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 v(2)/f(2) 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+ -> pi(+)nu(nu) over bar, K-L -> pi(0)nu(nu) over bar, B-s,B-d -> mu(+) mu(-), B -> X-s,X-d nu(nu) over bar, K-L -> pi(0) l(+) l(-) and B -> X-s,X-d l(+) 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 A A and As SL, that are very small in the SM. Imposing all available constraints we find that the decay rates for B-s,B-d -> mu(+) mu(-) and B -> X-s,X-d nu(nu) over bar can be enhanced by at most 50% and 35% relative to the SM values, while Br(K+ -> pi(+)nu(nu) over bar) and Br(K-L -> pi(0)nu(nu) over bar) can be both as high as 5 (.) 10(-10). Significant enhancements of the decay rates K-L -> pi(0) l(+) l(-) are also possible. Simultaneously, the CPasymmetries S-psi phi and A(SL)(s) can be enhanced by an order of magnitude, while the electroweak penguin e r ects in B -> K turn out to be small, in agreement with the recent data.