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

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 $r_{ch}^2=0.93$~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.

arXiv comment9 pages,1 table

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