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In this paper, the color-octet long distance matrix elements are studied through the inclusive \(J/\psi \) production in \(e^{+}e^{-}\) annihilation within the framework of non-relativistic QCD factorization. The calculations are up-to next-to-leading order with the radiative and relativistic corrections in the energy region of the B-factory and the near-threshold region of \(4.6{-}5.6~\mathrm{GeV}\). 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 \((\langle 0|^3P^8_0|0\rangle )\) should be of the order of \(0.008m_\mathrm{c}^2~\mathrm{GeV}^3\) or less. The constrained region is not compatible with the values of the long distance matrix elements fitted at hadron colliders.

Study of color-octet matrix elements through $$J/\psi $$ J / ψ production in $$e^{+}e^{-}$$ e + e - annihilation