The rare decays $h^0 ightarrow Zγ,V Z$ in the NB-LSSM

This study investigates the Higgs rare decays $h^0\rightarrow Zγ,V Z$ within the next to minimum B-L supersymmetric model(NB-LSSM), where $V$ represents a vector meson $(ϕ,J/ψ,Υ(1S),ρ^0,ω)$. Compared to the minimal supersymmetric standard model(MSSM), the NB-LSSM introduces three singlet Higgs superfields, which mix with the Higgs doublets and affect the lightest Higgs boson mass and the Higgs couplings. The loop-induced contributions resulting from the effective $h^0Zγ$ coupling can produce new physics(NP) contributions, thereby affecting the theoretical predictions of rare decays significantly through the new parameters such as $κ$, $λ$, $λ_2\cdot\cdot\cdot$. The results of this work can provide a reference for probing NP beyond standard model(SM).

💡 Research Summary

This paper investigates the rare Higgs boson decays h⁰ → Z γ and h⁰ → V Z (with V = φ, J/ψ, Υ(1S), ρ⁰, ω) within the Next‑to‑Minimal B‑L Supersymmetric Model (NB‑LSSM). The NB‑LSSM extends the Minimal Supersymmetric Standard Model (MSSM) by adding three gauge‑singlet Higgs superfields (η, \bar η, S) and an extra U(1){B‑L} gauge group. These additions generate a dynamical μ‑term (μ = λ v_S/√2) and introduce gauge‑kinetic mixing (parameter g{YB}) between the hypercharge and B‑L gauge bosons. Consequently, the Higgs sector is enlarged: the CP‑even Higgs mass matrix becomes a 5 × 5 object involving the doublet fields (H_d, H_u) and the three singlets. Tree‑level mixing, together with the new couplings κ, λ, λ₂, modifies the lightest Higgs mass and its couplings to gauge bosons and fermions. Radiative corrections from the top/stop sector are included at the leading‑log level, allowing the SM‑like Higgs mass to be tuned to the observed 125 GeV.

The decay h⁰ → Z γ is loop‑induced in the SM, receiving contributions from W bosons and SM fermions. In the NB‑LSSM, additional charged particles—charginos, charged Higgs bosons, and sfermions—run in the loop, altering the effective coupling C_{γZ} (and the CP‑odd counterpart \tilde C_{γZ}). The authors write the effective Lagrangian L_eff = (α/4πv²) C_{γZ} h F_{μν}Z^{μν} and decompose C_{γZ}=C_{γZ}^{SM}+C_{γZ}^{NP}. The NP part is expressed in terms of the new couplings g_{h⁰qq}, g_{Zqq}, and loop functions A_{1/2}, A_1, A_0. Non‑diagonal couplings are shown to be numerically negligible, so only diagonal sfermion and chargino contributions are retained. The CP‑odd term \tilde C_{γZ} is found to be essentially zero, both in the SM and NB‑LSSM, allowing the analysis to focus on CP‑even effects.

For the processes h⁰ → V Z, the authors distinguish direct and indirect contributions. Direct contributions involve the Higgs coupling directly to the quark current that creates the vector meson; they are suppressed by (m_q/m_h)² or (Λ_{QCD}/m_h)². Indirect contributions proceed via the effective h⁰ Z γ vertex: the Higgs first decays to an off‑shell Z* (or γ*), which then hadronizes into the vector meson. Using QCD factorization, the transition matrix element ⟨V| \bar q γ^μ q |0⟩ = −i f_V m_V ε^{*μ} defines the decay constants f_V, the meson charges Q_V, and the Z‑meson couplings g_{ZVV}. These constants are listed in Table II. The indirect amplitudes dominate over the direct ones for all considered mesons, especially for heavy quarkonia (J/ψ, Υ). The indirect form factors are proportional to C_{γZ} and thus inherit the NP sensitivity of the h⁰ → Z γ channel.

A comprehensive numerical scan is performed over the NB‑LSSM parameter space: κ∈