CP violation and CPT invariance in B+- decays with final state interactions

Abstract

We show that, besides the usual short distance contribution for CP violation, final state interactions together with CP T invariance can play an important role in the recent observation of CP violation in three-body charmless B ± decays. A significant part of the observed CP asymmetry distribution in the Dalitz plot is located in a region where hadronic channels are strongly coupled. We illustrate our discussion comparing the recent observation of CP violation in the B ± → K ± K + K − and B ± → K ± π + π − phase space, with a calculation based on ππ → KK scattering.

Global CP asymmetries in charmless three-body $B$ decays with final state interactions

“…The re-scattering process can be the source of strong phase and absorptive contributions in multi-body decays through the strong interaction including also loops, as proposed in several studies [17,18,19,20,21,22,23,24,25,26,27]. We should remind that, in the QCD-only approach, known as BSS model [28], the imaginary part from the strong interaction appears in the "penguin" diagram b → s (or d), plus uū or d d produced by the presence of an intermediary gluon.…”

“…As we discussed before, re-scattering ππ ↔ KK can be a CPV mechanism in B → hhh [17,18]. However, the question is how to connect the FSI between channels with the same quantum numbers with U-spin symmetry, that can only relate channels that have different ∆S.…”

“…( 13) -( 16) are consistent with the FSI formalism previously developed. To define our notation and the FSI framework we follow the discussion presented in [17] for implementing the CPT constraint in B meson decays, as developed in Refs. [13,36].…”

“…[16], although still compatible in modulus with unity. Exploring the possible final state interactions between the four charged channels and imposing the CPT constraint, we showed in [17,18] that ππ → KK re-scattering amplitude can explain the flip in the sign for A cp between channels coupled by the strong interaction. Therefore, returning to the observable ∆Γ CP in Table 1, we still do not completely understand data.…”

Heavy Meson Decay in Three-Mesons and FSI

“…One interesting application of the formalism is the study of the CP violation in three-body charged B decays, where recent experiments [13] showed a sizable effect, interpreted in Ref. [14] as resulting from the interference between the weak phase and the strong phase from the final state interaction.…”