Another look at the flavour structure of the Littlest Higgs model with T-parity

We discuss the mixing matrix V_{H d} that describes the charged and neutral current interactions between ordinary down-quarks and up- and down-mirror quarks in the Littlest Higgs model with T-parity (LHT). We point out that this matrix in addition to three mixing angles contains three physical complex phases and not only one as used in the present literature. We explain the reason for the presence of two additional phases, propose a new standard parameterization of V_{H d} and briefly comment on the relevance of these new phases for the phenomenology of FCNC processes in the LHT model. In a separate paper we present a detailed numerical analysis, including these new phases, of K and B physics, with particular attention to the most interesting rare decays.