Muon anomalous magnetic moment and the heavy photon in a little Higgs model

In the Littlest Higgs model, we comprehensively study the phenomenology of the heavy photon A_H which is lightest, in most of the parameter space, among newly introduced heavy gauge bosons and top-like vector quark. Unexpected behavior is that lighter A_H suppresses the corrections to the electroweak precision observables. For the global symmetry breaking scale f~3TeV, the heavy photon can be light enough to be produced at the 500 GeV linear collider. Through the calculation of the one-loop correction to the muon anomalous magnetic moment, we show that even the light A_H with mass around 200 GeV results in the negligible contribution. This is consistent with the current inconclusive status of the theoretical calculation of the (g-2)_mu in the SM. The effects of the Littlest Higgs model on the process e+ e- -> mu+ mu- are also studied, which is one of the most efficient signals to probe the A_H.