Problems of QCD factorization in exclusive decays of B meson to charmonium

Abstract

We study the exclusive decays of B meson into P-wave charmonium states χ cJ (J = 0, 1) in the QCD factorization approach with light-cone distribution functions describing the mesons in the processes. For B → χ c1 K decay, we find that there are logarithmic divergences arising from nonfactorizable spectator interactions even at twist-2 order and the decay rate is too small to accommodate the experimental data. For B → χ c0 K decay, we find that aside from the logarithmic divergences arising from spectator interactions at leading-twist order, more importantly, the factorization will break down due to the infrared divergence arising from nonfactorizable vertex corrections, which is independent of the specific form of the light-cone distribution functions. Our results may indicate that QCD factorization in the present form may not be safely applied to B-meson exclusive decays to charmonium states. PACS numbers: 13.25.Hw; 14.40.GxExclusive nonleptonic B-meson decays provide a important opportunity to determine the parameters of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, to explore CP violation and to observe new physics effects. Recently, B physics has received extensive experimental attention such as from high-energy experiments at the Tevatron and at the e + e − B factories. On the other hand, although the underlying weak decay of the b quark is simple, quantitative understanding of nonleptonic B-meson decays is difficult due to the complicated strong-interaction effects.Beneke et al. have considered two-body nonleptonic B-meson decays extensively including light-light as well as heavy-light final states within the QCD factorization approach [1,2,3]. The general idea is that in the heavy quark limit m b ≫ Λ QCD , the transition matrix elements of operators in the hadronic decay B → M 1 M 2 with M 1 being the recoiled meson and M 2 being the emitted meson can be calculated in an expansion in 1/m b and α s . The leading term in 1/m b assumes a simple form[2]:where M 2 is a light meson or a quarkonium and F BM 1 is the B → M 1 transition form factor; φ M is meson light-cone distribution amplitude and T I,II are perturbatively calculable hard scattering kernels. If we neglect strong interaction corrections, eq.(1) reproduces the result of naive factorization. However, hard gluon exchange between M 2 and BM 1 system implies a nontrivial convolution of hard scattering kernels T I,II with the light-cone distribution amplitude 1

B→χc1(1P,2P)Kdecays in QCD factorization andXMeng1, Gao2, Chao3 2013Phys. Rev. DSelf Cite604700View full textAdd to dashboardCite

“…Our prediction of Br(B 0 → χ c1 (3511)K 0 ) is about 2 times larger than that in [2] , although it is still about two times smaller than the recent data [22]. The difference between the theoretical predictions and experimental data may not be as serious as it looks like if we take into account the following uncertainties: (i) We have used a moderate value of R ′ 1P (0) predicted by different potential models [15] in our calculation, and a larger value of R ′ 1P (0) may enhance our prediction in Eq.…”

“…This might imply a possible interpretation for the newly discovered X(3872) that this state has a dominant J P C = 1 ++ (2P ) cc component but mixed with a substantial D 0D * 0 + D * 0D0 continuum component. The naively factorizable decay [1] B → χ c1 K was studied [2] in the QCD factorization approach [3] in which the nonfactorizable vertex and spectator corrections were also estimated, but the numerical results were four times smaller than experimental data. Recently, these decays were also studied in the PQCD approach [4].…”

“…(8) just like that in Ref. [2], and we parameterize it in a simple way, The mass of χ c1 (1P ) M χc1 = 3.511 Gev is known, but the mass of the missing charmonium χ c1 (2P ) has to be estimated by, say, potential models. We choose M χ ′ c1 =3.953 Gev following Ref.…”

The leading twist light-cone distribution amplitudes for the S-wave and P-wave quarkonia and their applications in single quarkonium exclusive productions

“…Many phenomenological applications along this line have been made for exclusive hard production of charmonium [7][8][9][10][11][12][13], exclusive charmonium production in B meson decays [14][15][16][17], etc. All of these applications require the understanding of the LCDAs for quarkonia.…”

Nonfactorizable B →χ c 0 K Decay and QCD Factorization

“…The naively factorizable decays [1] such as B → J/ψK [2,3], B → η c K [4], and B → χ c1 K [5] were studied in the QCD factorization approach [6] in which the nonfactorizable vertex and spectator corrections were also estimated.…”