Rare Higgs Decay into a Photon and a Z Boson in Radiatively-Driven Natural Supersymmetry

TL;DR

The study revisits the rare Higgs decay $h\rightarrow Z\gamma$ in the SM, incorporating full LO, NLO QCD, and two-loop EW corrections across four renormalization schemes for the coupling, highlighting a ~4% variation in the width within the current Higgs mass uncertainty. It then analyzes this decay in the MSSM within Radiatively-Driven Natural SUSY (RNS), using NUHM at the GUT scale and RGEs to obtain the EW-scale spectrum and one-loop amplitudes, with dominant chargino contributions in many regions. The results show that $\Gamma_{Z\gamma}$ can reach ~7.5 keV (about 20% above the SM NLO average) for parameter choices that also yield $M_h\approx125$ GeV, but at the cost of electroweak fine-tuning $\Delta_{EW} \gtrsim 100$, signaling a tension between naturalness and observable deviations. Overall, the RNS scenario offers a mildly better description than the SM in light of recent ATLAS measurements, and future HL-LHC or FCC-ee measurements could decisively test 10–20% level deviations in this rare Higgs channel.

Abstract

In this article, we study the rare decay process in which a Higgs boson decays into a $Z$ boson and a photon. In the first part of the paper, we analyze the Standard Model (SM) contributions to the corresponding decay width, including the full leading-order result, two-loop $O(α_s)$ QCD corrections, and the recently reported two-loop $O(α)$ electroweak corrections, evaluated under four different $α$ renormalization schemes. The dependence on the Higgs boson mass is studied within the experimentally allowed range reported by the LHC. In the considered schemes, a non-negligible variation of about $4\%$ is found when the mass is varied within its current experimental uncertainty. In the second part of the paper, we analyze the leading-order contributions to the same process within the Minimal Supersymmetric Standard Model (MSSM). The spectrum of soft SUSY-breaking parameters and SUSY particle masses at the electroweak scale, which enter the computation of the one-loop amplitudes contributing to the decay width, is obtained by evolving the GUT-scale parameters of a Radiatively-Driven Natural Supersymmetry (RNS) model with non-universal Higgs boson masses. Variations of the RNS parameters can enhance the average SM prediction by up to $\sim20\%$, reaching a value of $\sim7.5~$keV, while still satisfying the Higgs boson mass constraint. However, this comes at the cost of allowing a moderately large fine-tuning parameter, with values exceeding $100$, thereby placing the model outside its most natural parameter region. The predicted decay width in the RNS scenario is closer to the recent ATLAS RUN 2 + 3 combined measurement than the SM expectation.

Figures (7)

• Figure 1: Feynman diagrams for the $h \rightarrow Z\gamma$ process in the SM at the one-loop level. Virtual fermions are denoted by $f$; $W$ represents the charged electroweak gauge boson; $\Phi_i$ stands for fields that include Goldstone bosons, W bosons and ghosts; and $\varphi_i$ in the non-1PI diagrams denotes either a virtual $Z$ boson or a neutral Goldstone boson.
• Figure 2: The figure shows SM values for $\Gamma_{Z\gamma}$ at LO and NLO. Black dots represent NLO results in different renormalization schemes for $\alpha$. The red and blue dots represent the average of LO and NLO results among renormalization schemes. The error bar of the LO result is not shown. The blue (light blue) strip corresponds to the uncertainty of the NLO central value when only the dependence on the $M_h^2$ (the truncation of the perturbative series) is considered.
• Figure 3: The behavior of $\Gamma_{Z\gamma}$ within the $\alpha(M_{Z})$ scheme in the SM is observed across a range of Higgs masses, including the LO prediction and its EW and QCD corrections.
• Figure 4: Main diagrams contributing to $\mathcal{A}_{\text{SUSY}}$ in the $h\rightarrow Z\gamma$ decay width. The internal solid lines represent charginos or charged Higgs bosons, while the internal dashed lines represent sfermion fields.
• Figure 5: Variation of the Higgs decay width $\Gamma_{Z\gamma}$ and the MSSM Higgs boson mass $M_h$ as a function of the following input RNS parameters. (a) Higgsino mass, $\mu$, (b) CP-odd Higgs boson mass, $m_{A}$, (c) grand unified gaugino mass, $m_{\frac{1}{2}}$, and (d) ratio of the vevs of the two Higgs doublets, $t_{\beta}$. All of them evaluated at the GUT scale.