Pomeron and Reggeon contributions to elastic proton-proton and proton-antiproton scattering in holographic QCD

The total and differential cross sections of elastic proton-proton and proton-antiproton scattering are studied in a holographic QCD model, considering the Pomeron and Reggeon exchanges in the Regge regime. In our model setup, the Pomeron and Reggeon exchanges are described by the Reggeized spin-2 glueball and vector meson propagators, respectively. How those contributions change with the energy is explicitly shown, focusing on the contribution ratios. The adjustable parameters included in the model are determined with the experimental data, and it is presented that the resulting total and differential cross sections are consistent with the data in a wide kinematic region.

Figure 1

The left and right Feynman diagrams represent the $pp$ ($p\overline{p}$) scattering with the Pomeron and Reggeon exchanges in the $t$-channel, respectively. $p_1$, $p_2$ and $p_3$, $p_4$ are four-momenta of the initial and final states, respectively, and $k$ is the momentum transfer.

Figure 2

The contribution ratios for the total cross section as a function of $\sqrt{s}$. The left and right panels are for the $pp$ and $p\overline{p}$ scattering, respectively. The solid and dashed curves represent the results for the Pomeron and Reggeon exchanges, respectively.

Figure 3

The contribution ratios for the differential cross section at $|t|=0.1{\mathrm{GeV}}^2$ as a function of $\sqrt{s}$. The left and right panels are for the $pp$ and $p\overline{p}$ scattering, respectively. The solid, dashed and dotted curves represent results for the Pomeron exchange, the Reggeon exchange and the cross term, respectively.

Figure 4

The total cross section of the $pp$ and $p\overline{p}$ scattering as a function of $\sqrt{s}$. Our calculations are compared with the results obtained by the COMPETE Collaboration [9]. The experimental data are taken from Ref. [6].

Figure 5

The differential cross section of the $pp$ scattering as a function of $|t|$ for $10<\sqrt{s}<30\mathrm{GeV}$. The dashed curves represent our calculations, and the experimental data are depicted by stars with error bars.

Figure 6

The differential cross section of the $pp$ scattering as a function of $|t|$ for $30\mathrm{GeV}<\sqrt{s}\le 13\mathrm{TeV}$. The dashed curves represent our calculations, and the experimental data are depicted by stars with error bars.

Figure 7

The differential cross section of the $p\overline{p}$ scattering as a function of $|t|$ for $\sqrt{s}>30\mathrm{GeV}$. The dashed curves represent our calculations, and the experimental data are depicted by stars with error bars.

Figure 8

The differential cross section of the $pp$ (left) and $p\overline{p}$ (right) scattering as a function of $|t|$ for various $\sqrt{s}$. The dashed and dotted curves represent our calculations and the results obtained by Donnachie and Landshoff [80], respectively.