Rare and CP-violating K and B decays in the Littlest Higgs model with T-parity

We calculate the most interesting rare and CP-violating K and B decays in the Littlest Higgs model with T-parity. We give a collection of Feynman rules including v²/f² contributions that are presented here for the first time and could turn out to be useful also for applications outside flavour physics. We adopt a model-independent parameterization of rare decays in terms of the gauge independent functions X_i, Y_i, Z _i (i ≤ K,d,s), which is in particular useful for the study of the breaking of the universality between K, B_d and B_s systems through non-MFV interactions. Performing the calculation in the unitary and 't Hooft-Feynman gauge, we find that the final result contains a divergence which signals some sensitivity to the ultraviolet completion of the theory. Including an estimate of this contribution, we calculate the branching ratios for the decays K⁺π⁺ν, K_Lπ⁰ν, B_s,dμ⁺μ^-, BX_s,dν, K _Lπ⁰ℓ⁺ℓ^- and BX _s,dℓ⁺ℓ^-, paying particular attention to non-MFV contributions present in the model. The main feature of mirror fermion effects is the possibility of large modifications in rare K decay branching ratios and in those B decay observables, like S_ψφ and A ^s_SL, that are very small in the SM. Imposing all available constraints we find that the decay rates for B _s,dμ⁺μ^- and BX_s,dν can be enhanced by at most 50 and 35 relative to the SM values, while Br(K ⁺π⁺ν) and Br(K_Lπ⁰ν) can be both as high as 5.10^-10. Significant enhancements of the decay rates K_Lπ⁰ℓ⁺ℓ^- are also possible. Simultaneously, the CP-asymmetries S_ψφ and A ^s_SL can be enhanced by an order of magnitude, while the electroweak penguin effects in BπK turn out to be small, in agreement with the recent data.