Infrared divergences of $B$ meson exclusive decays to P-wave charmonia in QCD factorization and nonrelativistic QCD

Abstract

In the framework of QCD factorization, we study the $B$ meson exclusive decays $B\to {\chi }_{cJ}K$ where the spin-triplet P-wave charmonium states ${\chi }_{cJ}(J=0,1,2)$ are described by the color-singlet non-relativistic wave functions. We find that for these decays (except ${\chi }_{c1}$) there are infrared divergences arising from nonfactorizable vertex corrections as well as logarithmic end-point singularities arising from nonfactorizable spectator interactions at leading-twist order. The infrared divergences due to vertex corrections will explicitly break down QCD factorization within the color-singlet model for charmonia. Unlike in the inclusive decays where the higher Fock states with color-octet $c\bar{c}$ pair and soft gluon can make contributions to remove the infrared divergences, their contributions can not be accommodated in the exclusive two body decays. As a result, the infrared divergences encountered in exclusive processes involving charmonia may raise a new question to the QCD factorization and NRQCD factorization in B exclusive decays.

4 pages, revtex, 1 figure

References in corpus (3)

• QCD Factorization in B -> pi K, pi pi Decays and Extraction of Wolfenstein Parameters
• Problems of QCD factorization in exclusive decays of B meson to charmonium
• Exclusive non-leptonic B meson decays from QCD

Cited by in corpus (29)

• Predictions for $e^{+}{e}^{-}\to J/\psi {\eta }_c$ with Light-Cone Wave-Functions
• Nonfactorizable contributions to $B$ meson decays into charmonia
• Factorization and NLO QCD correction in e^+ e^- \to J/ψ(ψ(2S))+ χ_{c0} at B Factories}
• B -> chi_cJ K decays revisited
• NRQCD Factorization for Twist-2 Light-Cone Wave-Functions of Charmonia
• Using Line Shapes to Discriminate between Binding Mechanisms for the X(3872)
• $B\to {\chi }_{c1}(1P,2P)K$ decays in QCD factorization and X(3872)
• Factorization in exclusive quarkonium production
• Factorization theorems for exclusive heavy-quarkonium production
• Relativistic corrections to the form factors of $B_c$ into $P$-wave orbitally excited charmonium
• QCD corrections to e^+ e^- to J/ψ(ψ(2S))+χ_{cJ} (J=0,1,2) at B Factories
• $B \to (\jpsi,η_c) K$ decays in the perturbative QCD approach
• Breakdown of NRQCD Factorization in Processes Involving Two Quarkonia and its Cure
• ${\chi }_{QJ}\to {\ell }^{+}{\ell }^{-}$ within and beyond the Standard Model
• $B\to {\chi }_{c0,2}K$ decays: a model estimation
• $\psi (3770)$ and $B$ meson exclusive decay $B\to \psi (3770)K$ in QCD factorization
• Nonfactorizable $B\to {\chi }_{c0}K$ decay and QCD factorization
• Final-state interactions in the decays $B^0\to {\chi }_{c0}{K}^{\ast 0}$ and $B^{+}\to {\chi }_{c0}{K}^{\ast +}$
• Final state interactions in the decay $B^0\to {\eta }_c{K}^{\ast }$
• Reinvestigating the $B$ $\to$ $PV$ decays by including the contributions from ${\varphi }_{B2}$ with the perturbative QCD approach
• $B_{(s)}\to {\eta }_c(P,V)$ decays and effects of the next-to-leading order contributions in the perturbative QCD approach
• Observation prospects of leptonic and Dalitz decays of pseudoscalar quarkonia
• Revisiting nonfactorizable contributions to factorization-forbidden decays of $B$ mesons to charmonium
• The Fermi motion contribution to J/ψproduction at the hadron colliders
• Branching ratios and $CP$ asymmetries of $B\to {\chi }_{c1}K(\pi )$ decays
• $S$-wave contributions to the $B_{(s)}\to {\chi }_{c1}(\pi \pi ,K\pi ,KK)$ decays
• Possibility of experimental study on nonleptonic $B_c^{\ast }$ weak decays
• The QED nonfactorizable correction to the semileptonic charmed three-body $B$ decays
• Resonance contributions from ${\chi }_{c0}$ in the charmless three-body hadronic $B$ meson decays