We propose to use T-odd momentum correlations as physical observables to study T violation in B →K*l ϩ l Ϫ (lϭe,) decays. We show that these observables are zero in the standard model but sizable at the level of 10% in the supersymmetric model. These large T violating effects are measurable at the B factories in KEK and SLAC and future hadron colliders. We also point out that the T violating effects are insensitive to nonperturbative QCD contributions.The study of flavor changing neutral currents ͑FCNC͒ in B decays has achieved enormous progress since the CLEO observation ͓1͔ of the radiative b→s␥ decay. Recently, the process of B→K ϩ Ϫ has been observed ͓2͔ at the Belle detector in the KEKB e ϩ e Ϫ storage ring with the branching ratio of (7.5 Ϫ2.1 ϩ2.5 Ϯ0.9)ϫ10 Ϫ7 , while the standard model ͑SM͒ expectation is around 5ϫ10 Ϫ7 ͓3͔. Experimental searches at the B factories for B→K*l ϩ l Ϫ are also within the theoretically predicted ranges ͓5͔.Through B decays such as B→J/ K, we can test the origin of CP violation ͑CPV͒ in the SM which is a consequence of the Cabibbo-Kobayashi-Maskawa ͑CKM͒ quark mixing matrix ͓4͔. CP asymmetries ͑CPAs͒ in B decays are usually defined by a CP ϰ⌫Ϫ⌫ and A CP (t)ϰ⌫(t)Ϫ⌫ (t). The former case, called direct CPA or a CP-odd observable, needs both weak CP violating and strong phases, while the latter one of the time-dependent CPA contains not only a nonzero CP-odd phase but also B-B mixing. We note that the present world average for a CP ⌿ K is 0.79Ϯ0.12 ͓6,7͔ compared with the SM prediction of 0.70Ϯ0.10 ͓7͔.To study CPV, one can also define some other useful observables by the momentum correlations. For example, in a three-body decay, the simplest ones are the triple correlationswhere s ជ is the spin carried by one of the outgoing particles and p ជ i and p ជ j denote any two independent momentum vectors. Clearly, these triple momentum correlations are T-odd observables since they change sign under the time reversal ͑T͒ transformation of t→Ϫt. In terms of the CPT invariant theorem, the T violation ͑TV͒ implies CPV. Therefore, studying T-odd observables can also help us to understand the origin of CPV. We note that the T violating observables such as the above triple correlations do not require strong phases. In the decays of B→K*l ϩ l Ϫ (lϭe,, and ), the spin s can be the polarized lepton, s l , or the K* meson, ⑀*(). Considering the polarized lepton, as known, the polarization is always associated with the lepton mass, and thus we expect that the T violating effects are suppressed and less than 1% for the light lepton modes ͓9͔. Although the mode can escape from the suppression, the corresponding branching ratio ͑BR͒ which is O(10 Ϫ7 ) is about one order smaller than those of e and modes. It is known that CPAs such as a CP in B→K*l ϩ l Ϫ are small even with weak phases of O(1) due to the smallness of strong phases ͓10͔. In this paper we concentrate on the possibility of having large T-odd terms such as ⑀ ជ K * ()•( p ជ l ϩϫ p ជ K * )ϰ ␣ q ⑀* ()p l ␣ P  in the decays of B→K*l ϩ l Ϫ (lϭe...
We develop perturbative QCD formalism for three-body nonleptonic $B$ meson decays. Leading contributions are identified by defining power counting rules for various topologies of amplitudes. The analysis is simplified into the one for two-body decays by introducing two-meson distribution amplitudes. This formalism predicts both nonresonant and resonant contributions, and can be generalized to baryonic decays.Comment: 6 pages, 2 figures, version to appear in PL
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