$Z_H \rightarrow H^0 \gamma$ decay within the littlest Higgs model at $\mathcal{O}(\alpha_{{\rm ew}}^{3}\alpha_s)$ accuracy

TL;DR

This paper calculates the rare decay width of $Z_H ightarrow H^0 \gamma$ within the littlest Higgs model, including two-loop QCD corrections, showing that these corrections significantly reduce the decay width and are dominated by top-quark contributions.

Contribution

First detailed calculation of the $Z_H ightarrow H^0 \gamma$ decay at $ ext{NLO}$ with two-loop QCD corrections in the littlest Higgs model without T-parity.

Findings

Two-loop QCD corrections reduce the decay width.

Top-quark induced corrections dominate at NLO.

Decay width reaches about 75 keV for specific parameters.

Abstract

We study the rare decay $Z_H \rightarrow H^0 \gamma$ at $\mathcal{O}(\alpha_{{\rm ew}}^{3}\alpha_s)$ accuracy including two-loop QCD corrections in the context of the littlest Higgs model (LHM) without $T$-parity. We revisit analytically and numerically the leading-order (LO) contributions of the one-loop diagrams induced by massive fermions, scalars and charged gauge bosons in the LHM, and further study the NLO QCD correction to this decay process. We perform the numerical calculation by taking the LHM input parameters $f=3,~4~\text{TeV}$ and $0.1< c <0.6$, and discuss the numerical results of the decay width up to the QCD NLO within the recent experimentally constrained LHM parameter space region. Our results show that the two-loop QCD correction always reduces the LO decay width and the top-induced QCD correction is the dominant contribution at the QCD NLO. For $f=4~\text{TeV}$ and $c=0.3$, the NLO QCD corrected decay width reaches $75.099~\text{keV}$ and the NLO QCD relative correction is about $-11.0\%$.