Study of Color Octet Matrix Elements Through $J/\psi$ Production in $e^{+}e^{-}$ Annihilation

TL;DR

This study analyzes the color-octet matrix elements involved in $J/ au$ production in electron-positron annihilation, using next-to-leading order calculations to constrain these elements and compare with collider data.

Contribution

It provides the first detailed NLO analysis of color-octet matrix elements in $J/ au$ production at B-factory energies, including radiative and relativistic corrections.

Findings

The P-wave color-octet matrix element is estimated to be around 0.005 m_c^2 GeV^3 or less.

The constrained matrix elements are incompatible with values fitted from hadron collider data.

The study offers new bounds on long-distance matrix elements relevant for quarkonium production.

Abstract

In this paper, the color-octet long distance matrix elements are studied though the inclusive $J/\psi$ production in $e^{+}e^{-}$ annihilation within the non-relativistic QCD frame. The calculations are up-to next-to-leading order with the radiative corrections and relativistic corrections at the B-factory energy region and the near-threshold region of $4.6\sim5.6~{\rm GeV}$. A constraint of the long distance matrix elements ($\langle^1S_0^{8}\rangle$, $\langle^3P_0^{8}\rangle$) is obtained. Through our estimation, the P-wave color-octet matrix element ( $\langle0|^3P^8_0|0\rangle$ ) should be the order of $0.005m_c^2~{\rm GeV}^3$ or less. The constraint region is not compatible with the values of the long distance matrix elements fitted at hadron colliders.