Phenomenological description of the parton-parton interaction in high-transverse-momentum collisions

A phenomenological quark-quark scattering model is presented which reproduces the inclusive high-transverse-momentum data from CERN ISR and Fermilab for the processes $\mathrm{pp}\to \mathrm{cX}$ and $\mathrm{pn}\to \mathrm{cX}$, where $c={\pi }^{\pm }, {\pi }^0, K^{\pm }, p, \overline{p}$. This model is obtained by multiplying the usual parton-parton scattering amplitude by the factor ${(1-\frac{\hat{t}}{B})}^{-2\mathrm{}}$ where $-\hat{t}$ is the square of the gluon 4-momentum and $B=18\mathrm{}$ Ge${\mathrm{V}}^2$. The single parameter $B$ describes both the $x_{\perp }$ dependence at constant $s$ and the $s(or p_{\perp })$ dependence at constant $x_{\perp }$ for all $c$ at all energies. An additional normalization constant is needed for each particle to fix the overall scale of the total cross section.