ar X iv : h ep - p h / 06 02 23 1 v 1 2 5 Fe b 20 06 Importance of Higher Twist Effects to Understand Charmed Color - Suppressed B Decays

Working within the framework of the QCD light cone sum rules (LCSR), we compute and discuss the nonfactorizable higher twist effect in B̄0 → D∗0π0 to make an all-around examination of its role in the charmed color-suppressed B decays. Analogously to the case of B̄0 → D0π0, such effect turns out to be of the same strong phase as the factorizable amplitude, and modifies constructively the magnitude by order (40 − 90)% so that the effective coefficient af2 = C1 + C2/3 receives a positive correction comparable numerically with it. Nonleading as the soft effect in question is, our findings for it, along with the previous LCSR analyses of B̄0 → D0π0, are suggestive of the dominance of soft exchanges in these charmed color suppressed B decays. Also, the emphases are put on importance of understanding intensively various related higher twist and transverse momentum effects to interpret the data on B → D0(∗0)(π0, η, η), J/ψ K(∗). Email: [email protected] Email: [email protected] Mailing address The formulation of the QCD factorization (QCDF) [1] and soft-collinear effective theory (SCET) [2] has greatly renewed and deepened our understanding of QCD dynamics in the two-body hadronic decays of B-mesons, and as such considerably enhanced our confidence in precisely estimating the decay amplitudes and CP-asymmetry effects. Especially, ones have essentially changed minds in understanding of the charmed colorsuppressed B decays and realized that the nonfactorizable soft exchange contributions dominate over the hard-exchange ones. For all these progresses, however, being unable to deal with non-perturbative QCD dynamics from the first principle makes yet it difficult to theoretically interpret the experimental observations of the color suppressed process B̄ → Dπ [3]. One attempts to make sense of them by a global analysis of the data on B → Dπ decays, either in a model-independent manner [4, 5, 6], or in the framework of SCET [7] and Perturbative QCD [8]. The leading soft effects in such decays are supposed to include final-state rescattering processes and nonfactorizable contributions induced by the color-octet operators. Resorting to various phenomenological approaches, such as one-particle exchange model [9] and Regge theory [10], one models the soft contributions from the former. QCD sum rule approach is initially used [11] and QCD light-cone sum rule (LRSR) method [12] is subsequently applied [13] to obtain an estimate of the latter. Focusing on the B̄ → Dπ case, the author of [11] finds that the soft exchanges between the color-octet quark pair cq̄ and the pion, which concern higher-twist components of the pion, provide a negative correction at a level of 70% of the factorizable amplitude, while the LCSR approach predicts a positive numerical effect at (50− 110)% order [14]. As compared to the B → J/ΨK case where the effect in question contributes to the magnitude by (30 − 70)% [15], the higher-twist effect in B̄ → Dπ is, as it were, more important, as expected. Also, the similar calculations are carried out for B → ππ [13, 16] and B → Kπ [17], but the resulting numerical impacts are found to be far less than those in both B̄ → Dπ and B → J/ΨK cases, a result in accordance with the argument for QCD factorization. Whereas the nonfactorizable higher-twist effect, as estimated, plays a role comparable numerically with the factorizable amplitudes of the color-suppressed B̄ → Dπ and B → J/ΨK decays, in the letter we would like to examine how it affect B̄ → Dπ, to get an all-around understanding of its role in the charmed color suppressed B decays We start with looking briefly back at the dynamical features of the color suppressed B̄ → Dπ. In the Fierz transformed form, the relevant effective weak Hamiltonian reads [18] HW = GF √ 2 VcbV ∗ ud [ (C1(μ) + 1 3 C2(μ))O1(μ) + 2C2(μ)Õ1(μ) ]