Near threshold $J/\psi$ and $\mathrm{\Upsilon }$ photoproduction at JLab and RHIC

We update our previous calculation of $J/\psi$ photoproduction near threshold [Y. Hatta and D. L. Yang, Phys. Rev. D 98, 074003 (2018)] by incorporating the recent developments in theory and the new experimental data from Ali et al. [the GlueX Collaboration] at Jefferson Laboratory. We then propose to study the near threshold production of $\mathrm{\Upsilon }$ and $J/\psi$ in ultraperipheral $pA$ collisions at RHIC. These processes are sensitive to the gluon condensate in the proton which is related to the proton mass via the QCD trace anomaly. Our result emphasizes the role of gluons in generating the proton mass.

Figure 1

(Left) Fits of the GlueX data [6] for the total cross section. The red curve corresponds to $b=0$ and the blue curve corresponds to $b=1$. (Right) Comparisons between the GlueX data [6] and our model for differential cross sections, where $\delta t=t-t_{\min }$. Color assignments are the same as the left panel, while the solid, dashed, and dot-dashed curves correspond to $E_{\gamma }=10$, 10.3, and 10.6 GeV, respectively. The experimental data are taken for $10<E_{\gamma }<11.8\mathrm{GeV}$.

Figure 2

${\chi }^2$ as a function of the parameter $b$.

Figure 3

Kinematically allowed region of $J/\psi$ (left) and $\mathrm{\Upsilon }$ (right). The horizontal axis is $y$ and the vertical axis is $k_{\perp }$. The threshold region is in the lower-right corner.

Figure 4

(Left) The differential cross sections (nb ${\mathrm{GeV}}^{-2}$) for $J/\psi$ production in UPC at $y=3.8$ with varying $k_{\perp }$ (GeV), where red and blue curves correspond to $b=0$ and $b=1$. (Right) The ratio of $d{\sigma }_{\mathrm{pAR}}\equiv {(\frac{d{\widehat{\sigma }}_{pA}}{dyd{k}_{\perp }^2})}_{b=0}/{(\frac{d{\widehat{\sigma }}_{pA}}{dyd{k}_{\perp }^2})}_{b=1}$ for $J/\psi$ at $k_{\perp }=0.5\mathrm{GeV}$.

Figure 5

(Left) The normalized differential cross sections for $\mathrm{\Upsilon }$ production in UPC at $y=2.9$ with varying $k_{\perp }$ (GeV), where red and blue curves correspond to $b=0$ and $b=1$. (Right) The ratio of $d{\widehat{\sigma }}_{\mathrm{pAR}}\equiv {(\frac{d{\widehat{\sigma }}_{pA}}{dyd{k}_{\perp }^2})}_{b=0}/{(\frac{d{\widehat{\sigma }}_{pA}}{dyd{k}_{\perp }^2})}_{b=1}$ at $k_{\perp }=0.5\mathrm{GeV}$.