Complete Study of Hadroproduction of a $\Upsilon$ Meson Associated with a Prompt $J/\psi$

TL;DR

This paper provides a comprehensive theoretical analysis of simultaneous $$ and prompt $J/$ production in high-energy collisions, including all relevant contributions, to better understand the role of single and double parton scatterings.

Contribution

It offers the first complete calculation of $$ and $J/$ production, incorporating all significant QCD and electroweak contributions, and refines the estimate of double parton scattering effects.

Findings

Effective cross section for double-parton scattering is $\sigma_{ m eff}\le 8.2$ mb.

Complete theoretical evaluation improves understanding of simultaneous quarkonium production.

Refined the contribution estimate of double parton scattering in experimental data.

Abstract

We present the first complete study of $\Upsilon$ and prompt $J/\psi$ production from single-parton scattering, including the complete $\mathcal{O}(\alpha_S^6)$ color-singlet contribution, the $\mathcal{O}(\alpha_S^2\alpha^2)$ electroweak contribution, the complete nonrelativistic S-wave and P-wave color-octet contribution as well as the feeddown contribution. Our study was motivated by the recent evidence reported by D0 Collaboration of prompt $J/\psi$ and $\Upsilon$ simultaneous production at the Tevatron. With our complete evaluation, we are able to refine the determination of the double parton scattering contribution made by D0 Collaboration. We find that the effective cross section characterizing the importance of double-parton scatterings is $\sigma_{\rm eff}\le 8.2$ mb at $68\%$ confidence level from the D0 measurement.