Enhancement effects in exclusive $\pi\pi$ and $\rho\pi$ production in $\gamma^{\ast}\gamma$ scattering

TL;DR

This paper investigates the enhancement effects in exclusive $ ho ext{ } ext{and} ext{ } ext{pi} ext{pi}$ production during $ ext{ } ext{gamma}^* ext{ } ext{gamma}$ scattering, highlighting the significant impact of QCD evolution and pion pole contributions on cross sections.

Contribution

It provides the first detailed analysis of how QCD evolution and pion pole contributions significantly enhance cross sections in exclusive $ ho ext{ } ext{and} ext{ } ext{pi} ext{pi}$ production in $ ext{ } ext{gamma}^* ext{ } ext{gamma}$ scattering.

Findings

Cross section for $ ho ext{ } ext{pi}$ production increases by an order of magnitude after QCD evolution.

Pion pole contribution enhances the $ ext{ } ext{pi} ext{pi}$ cross section by two orders of magnitude.

Confirmed previous estimates for $ ho ext{ } ext{pi}$ production before evolution.

Abstract

The exclusive $\pi\pi$ and $\rho\pi$ production in hard $\gamma^{\ast}\gamma$ scattering in the forward kinematical region where the virtual photon is highly off-shell is studied using the $\gamma\to\pi^-$ Transition Distribution Amplitudes obtained in realistic models for the pion. For $\rho\pi$ production we confirm the previous estimates before QCD evolution. Nevertheless, once evolution is taken into account this cross section grows one order of magnitude. In the case of $\pi\pi$ production we have evaluated the cross section including the pion pole contribution. We observe that this contribution is responsible for an enhancement of two orders of magnitude with respect to the cross section evaluated without the pion pole term.