Role of Coulomb interaction in elastic pion-proton scattering from holography

Differential cross sections of the elastic pion-proton scattering are investigated at very small momentum transfer in a holographic QCD model, considering both the strong and Coulomb interaction in the Regge regime. The strong interaction is described by the Pomeron and Reggeon exchange, and the Coulomb interaction is characterized by the one photon exchange. The two interactions are linked through an interference term and we only need to determine a single adjustable parameter involved in this term. As to the parameters for the strong interaction, we can utilize the values determined in the previous studies. The differential cross sections can be predicted without any additional parameters, and it is shown that our predictions are consistent with the experimental data. We explicitly show the momentum transfer dependence for the interference effect. The energy dependence of the contribution ratios for each component is also discussed.

Figure 1

Gravitational and electromagnetic form factors of the proton and pion as a function of $Q^2$. The solid and dotted curves represent results for the pion gravitational and electromagnetic form factors, respectively. The dashed and dash-dotted curves represent results for the proton gravitational and electromagnetic form factors, respectively.

Figure 2

The differential cross section of the ${\pi }^{-}p$ scattering as a function of $|t|$. The dashed curves represent our calculations. The experimental data, represented by stars, are taken from Refs. [85, 86, 87, 88, 89].

Figure 3

The differential cross section of the ${\pi }^{+}p$ scattering as a function of $|t|$. The dashed curves represent our calculations. The experimental data, represented by stars, are taken from Ref. [90].

Figure 4

Contribution ratios of the interference effect in the ${\pi }^{-}p$ (left) and ${\pi }^{+}p$ (right) differential cross section as a function of $|t|$ for $\sqrt{s}=5$, 10, 20 GeV.

Figure 5

Contribution ratios in the ${\pi }^{-}p$ (left) and ${\pi }^{+}p$ (right) differential cross section as a function of $\sqrt{s}$ at $|t|=0.002{\mathrm{GeV}}^2$. The solid, dashed, and dotted curves represent results for the Coulomb interaction, strong interaction, and interference term, respectively.