Photoproduction of $J/\psi$ mesons in peripheral and semicentral heavy ion collisions

We calculate total and differential cross sections for $J/\psi$ photoproduction in ultrarelativistic lead-lead collisions at the LHC energy $\sqrt{s_{NN}}=2.76$ TeV. In the present approach we use a simple model based on vector dominance picture and multiple scattering of the hadronic $\left(c\overline{c}\right)$ state in a cold nucleus as an example. In our analysis we use both the classical mechanics and quantum (Glauber) formulas for calculating ${\sigma }_{\mathrm{tot},J/\psi Pb}$ which is a building block of our model. We compare our UPC results with ALICE and CMS data. For semicentral collisions $\left(b<R_A+R_B\right)$ a modification of the photon flux seems necessary. We discuss differences motivated by physics approximations. We try to estimate the cross sections for different centrality bins and for $J/\psi$ mesons emitted in forward rapidity range $\left(2.5<y<4\right)$ corresponding to recent ALICE experimental results. Reasonable results are obtained and open questions are discussed.

Figure 1

Schematic diagrams for the single vector meson production by photoproduction [photon-$\mathbf{IP}/\mathbf{IR}$ (left) or $\mathbf{IP}/\mathbf{IR}$-photon (right) fusion]. Here the symbol $\mathbf{IP}/\mathbf{IR}$ is an abbreviation for multiple diffractive scattering of the hadronic system in the nuclear medium.

Figure 2

Equivalent photon approximation fluxes as a function of impact parameter for gold (left panel) and for lead nucleus (right panel) for two different values of photon energy. The calculations for $\mathrm{Au}+\mathrm{Au}$ collisions are done at $\sqrt{s_{NN}}=200$ GeV $\left(\gamma =107\right)$ and for $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=2.76$ TeV $\left(\gamma =1471\right)$.

Figure 3

Impact parameter picture of the collision and the production of the $J/\psi$ meson for ultraperipheral (left panel) and for semicentral (right panel) collisions. It is assumed here that the first nucleus is the emitter of the photon which rescatters then in the second nucleus being a rescattering medium.

Figure 4

Standard photon fluxes $N(\omega ,b)$ [see Eq. (2.3)] calculated for realistic (left panel) monopole (middle panel) and pointlike (right panel) form factors.

Figure 5

Two-dimensional distributions of the photon fluxes $N^{\left(1\right)}(\omega ,b)$ [see Eq. (2.4)] and $N^{\left(2\right)}(\omega ,b)$ [see Eq. (2.5)] in the impact parameter $b$ and in the energy of photon $\omega$ for three different conditions (more in the text).

Figure 6

The ratio of the differential photon fluxes in the impact parameter $b$ and energy of the photon $\omega$. The left panel shows the case with the realistic form factor, the middle panel monopole form factor, and the right panel the form factor for pointlike charge.

Figure 7

Centrality of nuclear collisions as a function of the impact parameter as obtained from Eq. (2.14). For reference we marked $c=30\%$ and the corresponding impact parameter.

Figure 8

Differential cross section for coherent production of the $J/\psi$ meson in UPC as a function of rapidity of the $J/\psi$ meson compared with the ALICE and CMS data points. We show results for both realistic and monopole form factors, each of them used consistently in Eqs. (2.3) and (2.15).

Figure 9

Differential cross section for photoproduction of the $J/\psi$ meson as a function of impact parameter for $\sqrt{s_{NN}}=2.76$ TeV. Different lines correspond to different approximations: (dotted) standard UPC approach [Eq. (2.3)]; (dashed) first approximation and correction [Eq. (2.4)] (upper limit); (solid) second approximation and correction [Eq. (2.5)] (lower limit). Here the realistic (charge) nuclear form factor was used. For reference we show vertical lines corresponding to $c=30\%$ and $c=100\%$.

Figure 10

$d\sigma /dy$ cross sections for different centrality bins. Theoretical results for different models of the photon flux are compared with the ALICE data [15, 16]. The shaded area represents the experimental uncertainties.