Abstract
We study $J/\psi$ and $\eta_c$ inclusive production in $\Upsilon$ decay within the framework of nonrelativistic-QCD (NRQCD) factorization. In the latter case, for which no experimental data exist so far, we also include the $h_c$ feed-down contribution. We calculate the short distance coefficients completely through $\mathcal{O}(\alpha_s^5)$. The NRQCD predictions for the branching fraction $\mathcal{B}(\Upsilon\to J/\psi+X)$ via direct production, evaluated with different sets of long-distance matrix elements (LDMEs), all agree with the experimental data in a reasonable range of renormalization scale. Using $\eta_c$ and $h_c$ LDMEs obtained from $J/\psi$ and $\chi_c$ ones via heavy-quark spin symmetry, we find that the bulk of $\mathcal{B}(\Upsilon\to\eta_c+X)$ via prompt production arises from the $c\bar{c}({}^3\!S_1^{[8]})$ Fock state. The experimental study of this decay process would, therefore, provide a particularly clean probe of the color octet mechanism of heavy-quarkonium production.
Highlights
Heavy-quarkonium production serves as an ideal laboratory to study the interplay of perturbative and nonperturbative phenomena of QCD thanks to the hierarchy of energy scales mQv2Q ≪ mQvQ ≪ mQ characterizing kinetic energy, momentum, and mass, where mQ is the mass of the heavy quark Q and vQ is its relative velocity in the rest frame of the heavy quarkonium
Using ηc and hc long-distance matrix elements (LDMEs) obtained from J=ψ and χc ones via heavy-quark spin symmetry, we find that the bulk of BðΥ → ηc þ XÞ via prompt production arises from the ccð3S1⁄218Þ Fock state
We find that the color singlet (CS) contribution to BdirectðΥ → ηc þ XÞ ranges from 3.2 × 10−5 to 0.5 × 10−5 for 3.7 GeV < μ < 2μFAC and takes the value 1.1 × 10−5 for μ 1⁄4 μFAC, which is about 1.6 times smaller than the smallest NRQCD prediction for
Summary
Heavy-quarkonium production serves as an ideal laboratory to study the interplay of perturbative and nonperturbative phenomena of QCD thanks to the hierarchy of energy scales mQv2Q ≪ mQvQ ≪ mQ characterizing kinetic energy, momentum, and mass, where mQ is the mass of the heavy quark Q and vQ is its relative velocity in the rest frame of the heavy quarkonium. [2] is the standard theoretical approach to study quarkonium production and decay This conjecture states that the theoretical predictions can be separated into process-dependent short-distance coefficients (SDCs) calculated perturbatively as expansions in the strong-coupling constant αs and supposedly universal long-distance matrix elements (LDMEs), scaling with definite powers of vQ [3]. During the past quarter of a century, the NRQCD factorization approach has been very successful in describing Both heavy-quarkonium production and decay; see Refs. To shed more light on this notorious J=ψ puzzle, it is useful to consider yet further production modes This provides an excellent motivation to study J=ψ and ηc inclusive production in Υ decays, which is the goal of this paper.
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