Inclusive charmonium production via doublecc¯ine+

Abstract

Motivated by the recent observation of double-charm quark pair production by the Belle Collaboration, we calculate the complete O(␣ s 2 ) inclusive production cross sections for c , J/, and cJ (Jϭ0,1,2) plus cc in e ϩ e Ϫ annihilation through a virtual photon. We consider both color-singlet and color-octet contributions, and give the analytical expressions for these cross sections. The complete color-singlet calculations are compared with the approximate fragmentation calculations as functions of the center-of-mass energy ͱ s. We find that most of the fragmentation results substantially overestimate the cross sections ͑e.g., by a factor of ϳ4 for c1 and c2 ) at the Belle and BaBar energy ͱ sϭ10.6 GeV. The fragmentation results become a good approximation only when ͱ s is higher than about 100 GeV. We further calculate the color-octet contributions to these cross sections with analytical expressions. We find that while the color-octet contribution to J/ inclusive production via double charm is negligible ͑only about 7%͒, the color-octet contributions to c1 and c2 can be very significant.

Color-transfer enhancement for heavy quarkonium production

“…Although the direct octet contribution from 3 S to the J/ψ production rate at √ s = 10.6 GeV is only about three percent of the singlet contribution [20], the production rate, or coefficient function, for the active heavy quark pair is actually much higher for the octet mode than for the singlet,σ e + e − →cc[S8]+c ′c′ (s) ≫σ e + e − →cc[S1]+c ′c′ (s). The octet mode is suppressed because the octet NRQCD matrix element 3 S J/ψ 8 is much smaller than the singlet matrix element 3 S J/ψ 1 , by about two orders of magnitude [2].…”

“…(19), which measures the relative velocity of the spectator and the pair, as in Eq. (20). We are naturally led to suggest that these infrared sensitive corrections tend to increase the cross section for bound states, since we have found a new source of pairs with singlet color at smallβ S .…”

“…Equation (22) provides an explicit illustration of the enhancement of gluon exchange as the spectator approaches the active pair in phase space. We can summarize our analysis for the imaginary NLO pole in the amplitude at small q S by using (20) and (22) in (14), which gives…”

“…The inclusive rate of charmonium production associated with an additional pair of heavy quarks in e + e − annihilation has been studied extensively in the NRQCD formalism at both leading order (LO) [20,21] and next-to-leading order (NLO) [14]. The LO analytic expression for the singlet production of various charmonium states in terms of the variable z = 2E cc / √ s is available [20,21], while numerical results for the inclusive rate are available for the NLO contribution [14].…”

Search forXYZstates inϒ(1S)inclusive decays

“…The MC-determined efficiencies for the Υ(1S) and continuum data samples are found to be nearly the same for all the decay modes, and the dependence of the cross sections on s is assumed to be proportional to 1/s 2 [34][35][36]. The resulting scale factor is 0.098.…”