The $Z_H\to \gamma H$ decay in the littlest Higgs model

We present the calculation of the $Z_H\to \gamma H$ decay in the context of the littlest Higgs model at one-loop level. Our calculations include the contributions of fermions, scalars and gauge bosons in accordance with the most recent experimental constraints on the parameters space of the model. We find branching ratios of the order of 10⁻⁵ for the energy scale f = 2, 3, 4 TeV on the 0.1 < c < 0.9 region. In order to provide a complementary study we calculated the production cross section of the Z _H boson in pp collisions at the Large Hadron Collider (LHC) with a center-of-mass energy of 14 TeV. By using the integrated luminosity projected for the LHC in the last stage of operation, we estimated the number of events for this process. Moreover, we analyze the Standard Model (SM) background for the Higgs photon associated production and found that the $pp\to Z_{H}X\to \gamma H$ production is above the SM background. (paper)