Infrared renormalons and single meson production in proton-proton collisions

Abstract

In this article, we investigate the contribution of the higher-twist Feynman diagrams to the large-${p}_{T}$ inclusive pion production cross section in proton-proton collisions and present the general formulas for the higher-twist differential cross sections in the case of the running coupling and frozen coupling approaches. The structure of infrared renormalon singularities of the higher-twist subprocess cross section and the resummed expression (the Borel sum) for it are found. We compared the resummed higher-twist cross sections with the ones obtained in the framework of the frozen coupling approach and leading-twist cross section. We obtain, that ratio $R=({\ensuremath{\Sigma}}_{{\ensuremath{\pi}}^{+}}^{\mathrm{HT}}{)}^{\mathrm{res}}/({\ensuremath{\Sigma}}_{{\ensuremath{\pi}}^{+}}^{\mathrm{HT}}{)}^{0}$, for all values of the transverse momentum ${p}_{T}$ of the pion identically equivalent to ratio $r=({\ensuremath{\Delta}}_{\ensuremath{\pi}}^{\mathrm{HT}}{)}^{\mathrm{res}}/({\ensuremath{\Delta}}_{\ensuremath{\pi}}^{\mathrm{HT}}{)}^{0}$. It is shown that the resummed result depends on the choice of the meson wave functions used in calculation. Phenomenological effects of the obtained results are discussed.