from $b \to s\ell^+\ell^-$, not from $\mu_{ Z\gamma}$. Future precision measurements of $\mu_{ Z\gamma}$, which will reduce its current experimental uncertainty, are expected to enhance its capacity to constrain the FG2HDM parameter space.
Categories: hep-ph hep-ex