Understanding Two Slopes in the $pp(p\bar {p})$ Differential Cross Sections

Recent experiments have discovered two exponents in the $pp$ elastic differential cross sections with two d-ifferent slope parameters, of the order 16–20 GeV^–2 and 4–4.8 GeV^–2 in the regions –t ≲ 0.5 GeV² and ‒t ≳ 1 GeV², respectively. We suggest a simple model of the $pp$ elastic scattering with two types of particle exchanges: (i) when the exchanged particle transfers the momentum Q from a quark of the proton ${{p}_{1}}$ to one quark in another proton ${{p}_{2}}$, producing the slope ${{B}_{1}}$; (ii) 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 Q, but with different coefficients in the cases (i) and (ii). Using the only parameter of the proton charge radius $r_{{{\text{ch}}}}^{{\text{2}}} = 0.93$ fm², 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.