ar X iv : 0 80 2 . 11 75 v 2 [ he p - ph ] 1 4 Fe b 20 08 UdeM - GPP - TH - 07 - 164 The B → πK Puzzle and Supersymmetry

At present, there are discrepancies between the measurements of several observables in B → πK decays and the predictions of the standard model (the “B → πK puzzle”). Although the effect is not yet statistically significant – it is at the level of >∼ 3σ – it does hint at the presence of new physics. In this paper, we explore whether supersymmetry (SUSY) can explain the B → πK puzzle. In particular, we consider the SUSY model of Grossman, Neubert and Kagan (GNK). We find that it is extremely unlikely that GNK explains the B → πK data. We also find a similar conclusion in many other models of SUSY. And there are serious criticisms of the two SUSY models that do reproduce the B → πK data. If the B → πK puzzle remains, it could pose a problem for SUSY models. [email protected] [email protected] [email protected] Over the past several years, measurements have been made of a number of observables in the decays of B mesons which are in disagreement with the predictions of the standard model (SM): e.g. indirect CP asymmetries in penguin-dominated B decays [1], triple-product correlations in B → φK [2], polarizations in B → V1V2 decays (Vi is a vector meson) [3], etc. None of these discrepancies is statistically significant, so that these disagreements only point to a hint of physics beyond the SM. Still, if these hints are taken together, the statistical significance increases. Furthermore, they are intriguing since they all point to new physics (NP) in b̄ → s̄ transitions. Arguably, the most stringent discrepancy appears in B → πK decays. Briefly, the effect goes as follows. There are four B → πK decays: B → πK (designated as +0 below), B → πK (0+), B d → πK (−+) and B d → πK (00). In terms of diagrams [4], the amplitudes are given by A = −P ′ , √ 2A = P ′ − T e − C e − P ′ EW , A = P ′ − T e , √ 2A = −P ′ − P ′ EW − C e . (1) In the above, we have neglected small diagrams and written the amplitudes in terms of the color-favored and color-suppressed tree amplitudes T ′ and C , the t-quarkdominated gluonic penguin amplitude P , and the color-favored electroweak penguin amplitude P ′ EW . (The primes on the amplitudes indicate b̄ → s̄ transitions.) In addition, we have explicitly written the weak-phase dependence (including the minus sign from V ∗ tbVts [P ]), while the diagrams contain strong phases. (The phase information in the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix is conventionally parametrized in terms of the unitarity triangle, in which the interior (CP-violating) angles are known as α, β and γ [5].) The amplitudes for the CP-conjugate processes can be obtained from the above by changing the sign of the weak phase (γ). Note that these diagrams include the magnitudes of their associated CKM matrix elements. The diagram P ′ EW is not independent. To a good approximation, it can be related to T ′ and C ′ using flavor SU(3) symmetry [6]: