${\pi }^{-}\mathrm{p}\to {\mathrm{D}}^{-}{\mathrm{\Lambda }}_{\mathrm{c}}^{+}$ within the generalized parton picture

We investigate the reaction ${\pi }^{-}p\to D^{-}{\mathrm{\Lambda }}_c^{+}$ within the generalized parton picture. The process is described by a handbag-type mechanism with the charm-quark mass acting as the hard scale. As in the case of preceding work on $\overline{p}p\to {\overline{\mathrm{\Lambda }}}_c^{-}{\mathrm{\Lambda }}_c^{+}$ we assume that the process amplitude factorizes into one for the perturbatively calculable partonic subprocess $\overline{u}u\to \overline{c}c$ and hadronic matrix elements that can be parametrized in terms of generalized parton distributions. Modeling the generalized parton distributions by overlaps of (valence-quark) light-cone wave functions for the hadrons involved, we obtain numerical results for unpolarized differential and integrated cross sections as well as spin observables. Our approach works well above the production threshold ($s\gtrsim 20{\mathrm{GeV}}^2$) in the forward hemisphere and predicts unpolarized cross sections of the order of nb, a finding that could be of interest in view of plans to measure ${\pi }^{-}p\to D^{-}{\mathrm{\Lambda }}_c^{+}$ at J-PARC.

Figure 1

The double-handbag contribution to the process ${\pi }^{-}p\to D^{-}{\mathrm{\Lambda }}_c^{+}$ (in the DGLAP region). The momenta, LC helicities and colors of the quarks are specified.

Figure 2

The left plot shows the ${\pi }^{-}\to D^{-}$ transition GPD $H_{\pi D}^{\overline{cu}}$ vs ${\overline{x}}_2$ at Mandelstam $s=25{\mathrm{GeV}}^2$ and ${\mathbf{\Delta }}_{\perp }^2=0$, 3.0, $5.0{\mathrm{GeV}}^2$ (solid, dotted and dashed line), corresponding to $|t^{\prime }|=|t-t_0|=0$, 3.31, $5.69{\mathrm{GeV}}^2$ ($\eta =0.13$, 0.16, 0.18), for the hadron LCWFs introduced in the text (KK mass exponential). $t_0$ is the (nonvanishing) value of $t$ for forward scattering (${\mathbf{\Delta }}_{\perp }=0$, $p^{\prime 3}\ge 0$). The right plot shows the corresponding ${\pi }^{-}\to D^{-}$ transition form factor $G$ as a function of $|t^{\prime }|$ for $s=20,25$ and $30{\mathrm{GeV}}^2$ (solid, dotted and dashed line).

Figure 3

The differential ${\pi }^{-}p\to D^{-}{\mathrm{\Lambda }}_c^{+}$ cross section in the CMS versus $\cos \theta$ for $s=20,25,30{\mathrm{GeV}}^2$ (solid, dotted and dashed line). The left plot has been obtained with the wave-function parametrizations described in the text (KK mass exponential). The effects of uncertainties in the ${\mathrm{\Lambda }}_c$ and the $D^{-}$ wave-function parameters are indicated by the shaded band around the $s=20{\mathrm{GeV}}^2$ curve. Results obtained with a different analytic form of the ${\mathrm{\Lambda }}_c$ and $D^{-}$ LCWFs (BB mass exponential) are shown in the right plot.

Figure 4

Our prediction for the integrated cross section $\sigma$ versus Mandelstam $s$ (solid line with error band). For comparison we give also predictions obtained with the BB mass exponential (dashed line; see Ref. [1]).

Figure 5

The spin-correlation parameters $D_{LL}$ (left plot) and $D_{LS}$ (right plot) versus $\cos \theta$ for $s=20$, 25 and $30{\mathrm{GeV}}^2$.