Inclusive $J/\psi$ and $\eta_c$ production in $\Upsilon$ decay at $\mathcal{O}(\alpha_s^5)$ in nonrelativistic QCD factorization

TL;DR

This paper provides a detailed theoretical calculation of inclusive $J/\psi$ and $\eta_c$ production in $\Upsilon$ decay using NRQCD at high order, aligning with experimental data and offering insights into the color octet mechanism.

Contribution

It presents the first complete calculation of short distance coefficients for $\Upsilon$ decay to heavy quarkonia at $\mathcal{O}(\alpha_s^5)$ within NRQCD, including $h_c$ feed-down effects.

Findings

Predictions agree with experimental data for $J/\psi$ production.

$\eta_c$ production mainly from the $c\bar{c}({}^3\!S_1^{[8]})$ Fock state.

Decay study offers a clean probe of the color octet mechanism.

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.