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 '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 $S_{\psi \varphi }$ and $A_{\text{SL}}^s$ 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.

Comments: 65 pages, 19 figures. Note added on omitted term in Z-penguin contribution. For an updated analysis see arXiv:0906.5454