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 $K^+\to\pi^+\nu\bar\nu$, $K_L\to\pi^0\nu\bar\nu$, $B_{s,d}\to \mu^+\mu^-$, $B\to X_{s,d}\nu\bar\nu$, $K_L \to\pi^0\ell^+\ell^-$ and $B\to X_{s,d}\ell^+\ell^-$, paying particular attention to non-MFV contributions present in the model.   Imposing all available constraints we find that the decay rates for $B_{s,d} \to \mu^+ \mu^-$ and $B \to X_{s,d} \nu \bar \nu$ can be enhanced by at most 50% and 35% relative to the SM values, while $Br(K^+\to\pi^+\nu\bar\nu)$ and $Br(K_L\to\pi^0\nu\bar\nu)$ can be both as high as $5 \cdot 10^{-10}$. Significant enhancements of the decay rates $K_L \to\pi^0\ell^+\ell^-$ are also possible. Simultaneously, the CP-asymmetries $S_{\psi \phi}$ and $A^s_\text{SL}$ can be enhanced by an order of magnitude, while the electroweak penguin effects in $B \to \pi K$ turn out to be small, in agreement with the recent data. 
Monika Blanke, Andrzej J. Buras, Anton Poschenrieder, Stefan   Recksiegel, Cecilia Tarantino, Selma Uhlig and Andreas Weiler