Radiative decay Z_H-> γ A_H in the little Higgs model with T-parity

In the little Higgs model with T-parity (LHTM), the only tree-level kinematically allowed two-body decay of the Z_H boson is Z_H-> A_H H and thus one-loop induced two-body decays may have a significant rate. We study the Z_H-> \gamma A_H decay, which is induced at the one-loop level by a fermion triangle and is interesting as it depends on the mechanism of anomaly cancellation of the model. All the relevant two- and three-body decays of the Z_H gauge boson arising at the tree-level are also calculated. We consider a small region of the parameter space where the scale of the symmetry breaking f is still allowed to be as low as 500 GeV by electroweak precision data. We first analyze the scenario of a Higgs boson with a mass of 120 GeV. We found that the Z_H->\gamma A_H branching ratio can be of the order of a tree-level three-body decay and may be at the reach of detection at the LHC for f close to 500 GeV, but it may be difficult to detect for f=1 TeV. There is also an scenario where the Higgs boson has an intermediate mass such that the Z_H-> A_H H decay is closed, the Z_H-> \gamma A_H gets considerably enhanced and the chances of detection get a large boost.