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

Abstract

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 _s14t 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 $K^_s16_s18to_s18pi^_s16_s18nu_s18bar_s18nu$, $K_L_s18to_s18pi^0_s18nu_s18bar_s18nu$, $B_{s,d}_s18to _s18mu^_s16_s18mu^-$, $B_s18to X_{s,d}_s18nu_s18bar_s18nu$, $K_L _s18to_s18pi^0_s18ell^_s16_s18ell^-$ and $B_s18to X_{s,d}_s18ell^_s16_s18ell^-$, paying particular attention to non-MFV contributions present in the model. Imposing all available constraints we find that the decay rates for $B_{s,d} _s18to _s18mu^_s16 _s18mu^-$ and $B _s18to X_{s,d} _s18nu _s18bar _s18nu$ can be enhanced by at most 50% and 35% relative to the SM values, while $Br(K^_s16_s18to_s18pi^_s16_s18nu_s18bar_s18nu)$ and $Br(K_L_s18to_s18pi^0_s18nu_s18bar_s18nu)$ can be both as high as $5 _s18cdot 10^{-10}$. Significant enhancements of the decay rates $K_L _s18to_s18pi^0_s18ell^_s16_s18ell^-$ are also possible. Simultaneously, the CP-asymmetries $S_{_s18psi _s18phi}$ and $A^s__s18text{SL}$ can be enhanced by an order of magnitude, while the electroweak penguin effects in $B _s18to _s18pi K$ turn out to be small, in agreement with the recent data.