tbW vertex in the Littlest Higgs Model with T-parity

A study of the effective tbW vertex is done in the littlest Higgs model with T parity that includes the one loop induced weak dipole coefficient f_{2R}. The top's width, the W-boson helicity in the t-> bW^+ decay as well as the t-channel and the s-channel modes of single top quark production at the LHC are then obtained for the tbW coupling. Our calculation is done in the Feynman-'t Hooft gauge, and we provide details of the analysis, like exact formulas (to all orders of the expansion variable v/f) of masses and mixing angles of all the particles involved. Also, a complete and exact diagonalization (and normalization) of the scalar sector of the model is made.