Testing $Z$ boson rare decays $Z\to H_1 \gamma, A_1 \gamma$ with $(g-2)_\mu$, $M_W$, and $BR(h_{\rm SM}\to Z\gamma)$ in the NMSSM

TL;DR

This paper investigates rare Z boson decays into a photon and a scalar within the NMSSM, linking these processes to muon g-2, W mass anomalies, and Higgs decay measurements, proposing future collider tests for supersymmetry.

Contribution

It provides a model-independent framework for Z decays to scalars and photons, identifies parameter space in NMSSM for maximum branching ratios, and suggests future collider experiments to probe these rare processes.

Findings

Decays Z→H₁γ, A₁γ can complement Higgs Zγ decay measurements.

Benchmark points satisfy muon g-2 and W mass anomalies.

Future colliders can potentially observe these rare Z decays.

Abstract

We study the rare decay process of $Z$ boson into photon, accompanied by a CP-even or CP-odd scalar. We present the analytical delineation of the processes through the model-independent parametrizations of the new physics couplings and, finally, consider the Next-to-Minimal Supersymmetric Standard Model to mark out the parameter space where the branching fraction can have the maximum value. As a part of the necessary phenomenological and experimental cross-checks, we aim to fit the anomalous magnetic moment of the muon and $W$ boson mass anomaly through the supersymmetric contributions. We also find that the decays $Z\to H_1 \gamma, A_1 \gamma$ can serve as an excellent complementary test to $BR(h_{\rm SM}\to Z\gamma)$. In fact, to facilitate future searches, we unveil a few benchmark points that additionally satisfy the deviation of $BR(h_{\rm SM}\to Z\gamma)$ from the SM value based on the recent measurements of ATLAS and CMS. Future proposals such as ILC, CEPC, and FCC-ee are anticipated to operate for multiple years, focusing on center-of-mass energy near the $Z$ pole. Consequently, these projects will be capable of conducting experiments at the Giga-$Z$ ($10^{9}$ of $Z$ bosons) and Tera-$Z$ ($10^{12}$ of $Z$ bosons) phases, which may probe the aforesaid rare decay processes, thus the model as well. These unconventional yet complementary searches offer different routes to explore the supersymmetric models with extended Higgs sectors like NMSSM.