Small x gluon from exclusive J/psi production

TL;DR

This work tackles how to constrain the proton's small-$x$ gluon density using exclusive $J/\psi$ production at HERA, where the cross section is highly sensitive to the gluon via two-gluon exchange. The authors develop both LO and NLO descriptions, incorporating unintegrated gluons, skewedness, and real-part corrections within a $k_T$-factorisation framework to extract $xg(x,\bar{Q}^2)$ in the region $10^{-4} \lesssim x \lesssim 10^{-2}$ and $2 \lesssim Q^2 \lesssim 8$ GeV$^2$, comparing with global fits. The NLO analysis shows a substantial but calculable modification of the extracted gluon (roughly a $\sim\!22\%$ suppression at $x\sim10^{-3}$, dominated by skewedness) and yields gluon distributions that are broadly consistent with, yet distinct from, global fits, highlighting the complementary role of exclusive vector-meson data. The results underscore the value of exclusive $J/\psi$ production as a probe of small-$x$ QCD dynamics and provide predictions for related processes such as elastic $\Upsilon$ production. Overall, the study narrows uncertainties on the small-$x$ gluon and informs gluon evolution in a kinematic regime where inclusive DIS data are less constraining.

Abstract

Exclusive J/psi production, gamma* p -> J/psi p, offers a unique opportunity to determine the gluon density of the proton in the small x domain. We use the available HERA data to determine the gluon distribution in the region 10^{-4} <~ x <~ 10^{-2} and 2 <~ Q^2 <~ 10 GeV^2, where the uncertainty on the gluon extracted from the global parton analyses is large. The gluon density is found to be approximately flat at the lower scale; it is compared with those of recent global analyses.

Figures (5)

• Figure 1: Comparison of recent global fits of the gluon distribution at small $x$ at leading (LO), next-to-leading (NLO) and next-to-next-to leading (NNLO) order, for the two scales $Q^2 = 2.4$ (left) and $10$ GeV$^2$ (right panel). LO gluons (dash dot) compared are CTEQ6L pdfCTEQ6 and MRST2004F4LO pdfMRST2004F. The two (long) dashed lines indicate the error estimate of the CTEQ6.5 pdfCTEQ6.5 gluon and the shaded band is the error band for the MRST2001 pdfMRST2001 global gluon. Central values for the NLO global fits are from CTEQ6.5M (short dashed) and MRST2004NLO pdfMRST2004 (dotted). The solid line represents MRST2006NNLO MRST07.
• Figure 2: Schematic picture of high energy elastic $J/\psi$ production, $\gamma^* p \to J/\psi\,p$. The factorised form follows since, in the proton rest frame, the formation time $\tau_f \simeq 2E_\gamma/(Q^2+M^2_{J/\psi})$ is much greater than the $c\bar{c}$-proton interaction time $\tau_{\rm int}$. In the case of the simple two gluon exchange shown here, $\tau_{\rm int} \simeq R$, where $R$ is the radius of the proton.
• Figure 3: Leading order fit of elastic $J/\psi$ data as described in the text. Left panel: cross section compared to some of the H1 H1 and ZEUS ZEUS2ZEUS3 data, with values for $\bar{Q}^2$ as indicated; right panel: gluon compared to global fits for scales as indicated, where the solid (dashed) lines are the MRST2004F4LO pdfMRST2004F (CTEQ6L pdfCTEQ6) results. The width of the bands displays the uncertainty of the cross section and fitted gluon respectively, whereas the darker shaded areas indicate the region of the available data.
• Figure 4: As Fig. \ref{['fig:lo']}, but for the next-to-leading order fit and comparing to NLO global fits from CTEQ6.5M pdfCTEQ6.5 and MRST2004 pdfMRST2004.
• Figure 5: Prediction of elastic $\Upsilon$ photoproduction, using our LO and NLO gluon, compared to data. The dotted lines indicate the error band of the LO prediction, whereas the shaded band is our NLO prediction. The data points are the published ZEUS ZEUSupsilon and H1 H1upsilon results, and the preliminary results from ZEUS ZEUSupsprel07.