Infrared divergences ofB-meson exclusive decays toP-wave charmonia in QCD factorization and nonrelativistic QCD

Abstract

In the framework of QCD factorization, we study the B meson exclusive decays B → χcJ K where the spin-triplet P-wave charmonium states χcJ (J = 0, 1, 2) are described by the color-singlet nonrelativistic wave functions. We find that for these decays (except χc1) 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 cc 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.

Nonfactorizable B →χ c 0 K Decay and QCD Factorization

“…Our result of f II 2 is consistent with the previous ones [12,18]. However, our function f II 3 is different from that in Ref.…”

“…This implies that large nonfactorizable contributions may come from soft gluon exchanges. As argued in [12], unlike the inclusive B decays to charmonium, where the IR divergences can be factorized into the color-octet matrix elements associated with the higher Fock states of color-octet cc with soft gluons [13] in nonrelativistic QCD (NRQCD) [14], the IR divergences in the exclusive two-body decays are difficult to be factorized.…”

“…This implies that large nonfactorizable contributions may come from soft gluon exchanges. As argued in [12], unlike the inclusive B decays to charmonium, where the IR divergences can be factorized into the color-octet matrix elements associated with the higher Fock states of color-octet cc with soft gluons [13] in nonrelativistic QCD (NRQCD) [14], the IR divergences in the exclusive two-body decays are difficult to be factorized.At the qualitative level, the results of Ref.[13] may suggest that some fraction of the large color-octet contribution in the inclusive B decays to charmonium does in fact end up in two-body decay modes. That is, the soft gluon emitted by the color-octet cc pair may be reabsorbed by the quarks in the kaon or B meson, leading to a possible connection between the color-octet contribution and the infrared behavior of vertex and spectator corrections in QCD factorization approach.…”

B→χc1(1P,2P)Kdecays in QCD factorization andXMeng1, Gao2, Chao3 2013Phys. Rev. DSelf Cite614700View full textAdd to dashboardCite

“…As argued in Ref. [5], a more appropriate description of charmonium is the nonrelativistic (NR) wave functions which can be expanded in terms of the relative momentum q between charm and anticharm quarks. This argument is based on the nonrelativistic nature of heavy quarkonium [7].…”

“…where O(q) represent the rest of the decay amplitudes and P 1Sz (p, q) is the spin-triplet projection operator, and O α , P α stand for the derivatives of O, P with respect to the relative momentum q α [5]. The amplitudes O(q) can be further factorized as product of B → K form factors and hard kernel or as the convolution of a hard kernel with light-cone wave functions of B meson and K meson, within QCD factorization approach.…”