Accessing transverse nucleon and gluon distributions in heavy nuclei using coherent vector meson photoproduction at high energies in ion ultraperipheral collisions

By using the theoretical approaches that describe well the available data on $t$-integrated coherent photoproduction of light and heavy vector mesons in Pb-Pb ultraperipheral collisions (UPCs) at the Large Hadron Collider (LHC) in Run 1, we calculate the momentum transfer distributions for this process for $\rho$ and $J/\psi$ vector mesons in the kinematics of Run 2 at the LHC. We demonstrate that nuclear shadowing not only suppresses the absolute value of the cross sections but also shifts the momentum transfer distributions toward smaller values of the momentum transfer $\left|t\right|$. This result can be interpreted as a broadening in the impact parameter space of the effective nucleon density in nuclei by 14% in the case of $\rho$ and the nuclear gluon distribution by 5%–11% in the case of $J/\psi$.

Figure 1

The $d{\sigma }_{\gamma A\to VA}\left(W_{\gamma p}\right)/dt$ cross section for $\rho$ (upper panel) and $J/\psi$ (lower panel) for ${}^{208}\mathrm{Pb}$ normalized to its value at $t=t_{\min }$ as a function of $\left|t\right|$. The cross sections are calculated at $W_{\gamma p}=62$ GeV for $\rho$ and $W_{\gamma p}=124$ GeV for $J/\psi$, corresponding to the LHC Run $2\sqrt{s_{NN}}=5.02$ TeV and $y=0$. The resulting $t$ dependence is compared with that given by the normalized nuclear form factor squared $|F_A{\left(t\right)/A|}^2$. For the $\rho$ meson, we also show the result of the calculation at $W_{\gamma p}=10$ GeV corresponding to the RHIC kinematics (the green dashed line labeled “RHIC”).

Figure 2

Photoproduction of $\rho$ mesons in Pb-Pb UPCs at $y=0$ and $\sqrt{s_{NN}}=5.02$ TeV: $d{\sigma }_{AA\to \rho AA}(y=0)/dydt$ as a function of $\left|t\right|$ (top panel) and $d{\sigma }_{AA\to \rho AA}(y=0)/dyd{p}_t$ as a function of $p_t$ (bottom panel). The blue dot-dashed and black dotted curves give separately the coherent and incoherent contributions, while the red solid curve is their sum.

Figure 3

Photoproduction of $J/\psi$ mesons in Pb-Pb UPCs at $y=0$ and $\sqrt{s_{NN}}=5.02$ TeV: $d{\sigma }_{AA\to J/\psi AA}(y=0)/dydt$ as a function of $\left|t\right|$. (top panel) The blue dot-dashed and black dotted curves give separately the coherent and incoherent contributions calculated by using the higher gluon shadowing, while the red solid curve is their sum. (bottom panel) The sum of coherent and incoherent contributions calculated using the higher (red solid curve) and lower (blue dot-dashed curve) gluon nuclear shadowing.

Figure 4

The $J/\psi$ rapidity distribution in Pb-Pb UPCs at $\sqrt{s_{NN}}=5.02$ TeV: the lower band labeled “b-dep.” corresponds to impact-parameter-dependent nuclear shadowing [Eq. (9)], while the upper band labeled “b-indep.” is obtained using Eq. (6) neglecting the nontrivial impact-parameter dependence of gluon nuclear shadowing.

Figure 5

The shift of the first diffractive minimum of $d{\sigma }_{\gamma A\to J/\psi A}/dt$ (red solid curve) and $d{\sigma }_{\gamma A\to \rho A}/dt$ (blue dot-dashed curve) with respect to that of $F_A^2\left(t\right), \mathrm{\Delta }{p}_t$, as a function of atomic number $A$ at $W_{\gamma p}=45$ GeV. In the $J/\psi$ case, it corresponds to $x=M_{J/\psi }^2/W_{\gamma p}^2=0.005$.