From the $\gamma \gamma \to p\overline{p}$ reaction to the production of $p\overline{p}$ pairs in ultraperipheral ultrarelativistic heavy-ion collisions at the LHC

In this paper we consider the production of proton-antiproton pairs in two-photon interactions in electron-positron and heavy-ion collisions. We try to understand the dependence of the total cross section on the photon-photon c.m. energy as well as corresponding angular distributions measured by the Belle Collaboration for the $\gamma \gamma \to p\overline{p}$ process. To understand the Belle data we include the proton-exchange, the $f_2(1270)$ and $f_2(1950)$ $s$-channel exchanges, as well as the hand-bag mechanism. The helicity amplitudes for the $\gamma \gamma \to f_2\to p\overline{p}$ process are written explicitly based on a Lagrangian approach. The parameters of vertex form factors are adjusted to the Belle data. Having described the angular distributions for the $\gamma \gamma \to p\overline{p}$ process we present first predictions for the ultraperipheral, ultrarelativistic, heavy-ion reaction ${}^{208}Pb{}^{208}Pb\to {}^{208}Pb{}^{208}Pbp\overline{p}$. Both, the total cross section and several differential distributions for experimental cuts corresponding to the ALICE, ATLAS, CMS, and LHCb experiments are presented. We find the total cross section $100\mu \mathrm{b}$ for the ALICE cuts, $160\mu \mathrm{b}$ for the ATLAS cuts, $500\mu \mathrm{b}$ for the CMS cuts, and $104\mu \mathrm{b}$ taking into account the LHCb cuts. This opens a possibility to study the $\gamma \gamma \to p\overline{p}$ process at the LHC.

Figure 1

Diagrams for the production of $p\overline{p}$ in $\gamma \gamma$ collisions. We consider the $t$- and $u$-channel proton exchange [diagrams (a) and (b), respectively], the exchange of $f_2$ meson in the $s$-channel [diagram (c)], and the hand-bag mechanism [diagram (d) plus the one with the photon vertices interchanged]. Here $f_2$ stands generically for a $J^{PC}=2^{++}$ meson.

Figure 2

Diagram representing proton-antiproton production in ultrarelativistic ultraperipheral collisions (UPC) of heavy ions.

Figure 3

The $\gamma \gamma \to p\overline{p}$ cross section as a function of photon-photon energy $W_{\gamma \gamma }\equiv \sqrt{s}$. We present the results for the nonresonant contribution (see Sec. 2a) for ${\mathrm{\Lambda }}_p=1.1\mathrm{GeV}$ in (2.13). The solid line represents the complete result with both Dirac- and Pauli-type couplings included in the amplitude. Other combinations of electromagnetic couplings in the $\gamma NN$ vertices are also shown: only Dirac couplings, and only Pauli couplings at the two vertices in Figs. 1 and 1. The Belle experimental data from [5] are shown for comparison.

Figure 4

The angular distributions for $\sqrt{s}=2.0$, 2.5, and 3.0 GeV for the nonresonant proton-exchange mechanism.

Figure 5

The helicity components of $d\sigma /d\cos \theta$ as a function of $\cos \theta$ for the proton exchange mechanism for $\sqrt{s}=2.0$ (the left panel) and 2.5 GeV (the right panel). Contributions of different helicities $(2s_{3}2s_4{m}_1{m}_2)$ of the photons and baryons are shown.

Figure 6

The helicity components of the differential cross sections $d\sigma /d\cos \theta$ for the $\gamma \gamma \to f_2(1950)\to p\overline{p}$ reaction for $\sqrt{s}=2.1\mathrm{GeV}$. Here, the coupling constants are fixed arbitrarily, for $j=1$, 2: $a_{f_2\gamma \gamma }{g}_{f_{2}pp}^{(j)}=\frac{e^2}{4\pi }1{\mathrm{GeV}}^{-3}$ (the left panel) and $b_{f_2\gamma \gamma }{g}_{f_{2}pp}^{(j)}=\frac{e^2}{4\pi }1{\mathrm{GeV}}^{-1}$ (the right panel). The calculations have been done for ${\mathrm{\Lambda }}_{f_2,pow}=1.15\mathrm{GeV}$ in (2.29).

Figure 7

Energy dependence of the total cross section for $\gamma \gamma \to p\overline{p}$ for $|\cos \theta |<0.6$. The experimental data are from the CLEO [1], VENUS [2], OPAL [3], L3 [4], and Belle [5] experiments. In the panel (a) we show the results for the tensor meson exchanges and the proton-exchange contributions, and their coherent sum (see the red solid line). In the panels (b) and (c) we show the results including, in addition, the hand-bag contribution. In the panels (a) and (b) we used the parameter set A while in the panel (c) we used the parameter set B; see Table 2.

Figure 8

Differential cross sections for the $\gamma \gamma \to p\overline{p}$ reaction as a function of $|\cos \theta |$ for different $W_{\gamma \gamma }$ ranges. For the Belle data [5] both statistical and systematic uncertainties are included. Calculations were done with ${\mathrm{\Lambda }}_{f_2,pow}=1.15\mathrm{GeV}$ in (2.29), and ${\mathrm{\Lambda }}_p=1.08\mathrm{GeV}$ in (2.13). The hand-bag model contribution is not included here. Here we used the parameter set A from Table 2.

Figure 9

The same as in Fig. 8 but here the hand-bag contribution is included. The green dotted line shows the contribution of the hand-bag mechanism. Here we used the parameter set A from Table 2.

Figure 10

The same as in Fig. 9 but here we used the parameter set B from Table 2.

Figure 11

Differential cross sections for the $\gamma \gamma \to p\overline{p}$ reaction as a function of $|\cos \theta |$ for different $W_{\gamma \gamma }$ ranges. We compare our total model results (including the hand-bag contribution) with the Belle data [5], the L3 data [4], and the OPAL data [3]; see the black solid line, the red long-dashed line, and the blue short-dashed line, respectively. Here we used the parameter set A from Table 2.

Figure 12

The distribution in $z=\cos \theta$, integrating over $2m_p<W_{\gamma \gamma }<4\mathrm{GeV}$, for the $PbPb\to PbPbp\overline{p}$ reaction at the $PbPb$ collision energy $\sqrt{s_{NN}}=5.02\mathrm{TeV}$.

Figure 13

Distribution in ($z,W_{\gamma \gamma }$) for the $PbPb\to PbPbp\overline{p}$ reaction (3.1) at the LHC energy $\sqrt{s_{NN}}=5.02\mathrm{TeV}$.

Figure 14

The differential nuclear cross sections for the $PbPb\to PbPbp\overline{p}$ reaction (3.1) at $\sqrt{s_{NN}}=5.02\mathrm{TeV}$. Results for the full range of $z$ (the black lines) and for $|z|<0.6$ (the red lines) are presented. In panels (b)—(d) we integrate for $2m_p\le W_{\gamma \gamma }<4\mathrm{GeV}$. No other cuts have been imposed here.

Figure 15

The two-dimensional distributions in proton and antiproton rapidities for the reaction (3.1) at $\sqrt{s_{NN}}=5.02\mathrm{TeV}$ for two different $z$-ranges of outgoing nucleons. The results include the hand-bag contribution. The results are integrated for $2m_p<W_{\gamma \gamma }<4\mathrm{GeV}$.

Figure 16

The differential nuclear cross sections as a function of $p\overline{p}$ invariant mass (the left panel) and ${\mathrm{y}}_{\text{diff}}={\mathrm{y}}_p-{\mathrm{y}}_{\overline{p}}$ (the right panel) for the $PbPb\to PbPbp\overline{p}$ reaction (3.1). The results for different experimental cuts are presented.

Figure 17

Coordinate system and momentum vector $\mathit{p}$.

Figure 18

The reaction $\gamma \gamma \to p\overline{p}$ in the c.m. system.