Charged current electroproduction of a charmed meson at an electron-ion collider

We calculate the amplitude for exclusive electroweak production of a pseudoscalar $D_s$ or a vector $D_s^{*}$ charmed strange meson on an unpolarized nucleon, through a charged current, in leading order in ${\alpha }_s$. We work in the framework of the collinear QCD approach where generalized gluon distributions factorize from perturbatively calculable coefficient functions. We include both $O(m_c)$ terms in the coefficient functions and $O(M_D)$ mass term contributions in the heavy meson distribution amplitudes. We show that this process may be accessed at future electron-ion colliders.

Figure 1

Feynman diagrams for the factorized amplitude for the $e^{-}+N\to {\nu }_e+D_s^{-}+N^{\prime }$ process involving the gluon GPDs; the thick line represents the heavy antiquark $\overline{c}$.

Figure 2

The correspondence between $\xi$ and the variable $y$ in the low-energy (LE) and high-energy (HE) scenarios of the EIC.

Figure 3

The $D_s$ meson distribution amplitudes proposed by Ref. [14] (dashed curve) and by Ref. [15] (solid curve).

Figure 4

The $x$ dependence of gluon GPD $H^g(x,\xi ,t,{\mu }_F^2)$ given by the GK (blue lines), and simple [20] (black lines) GPD models, for typical values of the parameter in an EIC experiment: $\xi =0.05$, $Q^2=0.1{\mathrm{GeV}}^2$, $t=-0.1{\mathrm{GeV}}^2$ and factorization scale ${\mu }_F^2=M_D^2+Q^2$.

Figure 5

The $\xi$ dependence of the dominant form factor $\mathcal{H}(\xi )$ divided by the charm quark mass $m_c$ for ${\mathrm{\Delta }}_T=0$ and $Q^2=0.1{\mathrm{GeV}}^2$. Solid (dashed) lines refer to the real (imaginary) parts.

Figure 6

Left panel: The $Q^2$ dependence of the cross section $\frac{d\sigma (e^{-}N\to \nu N{D}_s^{-})}{dyd{Q}^{2}dt}$ (in pb ${\mathrm{GeV}}^{-4}$) for ${\mathrm{\Delta }}_T=0$ and $s=820{\mathrm{GeV}}^2$ and $y=0.2$ (solid curve), $y=0.5$ (dashed curve) and $y=0.8$ (dotted curve). Right panel: The $y$ dependence of the cross section $\frac{d\sigma (e^{-}N\to \nu N{D}_s^{-})}{dyd{Q}^{2}dt}$ (in pb ${\mathrm{GeV}}^{-4}$) for $Q^2=0.1{\mathrm{GeV}}^2$, ${\mathrm{\Delta }}_T=0$, and $s=820{\mathrm{GeV}}^2$.

Figure 7

Left panel: The $Q^2$ dependence of the cross section $\frac{d\sigma (e^{-}N\to \nu N{D}_s^{-})}{dyd{Q}^{2}dt}$ (in pb ${\mathrm{GeV}}^{-4}$) for ${\mathrm{\Delta }}_T=0$ and $s=20000{\mathrm{GeV}}^2$ and $y={10}^{-3}$ (solid curve), $y=5\times {10}^{-3}$ (dashed curve) and $y={10}^{-2}$ (dotted curve). Right panel: The $y$ dependence of the cross section $\frac{d\sigma (e^{-}N\to \nu N{D}_s^{-})}{dyd{Q}^{2}dt}$ (in pb ${\mathrm{GeV}}^{-4}$) for $Q^2=0.1{\mathrm{GeV}}^2$, ${\mathrm{\Delta }}_T=0$, and $s=20000{\mathrm{GeV}}^2$.

Figure 8

The $Q^2$ dependence of the cross section $\frac{d\sigma (e^{-}N\to \nu N{D}_s^{-})}{dyd{Q}^{2}dt}$ (in pb ${\mathrm{GeV}}^{-4}$) for ${\mathrm{\Delta }}_T=0$, $s=20000{\mathrm{GeV}}^2$, and $y={10}^{-4}$ with GK (blue lines), and simple [21] (black lines) GPD models, and with DAs from [14] (solid lines) and [15](dashed lines).

Figure 9

The $t$-dependence of the cross section $\frac{d\sigma (e^{-}N\to \nu N{D}_s^{-})}{dyd{Q}^{2}dt}$ (in pb ${\mathrm{GeV}}^{-4}$) for $y=2\times {10}^{-3}$, $s=20000{\mathrm{GeV}}^2$, and $Q^2=0.1{\mathrm{GeV}}^2$.

Figure 10

Left panel: The $y$ dependence of the longitudinal cross section $\frac{d\sigma (e^{-}N\to \nu N{D}_s^{-*})}{dyd{Q}^{2}dt}$ (in pb ${\mathrm{GeV}}^{-4}$) for ${\mathrm{\Delta }}_T=0$, $s=20000{\mathrm{GeV}}^2$, and $Q^2=0.1{\mathrm{GeV}}^2$. Right panel: idem for the production cross section of a transversely polarized $D_s^{-*}$.