Decays of Standard Model like Higgs boson $h \rightarrowγγ, Z γ$ in a minimal left-right symmetric model

Technical Summary: Decays of Standard Model-like Higgs Boson $h \to \gamma\gamma, Z\gamma$ in a Minimal Left-Right Symmetric Model

Problem Statement
The Standard Model (SM) prediction for the loop-induced Higgs decay $h \to Z\gamma$ is currently constrained by experimental data from ATLAS and CMS, which agree with the SM within 1.9 standard deviations. While the effective coupling $h\gamma\gamma$ is tightly constrained by the $h \to \gamma\gamma$ decay rate, the $hZ\gamma$ coupling in Beyond Standard Model (BSM) scenarios can deviate significantly because $Z$ couplings to new particles are less restricted than photon couplings. Previous studies of the Minimal Left-Right Symmetric Model (MLRSM) regarding $h \to Z\gamma$ neglected specific one-loop contributions involving diagrams with both virtual Higgs and gauge bosons in the loops, often assuming suppressed $h$-Higgs-gauge boson couplings. This paper investigates these neglected contributions and their impact on the signal strengths of $h \to \gamma\gamma$ and $h \to Z\gamma$ under recent and future experimental sensitivities.

Methodology
The authors analyze the MLRSM, constructed on the gauge group $SU(2)_L \otimes SU(2)_R \otimes U(1)_{B-L}$, which includes a bi-doublet Higgs field $\Phi$ and two triplet fields $\Delta_{L,R}$.

1. Model Setup: The paper derives the physical spectrum, including fermion masses, gauge boson masses ($W^\pm_{1,2}, Z_{1,2}, A$), and Higgs boson masses ($h, H^0, H^\pm, H^{\pm\pm}$). The analysis avoids the approximation $k_1 \gg k_2$ (large $\tan\beta$) used in some prior works, instead maintaining general relations where $t_\beta \geq 1.2$.
2. Coupling Derivation: Analytic formulas for all relevant couplings are derived from the scalar potential and kinetic terms. This includes:
   • Yukawa couplings of the SM-like Higgs to fermions (identical to SM results).
   • Couplings of the Higgs to charged Higgs bosons ($H^\pm_{1,2}, H^{\pm\pm}_{1,2}$).
   • Couplings of the Higgs to charged gauge bosons ($W^\pm_{1,2}$) and mixed Higgs-gauge vertices.
   • Triple gauge couplings ($Z W^\pm W^\mp$ and $\gamma W^\pm W^\mp$).
3. Amplitude Calculation: The one-loop decay amplitudes for $h \to Z\gamma$ and $h \to \gamma\gamma$ are calculated in the unitary gauge. The total amplitude $F_{21}$ is decomposed into fermion ($F_f$), charged scalar ($F_S$), charged gauge boson ($F_V$), and mixed scalar-gauge boson ($F_{VS}$) contributions.
   • Crucially, the mixed contributions $F_{VS}$ (diagrams with both $W$ and $H$ in the loop) are explicitly included. These were omitted in previous MLRSM studies [17, 18] but are shown to affect the $h \to Z\gamma$ amplitude while leaving $h \to \gamma\gamma$ unaffected.
4. Numerical Analysis: Using the LoopTools package, the authors scan the parameter space defined by charged Higgs masses ($m_{H^\pm}, m_{H^{\pm\pm}}$), the right-handed scale $v_R$, the mixing angle $\tan\beta$, the gauge coupling ratio $g_R/g_L$, and scalar self-couplings. The signal strengths $\mu_{Z\gamma}$ and $\mu_{\gamma\gamma}$ are computed and compared against current experimental constraints ($|\Delta\mu_{\gamma\gamma}| < 38\%$ at 2$\sigma$) and projected future sensitivities ($|\Delta\mu_{\gamma\gamma}| \approx 4\%$).

Key Contributions

• Inclusion of Neglected Diagrams: The paper identifies and calculates one-loop contributions involving mixed virtual Higgs and gauge boson exchanges ($F_{VS}$) for the $h \to Z\gamma$ decay. These terms are non-zero in the MLRSM and were previously ignored.
• Differential Impact: It is demonstrated that these new contributions modify the $h \to Z\gamma$ amplitude but do not contribute to the $h \to \gamma\gamma$ amplitude. This decoupling allows for larger deviations in the $Z\gamma$ channel without violating the strict constraints on the $\gamma\gamma$ channel.
• Parameter Dependence: The study maps the dependence of the signal strength deviation $\Delta\mu_{Z\gamma}$ on key model parameters, specifically $\tan\beta$, $v_R$, $g_R$, and charged Higgs masses.

Results

• Correlation between Channels: Numerical investigations show that $\Delta\mu_{Z\gamma}$ is strictly constrained by $\Delta\mu_{\gamma\gamma}$. Under current 2$\sigma$ experimental limits ($|\Delta\mu_{\gamma\gamma}| < 38\%$), the maximum deviation for the $Z\gamma$ channel is found to be $|\Delta\mu_{Z\gamma}| < 46\%$.
• Future Sensitivity: Even under the projected future experimental sensitivity where $|\Delta\mu_{\gamma\gamma}| = 4\%$, the model allows for $|\Delta\mu_{Z\gamma}|$ to reach values exceeding the expected sensitivity of $23\%$.
• Parameter Dependencies:
  • Large deviations in $\Delta\mu_{Z\gamma}$ require small values of $\tan\beta$ (approaching the lower bound of 1.2).
  • The deviation depends weakly on the right-handed scale $v_R$ and the masses of the charged Higgs bosons.
  • A large value of the right-handed gauge coupling $g_R$ (up to 1.6) is necessary to achieve large $\Delta\mu_{Z\gamma}$, with values reaching $\sim 46\%$ when $g_R$ is large.
• Consistency: The model contains regions of parameter space where both $\Delta\mu_{Z\gamma}$ and $\Delta\mu_{\gamma\gamma}$ approach zero, ensuring consistency with SM predictions.

Significance
The paper claims that the inclusion of previously neglected one-loop diagrams (involving both Higgs and gauge bosons) is essential for an accurate prediction of $h \to Z\gamma$ in the MLRSM. These contributions enhance the $Z\gamma$ amplitude without affecting the $\gamma\gamma$ rate, thereby relaxing the constraints on the $Z\gamma$ channel imposed by the $\gamma\gamma$ data. The authors conclude that future experimental searches for $h \to Z\gamma$ and $h \to \gamma\gamma$ are critical for constraining the parameter space of the MLRSM, particularly the values of $\tan\beta$ and $g_R$, as the model can predict observable deviations in $Z\gamma$ even when $\gamma\gamma$ remains consistent with the SM.