Pion-production cross sections in neutrino reactions for studying generalized parton distributions of the nucleon

Spacelike and timelike generalized parton distributions (GPDs) have been investigated at charged-lepton accelerator facilities, for example, by the virtual Compton scattering and the two-photon process, respectively. In this work, we show the \(\pi ^\pm \) and \(\pi ^0\) production cross sections in neutrino (antineutrino) reactions \(\nu \,(\bar{\nu }) + N \rightarrow \ell + \pi + N'\) for studying the GPDs of the nucleon by using the theoretical formalism of Pire, Szymanowski, and Wagner. The \(\pi ^\pm \)-production cross sections are useful for finding mainly gluon GPDs, whereas the \(\pi ^0\) production probes quark GPDs, although there are sizable quark-gluon interference terms in the \(\pi ^\pm \) production. In particular, we show the roles of the pion- and rho-pole terms, the contribution from each GPD term (H, E, \({\tilde{H}}\), \({\tilde{E}}\)), the effects of the gluon GPDs \(H_g\) and \(E_g\), and the dependence on the energy of the process in the neutrino cross sections. These cross sections could be measured at Fermilab in future. The neutrino GPD studies will play a complementary role to the projects of charged-lepton and hadron reactions for determining the accurate GPDs.