Leptoproduction of J/psi

TL;DR

This work tests NRQCD factorization in $J/\psi$ leptoproduction at large $Q^2$ by showing the cross section is dominated by ${\cal O}(\alpha_s)$ color-octet contributions, enabling extraction of the color-octet matrix elements ${\langle O_8^{\psi}(^1S_0)\rangle}$ and ${\langle O_8^{\psi}(^3P_0)\rangle}$ from cross sections. It develops the perturbative calculations for both color-octet and color-singlet channels, analyzes nonperturbative corrections (diffractive contributions, higher twists, and shape functions), and argues these corrections are suppressed at large $Q^2$, making the extraction reliable. The authors then show that once these matrix elements are fixed, the polarization of the produced $J/\psi$ is predicted without new parameters, providing a stringent test of NRQCD. They also discuss the dominant theoretical uncertainties, notably the charm-quark mass, and outline how measurements of $d\sigma/dQ^2$ and polarization at high $Q^2$ can decisively test the NRQCD framework and the color-octet mechanism.

Abstract

We study leptoproduction of $J/ψ$ at large $Q^2$ within the nonrelativistic QCD (NRQCD) factorization formalism. The cross section is dominated by color-octet terms that are of order $α_s$. The color-singlet term, which is of order $α^2_s$, is shown to be a small contribution to the total cross section. We also calculate the tree diagrams for color-octet production at order $α^2_s$ in a region of phase space where there is no leading color-octet contribution. We find that in this regime the color-singlet contribution dominates. We argue that non-perturbative corrections arising from diffractive leptoproduction, higher twist effects, and higher order terms in the NRQCD velocity expansion should be suppressed as $Q^2$ is increased. Therefore, the color-octet matrix elements $< {\cal O}_8^ψ(^1S_0)>$ and $<{\cal O}_8^ψ(^3P_0)>$ can be reliably extracted from this process. Finally, we point out that an experimental measurement of the polarization of leptoproduced $J/ψ$ will provide an excellent test of the NRQCD factorization formalism.

Figures (10)

• Figure 1: Leading order diagrams for color-octet leptoproduction of $J/\psi$
• Figure 2: $O(\alpha_s^2)$ diagrams for leptoproduction of $J/\psi$. There are six diagrams of the type shown in (a), two diagrams of the type shown in (b), and two diagrams of the type shown in (c). The remaining quark diagrams, which are not shown, can be obtained from the diagrams in (b) by replacing the external gluon lines with quarks. Note, that only the diagrams in (a) contribute to the production of a $c\bar{c}$ pair in a color-singlet ${}^3S_1$ configuration.
• Figure 3: $O(\alpha_s)$ color-octet (upper histograms) and $O(\alpha_s^2)$ color-singlet (lower histograms) contributions to the differential cross section as a function of $Q^{2}$ for two sets of kinematic cuts. The solid histograms were generated with a $Q^2$ cut of $4 \; \hbox{GeV}^2$, and the dashed histograms were generated cutting on both $Q^2 > 4 \; \hbox{GeV}^2$, and $P^2_{\perp} > 4 \; \hbox{GeV}^2$.
• Figure 4: $O(\alpha_s)$ color-octet differential cross section as a function of $Q^{2}$ for three different choices of scale: $\mu^2 = Q^{2}+(2m_{c})^{2}$ (solid histogram), $\mu^2/4$ (dotted histogram), and $4 \mu$ (dashed histogram).
• Figure 5: $O(\alpha_s)$ color-octet differential cross section as a function of $Q^{2}$ for three different choices of $m_{c}$. $m_{c}=1.3 \; \hbox{GeV}$ (dotted histogram), $m_{c}=1.5 \; \hbox{GeV}$ (solid histogram), and $m_{c}=1.7 \; \hbox{GeV}$ (dashed histogram).