One of the most challenging open problems in heavy quarkonium physics is the double charm production in e + e − annihilation at B factories. The measured cross section of e + e − → J/ψ + ηc is much larger than leading order (LO) theoretical predictions. With the nonrelativistic QCD factorization formalism, we calculate the next-to-leading order (NLO) QCD correction to this process. Taking all one-loop self-energy, triangle, box, and pentagon diagrams into account, and factoring the Coulomb-singular term into the cc bound state wave function, we get an ultraviolet and infrared finite correction to the cross section of e + e − → J/ψ + ηc at √ s = 10.6 GeV. We find that the NLO QCD correction can substantially enhance the cross section with a K factor (the ratio of NLO to LO ) of about 1.8-2.1; hence it greatly reduces the large discrepancy between theory and experiment.With mc = 1.4GeV and µ = 2mc, the NLO cross section is estimated to be 18.9 fb, which reaches to the lower bound of experiment.
Using 34.7 pb −1 of data collected with the LHCb detector, the inclusive production of the X(3872) meson in pp collisions at √ s = 7 TeV is observed for the first time. Candidates are selected in the X(3872) → J /ψπ + π − decay mode, and used to measure σ pp → X(3872) + anything B X(3872) → J /ψπ + π − = 5.4 ± 1.3 (stat) ± 0.8 (syst) nb, where σ (pp → X(3872) + anything) is the inclusive production cross section of X(3872) mesons with rapidity in the range 2.5-4.5 and transverse momentum in the range 5-20 GeV/c. In addition the masses of both the X(3872) and ψ(2S) mesons, reconstructed in the J /ψπ + π − final state, are measured to be m X(3872) = 3871.95 ± 0.48 (stat) ± 0.12 (syst) MeV/c 2 and m ψ(2S) = 3686.12 ± 0.06 (stat) ± 0.10 (syst) MeV/c 2 .
B → χc1(1P, 2P )K decays are studied in QCD factorization by treating charmonia as nonrelativistic bound states. No infrared divergences exist in the vertex corrections, while the logarithmic end-point singularities in the hard spectator corrections can be regularized by a momentum cutoff. Within certain uncertainties we find that the B → χc1(2P )K decay rate can be comparable to B → χc1(1P )K, and get Br(B 0 → χ. 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]. In both the above approaches, light-cone distribution amplitudes(LCDAs) were used to describe χ c1 . 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]. With careful studies, we find that the two descriptions (i.e.LCDAs and NR) are equivalent for the S-wave charmonium states (see,e.g. [6]), but in the case of P-wave states the light-cone descriptions lose some important contributions in the leading-twist approximation. This is not surprising since q can be neglected in S-wave states, but cannot be neglected for P-wave states even in leading order approximation.On the phenomenological hand, the study of B → χ c1 (2P )K may help clarify the nature of the recently discovered resonance X(3872) [8], since the measurements for X(3872) favor J P C = 1 ++ [9] and hence χ c1 (2P ) becomes one of the possible assignments for it. On the other hand, aside from the conventional charmonium [10,11], a loosely bound S-wave molecule of D 0D * 0 + D * 0D0 has been suggested for X(3872) [12,14].Motivated by the above considerations, in this paper we study the decays B → χ c1 (1P, 2P )K within the framework of QCD factorization by treating the charmonia χ c1 (1P, 2P ) as nonrelativistic bound states with m c /m b taken to be a fixed value in the heavy b quark limit. We will estimate the production rate of χ c1 (2P ) and argue that the X(3872) may be dominated by the χ c1 (2P ) charmonium but mixed with some D 0D * 0 + D * 0D0 continuum component. In the non-relativistic bound-state picture, charmonium can be described by the color-singlet NR wave function. Let p be the total momentum of the charmonium and 2q be the relative momentum between c andc quarks, then v 2 ∼ 4q 2 /p 2 ∼ 0.25 can be treated as a small expansion parameter [7]. For P-wave charmonium χ c1 , because the wave function at the origin R P (0)=0, which corresponds to the zeroth order in q, we must expand the a...
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