Loop corrections to pion and kaon neutrino production

In this paper, we study the next-to-leading-order corrections to deeply virtual pion and kaon production in neutrino experiments. We estimate these corrections in the kinematics of the minerva experiment at Fermilab, and find that they are sizable and increase the leading-order cross section by up to a factor of 2. We provide a computational code which can be used for the evaluation of the cross sections, taking into account these corrections and employing various generalized parton distribution models.

Figure 1

Leading-order contributions to the DVMP hard coefficient functions. The green blob stands for the pion wave function. Additional diagrams (not shown) may be obtained by reversing the directions of the quark lines.

Figure 2

Next-to-leading-order contributions to the DVMP hard coefficient functions. The green blob stands for the pion wave function. The blue circle in the third diagram on the first line stands for all possible gluon mass corrections (sum of quark and gluon loops). Additional diagrams (not shown) may be obtained by reversing the directions of the quark lines.

Figure 3

Factorization-scale dependence of the charged-current ${\pi }^{+}$ production for the process $\nu p\to {\mu }^{-}{\pi }^{+}p$ for several values of $x_B$. Similar dependence is observed for all other processes.

Figure 4

Pion production on nucleons, with neutral and charged currents and a fixed-energy neutrino beam ($E_{\nu }\approx 6\mathrm{GeV}$). The dashed line stands for the leading-order evaluation, whereas the solid line surrounded by green error bands (marked as “Full”) stands for the full result with NLO corrections. The width of the band represents the uncertainty due to the factorization-scale choice ${\mu }_F\in (Q/2,2Q)$, as explained in the text.

Figure 5

Selected neutral- and charged-current mediated kaon production cross sections for a fixed-energy neutrino beam ($E_{\nu }\approx 6\mathrm{GeV}$). The dashed line stands for the leading-order evaluation, whereas the solid line surrounded by green error bands (marked as “Full”) stands for the full result, which takes into account NLO corrections. The width of the band represents the uncertainty due to the factorization-scale choice ${\mu }_F\in (Q/2,2Q)$, as explained in the text.