Color-octet mechanism inγ+p→Jψ+X

Photoproduction of $\frac{J}{\psi }$ is considered including the color-octet contributions from the various partial wave states, ${}_{}{}^{2S+1}{}_{}{}^{}L_J^{}{}_{}{}^{}={}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}, {}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}, \mathrm{and} {}_{}{}^3{}_{}{}^{}P_J^{}{}_{}{}^{}$. The production cross section depends on three new nonperturbative parameters defined in NRQCD, called the color-octet matrix elements. Using the color-octet matrix elements determined by fitting the $\frac{J}{\psi }$ production at the Fermilab Tevatron, we find that the color-octet ${\left(c\overline{c}\right)}_8\left({}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\mathrm{and} {}_{}{}^3{}_{}{}^{}P_J^{}{}_{}{}^{}\right)$ contributions to the $\frac{J}{\psi }$ photoproduction at the fixed target experiments and at DESY HERA are too large compared to the data on $\sigma (\gamma +p\to \frac{J}{\psi }+X)$ in the forward direction, and the $z$ distribution of $\frac{J}{\psi }$. The $P_T^2$ distribution of $\frac{J}{\psi }$ and the total inelastic $\frac{J}{\psi }$ production rate as a function of $\sqrt{s_{\gamma p}}$ are predicted including color-octet contributions. We also briefly digress on the $B\to \frac{J}{\psi }+X$ and observe the similar situation. This may be an indication that the color-octet matrix elements determined from the $\frac{J}{\psi }$ production at the Tevatron, especially $〈0\left|{\mathcal{O}}_8^{\psi }\right({}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\left)\right|0\mathrm{}〉$ and $〈0\left|{\mathcal{O}}_8^{\psi }\right({}_{}{}^3{}_{}{}^{}P_J^{}{}_{}{}^{}\left)\right|0\mathrm{}〉$, might have been overestimated by an order of magnitude.