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

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 $4.6\sim 5.6\mathrm{GeV}$. A constraint of the long distance matrix elements (${⟨}^1{S}_0^8⟩$, ${⟨}^3{P}_0^8⟩$) is obtained. Through our estimation, the P-wave color-octet matrix element ( $⟨0{|}^3{P}_0^8|0⟩$ ) should be the order of $0.005m_c^2{\mathrm{GeV}}^3$ or less. The constraint region is not compatible with the values of the long distance matrix elements fitted at hadron colliders.