Non-factorizable Contributions to B→ππ Decays

Abstract

We investigate to what extent the experimental information on B → ππ branching fractions and CP asymmetries can be used to better understand the QCD dynamics in these decays. For this purpose we decompose the independent isospin amplitudes into factorizable and non-factorizable contributions. The former can be estimated within the framework of QCD factorization for exclusive B decays. The latter vanish in the heavy-quark limit, m b → ∞, and are treated as unknown hadronic parameters. We discuss at some length in which way the non-factorizable contributions are treated in different theoretical and phenomenological frameworks. We point out the potential differences between the phenomenological treatment of power-corrections in the "BBNS approach", and the appearance of power-suppressed operators in soft-collinear effective theory (SCET). On that basis we define a handful of different (but generic) scenarios where the non-factorizable part of isospin amplitudes is parametrized in terms of three or four unknowns, which can be constrained by data. We also give some short discussion on the implications of our analysis for B → πK decays. In particular, since nonfactorizable QCD effects in B → ππ may be large, we cannot exclude sizeable nonfactorizable effects, which violate SU (3) F flavour symmetry, or even isospin symmetry (via long-distance QED effects). This may help to explain certain puzzles in connection with isospin-violating observables in B → πK decays.

Differences between soft collinear effective theory and QCD factorization forB→ππdecays

“…[2,4,24] it was argued that the NRQCD cc region does not require special treatment due to quarkhadron duality, with smearing from the q 2 =xm 2 b of the gluon which the charm annihilate into (0 ≤ q 2 ≤ m 2 b ). Using duality in this sense requires an inclusive hadronic final state, to make it possible for there to be a cancellation of infrared divergences between the virtual and real diagrams to all orders in α s .…”

“…The δ-function is expected [24], and is analogous to Eq. (3.13) of [32] for the factorization formula used in production of energetic cc state's, whose hadronization is governed by NRQCD.…”

Power corrections in charmless nonleptonicBdecays: Annihilation is factorizable and real

“…In Ref. [15] annihilation diagrams were investigated in the soft-collinear effective theory (SCET) [16] and parameterized by a complex amplitude. When annihilation is considered in SU(3) flavor analyses a complex parameter is also used [17].…”

Soft collinear effective theory analysis ofB→Kπ,B→KK¯, andB<

“…There has been tremendous progress over the last few years in understanding charmless two-body, non-leptonic B decays in the heavy quark limit of QCD [25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40]. In this limit one can prove factorization theorems of the matrix elements describing the strong dynamics in the decay into simpler structures such as light cone distribu-tion amplitudes of the mesons and matrix elements describing a heavy to light transition [25] (for earlier work see Refs.…”