Soft Gluon Approach for Diffractive Photoproduction of J/psi

Abstract

We study diffractive photoproduction of $J/ψ$ by taking the charm quark as a heavy quark. A description of nonperturbative effect related to $J/ψ$ can be made by using NRQCD. In the forward region of the kinematics, the interaction between the $c\bar c$-pair and the initial hadron is due to exchange of soft gluons. The effect of the exchange can be studied by using the expansion in the inverse of the quark mass $m_c$. At the leading order we find that the nonperturbative effect related to the initial hadron is represented by a matrix element of field strength operators, which are separated in the moving direction of $J/ψ$ in the space-time. The S-matrix element is then obtained without using perturbative QCD and the results are not based on any model. Corrections to the results can be systematically added. Keeping the dominant contribution of the S-matrix element in the large energy limit we find that the imaginary part of the S-matrix element is related to the gluon distribution for $x\to 0$ with a reasonable assumption, the real part can be obtained with another approximation or with dispersion relation. Our approach is different than previous approaches and also our results are different than those in these approaches. The differences are discussed in detail. A comparison with experiment is also made and a qualitative agreement is found.

Figures (6)

• Figure 1: One of six Feynman diagrams for elastic photoproduction of $J/\psi$.
• Figure 2: The cross section of elastic photoproduction of $J/\psi$ versus $W_{\gamma p}$, the photon-proton center-of-mass energy. The data points are published HERA resultsHerajpsi. The full solid line represents a fit of the form $\sigma (J/\psi) \propto W_{\gamma p}^{\delta}$. The theoretical predictions of present work using various parameterizations of the leading gluon density in the proton at $m_c$ scale are also shown.
• Figure 3: The cross section of elastic photoproduction of $J/\psi$ versus $W_{\gamma p}$, the photon-proton center-of-mass energy. The data points are published HERA resultsHerajpsi. The full solid line represents a fit of the form $\sigma (J/\psi) \propto W_{\gamma p}^{\delta}$. The theoretical predictions of present work using various parameterizations of the next-to-leading gluon density in the proton at $m_c$ scale are also shown.
• Figure 4: The cross section of elastic photoproduction of $\Upsilon (1S)$ versus $W_{\gamma p}$, the photon-proton center-of-mass energy. The data points are published HERA resultsHeraup. The theoretical predictions of present work using various parameterizations of the gluon density in the proton at $m_b$ scale are also shown.
• Figure 5: The cross section of elastic photoproduction of $\Upsilon (1S)$ versus $W_{\gamma p}$, the photon-proton center-of-mass energy. The data points are published HERA resultsHeraup. The theoretical predictions of present work using various parameterizations of the gluon density in the proton at $m_b$ scale are also shown.