Generalized parton distributions from charged current meson production

In this paper we prove that the simultaneous study of both $\rho$- and $\pi$-meson production by charged currents in Bjorken kinematics allows for a very clean extraction of the leading twist generalized parton distributions of the target, with inherent control of the contribution of higher-twist corrections. Also, it might provide target-independent constraints on the distribution amplitudes of the produced mesons. We expect that such processes might be studied either in neutrino-induced or in electron-induced processes. According to our numerical estimates, the cross sections of these processes are within the reach of JLab and EIC experiments.

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 reversing directions of the quark lines and in case of the last diagram, also permuting vector boson vertices.

Figure 2

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

Figure 3

Left plot: Charged current meson production cross section on a proton target, within JLab kinematics (fixed electron energy $E=11\mathrm{GeV}$). Evaluations are performed using NLO coefficient functions, as discussed in Sec. 2b. 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. Right plot: $x_B$-dependence of the cross section in EIC kinematics with ${\sqrt{s}}_{ep}\approx 100\mathrm{GeV}$. For other values of ${\sqrt{s}}_{ep}$ and fixed $(x_B,Q^2)$ the cross section might be obtained by rescaling the factor (18). This factor is responsible for the suppression of the cross section at small $x_B\ll 1$ and at fixed energy $\sqrt{s_{ep}}$.

Figure 4

Left: Values of the coefficients $r_{2n}(x_B,Q^2)$. The two bottom curves correspond to $r_2(x_B,Q^2)$; the two upper curves correspond to $r_4(x_B,Q^2)$. For both cases dashed lines correspond to $Q^2=4{\mathrm{GeV}}^2$, solid lines correspond to $Q^2=9{\mathrm{GeV}}^2$. All evaluations performed with account of NLO correction. See the text for more explanations of the behavior of the curves. Right: expected value of the variable $R_{\rho /\pi }{(f_{\pi }/f_{\rho })}^2$ as a function of possible values of $a_2^{(\rho -\pi )}$ and $a_4^{(\rho -\pi )}$ for $x_B=0.1$ and $Q^2=4{\mathrm{GeV}}^2$. For the case of asymptotic form distributions of both mesons ($a_2^{(\rho -\pi )}=a_4^{(\rho -\pi )}=0$) the variable $R_{\rho /\pi }{(f_{\pi }/f_{\rho })}^2=1$.

Figure 5

Upper values of the coefficient $|\mathrm{\Delta }{c}_0|$ for several values of $Q^2$, within JLab kinematics ($E=11\mathrm{GeV}$).