Understanding two slopes in the pp (p\bar p) differential cross sections

TL;DR

This paper proposes a simple two-exchange model for proton-proton elastic scattering that explains the two observed slopes in the differential cross sections, matching experimental data with minimal parameters.

Contribution

The model introduces two types of particle exchanges to account for the two different slopes, providing a straightforward explanation consistent with experimental observations.

Findings

Predicted slopes B1 and B2 match experimental values

The ratio B1/B2 is exactly 4, independent of proton charge radius

Model aligns with data for both pp and p̄p scattering

Abstract

Recent experiments have discovered two exponents in the $pp$ elastic differential cross sections with two different slope parameters, of the order $(16-20)$~GeV$^{-2}$ and $(4-4.8)$~GeV$^{-2}$ in the regions $ -t \la 0.5 $~GeV$^2$ and $ -t \ga 1$~GeV$^2$, respectively. We suggest a simple model of the $pp$ elastic scattering with two types of particle exchanges: 1) when the exchanged particle transfers the momentum $\veQ$ from a quark of the proton $p_1$ to one quark in another proton $p_2$, producing the slope $B_1$; 2) when the transfer occurs from two quarks in the $p_1$ to two quarks in the $p_2$, giving the exponent with the slope $B_2$. The resulting amplitude is proportional to the product of the form factors of two protons, depending on $\veQ$, but with different coefficients in the cases 1) and 2). Using the only parameter - the proton charge radius $r^2_{ch}= 0.93$~fm$^2$, one obtains $B_1 = 16$~GeV$^{-2}$,~$ B_2 = 4$~GeV$^{-2}$ with the strict value of the ratio, $\frac{B_1}{B_2} = 4.0$, independent of $r_{ch}$. These predictions are surprisingly close to the data both in the $pp$ and in the $\bar p p$ differential cross sections. Comparison to experimental data and theoretical approaches is discussed, together with possible implications for the future development of the theory.