Study of $h\to Zγ$ in Flavor Gauged Two Higgs Doublet Model

TL;DR

The study analyzes the decay $h\to Z\gamma$ within the flavor-gauged two-Higgs-doublet model (FG2HDM), an extension of the SM with a second Higgs doublet, a scalar singlet, and a $U(1)'$ flavor gauge symmetry that yields five extra scalars and a $Z'$. The authors compute the one-loop amplitudes for $h\to Z\gamma$ and $h\to\gamma\gamma$ in the unitary gauge, isolating contributions from fermion loops, $W$ loops, charged-Higgs loops, and novel $W$–charged-Higgs mixing in FG2HDM; they also quantify corrections to the $f\bar f Z$ vertex, dominated by the top quark. Numerically, SM predictions for the branching ratios are $\mathcal{B}(h\to Z\gamma)_{\text{SM}}\approx1.54\times10^{-3}$ and $\mathcal{B}(h\to\gamma\gamma)_{\text{SM}}\approx2.28\times10^{-3}$, against which FG2HDM contributions are constrained. The analysis shows regions where charged-Higgs effects ($m_{H^{\pm}}>200$ GeV, $\lambda_{hH^+H^-}<0$) can fit both $\mu_{Z\gamma}$ and $\mu_{\gamma\gamma}$, while top-quark–loop corrections to $Z\gamma$ can be compatible with top-quark observables and $b\to s\ell^+\ell^-$ data; current $\mu_{Z\gamma}$ precision thus provides weaker constraints than those from $\mu_{\gamma\gamma}$ and flavor observables, though future measurements of $\mu_{Z\gamma}$ could substantially tighten the FG2HDM parameter space.

Abstract

We study the $h \to Zγ$ 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 $h \to Zγ$ 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 $μ_{Zγ}$ measurement with the more stringent result from $μ_{γγ}$, we identify a parameter region (with $m_{H^\pm}>200$~GeV and $λ_{hH^+H^-}<0$) that satisfies both constraints at the $1σ$ level. However, due to the larger uncertainty in $μ_{Zγ}$, this region is primarily constrained by $μ_{γγ}$. 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 $μ_{Zγ}$, 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 $μ_{Zγ}$. Future precision measurements of $μ_{Zγ}$, which will reduce its current experimental uncertainty, are expected to enhance its capacity to constrain the FG2HDM parameter space.

Figures (5)

• Figure 1: One-loop Feynman diagrams for $h\to Z\gamma$.
• Figure 2: One-loop Feynman diagrams for $h\to\gamma\gamma$.
• Figure 3: Left: The magnitude of $T_{Z\gamma}^{WH}$ as a function of $m_{H^\pm}$ with input $|a|=0.01$. Right: the $1\sigma$ and $2\sigma$ allowed regions for $m_{H^\pm}$ and $\lambda_{hH^+H^-}$ with constraints from $\mu_{Z\gamma}$ (blue) and $\mu_{\gamma\gamma}$ (red).
• Figure 4: The $\mathcal{Q}_{tL}$-$\mathcal{Q}_{tR}$ allowed regions obtained from $\mu_{Z\gamma}$ (blue), top quark observables (orange), and $b\to s\ell^+\ell^-$ (purple), with $g'=1$ and $\sin\theta'_2=0.1$.
• Figure 5: Feynman rules for the relevant vertices and propagators in the unitary gauge.