Generalized parton distributions from charged current meson production in $ep$ experiments

We suggest that generalized parton distributions (GPDs) can be probed in the charged current meson production process, $ep\to {\nu }_e{\pi }^{-}p$. In contrast to pion photoproduction, this process is sensitive to the unpolarized GPDs $H$, $E$, and for this reason has a very small contamination by higher twist and Bethe-Heitler type contributions. Since all produced hadrons are charged, we expect that the kinematics of this process could be reconstructed from experiment. We estimated the cross sections in the kinematics of upgraded 12 GeV Jefferson Laboratory experiments and found that thanks to large luminosity the process can be measured with reasonable statistics.

Figure 1

Leading-order contributions to the DVMP hard coefficient functions. Green blob stands for the pion wave function. Additional diagrams (not shown) may be obtained reversing the directions of the quark lines and, in the case of the last diagram, permuting also the vector boson vertices.

Figure 2

Sea quark contributions to the DVMP, which appear in the next-to-leading-order contributions. Additional diagrams (not shown) may be obtained by reversing the directions of the quark lines.

Figure 3

Bethe-Heitler contribution in the charged current DVMP. Formally it is suppressed as $\mathcal{O}({\alpha }_{\mathrm{em}})$ compared to DVMP contribution; however, for the asymptotic Bjorken limit it becomes the dominant mechanism due to relative enhancement by a kinematical factor $\sim Q^2/t{\alpha }_s(Q^2)$. The green blob stands for the pion wave function.

Figure 4

Factorization scale dependence of the charged current process $ep\to {\nu }_e{\pi }^{-}p$. The ratio $R$ is defined as $R(x_B,Q^2,{\mu }_F)=d\sigma (x_B,Q^2,{\mu }_F)/d\sigma (x_B,Q^2,{\mu }_F=Q)$. A similar dependence is observed for all other processes.

Figure 5

Left and central plots: Charged current pion production cross section on a proton target at fixed electron energy, for virtualities $Q^2=2.5{\mathrm{GeV}}^2$ (left) and $Q^2=4{\mathrm{GeV}}^2$ (center). Evaluations are performed using NLO coefficient functions, as discussed in Sec. 2. 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. The dashed line corresponds to the evaluation with omitted NLO corrections in the region of $x\approx \pm \xi$, where collinear factorization might give sizable corrections $\sim \mathcal{O}(l_{\perp }^2/Q^2)$. Right plot: Relative contribution of GPDs $H^u$, $H^d$ to the total result.

Figure 6

Left: Harmonics $c_n$, $s_n$ in charged current pion production on a proton target, due to the interference with the Bethe-Heitler contribution. Right: Harmonics $c_n$, $s_n$ generated due to twist-two and twist-three GPDs interference. In both plots the evaluations are performed using NLO coefficient functions, as discussed in Sec. 2. 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 7

Left: Charged current kaon production cross sections for fixed energy electron beam ($E_e\approx 11\mathrm{GeV}$). Central: Relative fractions of different GPD components to the kaon production cross section. We can see that the interference between quark and gluons is large and contributes with a negative sign. Right: Charged current pion production on a neutron target. In all plots the evaluations are performed using NLO coefficient functions, as discussed in Sec. 2. 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.