Doubly CKM-suppressed corrections to CP asymmetries

The success of the Kobayashi-Maskawa (KM) model of CP violation [1] in predicting correctly CP asymmetries in B meson decays has been recently recognized by the Nobel committee [2]. The large asymmetry measured in B → J/ψKS(L) [3, 4] given by sin 2β, where β ≡ φ1 = arg(−V ∗ cbVcd/V ∗ tbVtd), proved unambiguously that the KM phase is the dominant source of CP violation in B decays. This test involves an interference between B-B̄ mixing and a B decay amplitude [5], consisting of a dominant color-suppressed b̄ → c̄cs̄ tree amplitude and a small contribution from a b̄→ s̄uū penguin amplitude [6, 7, 8]. (We use the unitarity of the Cabibbo-Kobayashi-Maskawa [1, 9] (CKM) matrix, V ∗ tbVts = −V ∗ cbVcs − V ∗ ubVus, and will not discuss order 10 effects due to CP violation in B0−B mixing [10] and K −K mixing [11].) The magnitude ξ of the ratio of these two amplitudes, which determines the theoretical precision of this test, involves three suppression factors: A ratio of CKM matrix elements, |V ∗ ubVus|/|V ∗ cbVcs| ≃ 0.02 [12], small Wilson coefficients of penguin operators in the effective Hamiltonian, ci ∼ 0.04 (i = 3, 4, 5, 6), and a suppression by the Okubo-Zweig-Iizuka (OZI) rule [13]. The parameter ξ is expected to be somewhat larger than the product of these three factors due to color-suppression of the dominant tree amplitude which normalizes ξ. Thus, with ξ ∼ 10, it has been commonly accepted that the measurement of sin 2β in B → J/ψKS(L) may involve only a very small uncertainty at a level of 10, or at most a fraction of a percent [6].