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

Abstract

Abstract In this paper, the color-octet long distance matrix elements are studied through the inclusive $$J/\psi $$ J / ψ production in $$e^{+}e^{-}$$ 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 $$4.6{-}5.6~\mathrm{GeV}$$ 4.6 - 5.6 GeV . A constraint of the long distance matrix elements ( $$\langle ^1S_0^{8}\rangle $$ ⟨ 1 S 0 8 ⟩ , $$\langle ^3P_0^{8}\rangle $$ ⟨ 3 P 0 8 ⟩ ) is obtained. Through our estimation, the P-wave color-octet matrix element $$(\langle 0|^3P^8_0|0\rangle )$$ ( ⟨ 0 | 3 P 0 8 | 0 ⟩ ) should be of the order of $$0.008m_\mathrm{c}^2~\mathrm{GeV}^3$$ 0.008 m c 2 GeV 3 or less. The constrained region is not compatible with the values of the long distance matrix elements fitted at hadron colliders.