The B → πK Puzzle : 2009 Update

The measurements of B → πK decays have been in disagreement with the predictions of the Standard Model (SM) for some time. In this paper, we perform an update of this puzzle using the latest (2008) data. We find that the situation has become far less clear. A fit to the B → πK data alone suggests the presence of new physics (NP). Indeed, if one adds a constraint on the weak phase γ coming from independent measurements – the SM fit – one finds that the fit is poor. On the other hand, it is not terrible. If one is willing to accept some deficiencies in the fit, it can be argued that the SM can explain the B → πK data. If one assumes NP, it is found to be present only in the electroweak penguin amplitude, as before. However, the fit is fair at best, and the improvement over the SM is not particularly strong. All and all, while the B → πK puzzle has not disappeared, it has become weaker. [email protected] [email protected] [email protected] The four B → πK decays – B → πK (designated as +0 below), B → πK (0+), B d → πK (−+) and B d → πK (00) – have evoked a great deal of interest in recent years. There are nine measurements of these processes that can be made: the four branching ratios, the four direct CP asymmetries ACP , and the mixing-induced CP asymmetry SCP in B 0 d → πK. There has been a continual disagreement between this set of measurements and the predictions of the standard model (SM); this discrepancy has been dubbed the “B → πK puzzle” [1]. The fourB → πK amplitudes, which obey a quadrilateral isospin relation, can be written within the diagrammatic approach [2]. Here, the amplitudes are expressed in terms of six diagrams: the color-favored and color-suppressed tree amplitudes T ′ and C , the gluonic penguin amplitudes P ′ tc and P ′ uc, and the color-favored and color-suppressed electroweak penguin amplitudes P ′ EW and P ′C EW . (The primes on the amplitudes indicate b̄ → s̄ transitions.) The amplitudes are given by A = −P ′ tc + P ′ uceiγ − 1 3 P ′C EW , √ 2A = −T e − C e + P ′ tc − P ′ uceiγ − P ′ EW − 2 3 P ′C EW , A = −T e + P ′ tc − P ′ uceiγ − 2 3 P ′C EW , √ 2A = −C e − P ′ tc + P ′ uceiγ − P ′ EW − 1 3 P ′C EW . (1) We have explicitly written the weak-phase dependence (including the minus sign from V ∗ tbVts [in P ′ tc]), while the diagrams contain strong phases. The amplitudes for the CP-conjugate processes can be obtained from the above by changing the sign of the weak phase (γ). Within the SM, to a good approximation, the diagrams P ′ EW and P ′C EW can be related to T ′ and C ′ using flavor SU(3) symmetry [4]: