Production of strange and charmed baryons in pion induced reactions

We study the strangeness and charm productions induced by the pion beam, i.e., the ${\pi }^{-}p\to K^{*0}\mathrm{\Lambda }$ and ${\pi }^{-}p\to D^{*-}{\mathrm{\Lambda }}_c^{+}$ reactions, based on two different theoretical frameworks: an effective Lagrangian method and a Regge approach. In order to estimate the magnitude of the charm production relative to that of the strangeness production, we assume that the coupling constants for the charmed meson and baryon vertices are the same as those for the strangeness channel. We found that the total cross section for the charm production was about ${10}^3–{10}^6$ times smaller than that for the strangeness production, depending on theoretical approaches and kinematical regions. We also discuss each contribution to observables for both reactions. In general, the Regge approach explains the experimental data very well over the whole energy region.

Figure 1

Tree-level diagrams for ${\pi }^{-}p\to K^{*0}\mathrm{\Lambda }$.

Figure 2

Tree-level diagrams for ${\pi }^{-}p\to D^{*-}{\mathrm{\Lambda }}_c^{+}$.

Figure 3

Each contribution to the total cross sections for the ${\pi }^{-}p\to K^{*0}\mathrm{\Lambda }$ reaction given as a function of $s/s_{\mathrm{th}}$, based on an effective Lagrangian approach. The dotted and dashed curves show the contributions of $K$ exchange and $K^{*}$ exchange, respectively. The dot-dashed and dot-dot-dashed ones draw the effects of $N$ and $\mathrm{\Sigma }$ exchanges, respectively. The solid curve represents the total result. The experimental data are taken from Ref. [24] (triangles) and from Ref. [25] (circles).

Figure 4

Differential cross sections for the ${\pi }^{-}p\to K^{*0}\mathrm{\Lambda }$ reaction as functions of $\cos \theta$ at three different pion momenta (${\mathrm{P}}_{\text{lab}}$), based on an effective Lagrangian approach. The experimental data are taken from Ref. [25]. The notations are the same as Fig. 3.

Figure 5

Differential cross sections for the ${\pi }^{-}p\to K^{*0}\mathrm{\Lambda }$ reaction as functions of $-t^{\prime }$ at four different pion momenta (${\mathrm{P}}_{\text{lab}}$), based on an effective Lagrangian approach. The experimental data denoted by the squares are taken from Ref. [26], and those denoted by the stars are from Ref. [27]. Those designated by the circles are taken from Ref. [25]. The notations are the same as Fig. 3.

Figure 6

In the left panel, each contribution to the total cross sections for the ${\pi }^{-}p\to D^{*-}{\mathrm{\Lambda }}_c^{+}$ reaction is drawn as a function of $s/s_{\mathrm{th}}$ from an effective Lagrangian approach. The dotted and dashed curves show $t$-channel contributions, i.e., those of $D$ exchange and $D^{*}$ exchange, respectively. The dot-dashed and dot-dot-dashed ones depict the contributions of baryon exchange ($N$ and ${\mathrm{\Sigma }}_c$), respectively. The solid curve represents the full result of the total cross section. In the right panel, the total cross section for the ${\pi }^{-}p\to D^{*-}{\mathrm{\Lambda }}_c^{+}$ reaction (solid curve) is compared with that for the ${\pi }^{-}p\to K^{*0}\mathrm{\Lambda }$ one (dashed one). The experimental data for the ${\pi }^{-}p\to K^{*0}\mathrm{\Lambda }$ reaction are taken from Ref. [24] (triangles) and from Ref. [25] (circles).

Figure 7

Comparison of the differential cross section for the ${\pi }^{-}p\to D^{*-}{\mathrm{\Lambda }}_c^{+}$ with that for the ${\pi }^{-}p\to K^{*0}\mathrm{\Lambda }$ based on an effective Lagrangian approach. The experimental data are taken from Ref. [25].

Figure 8

Planar and nonplanar diagrams for the ${\pi }^{-}p\to K^{*0}\mathrm{\Lambda }$ process in the left and right panels, respectively.

Figure 9

$K$ and $K^{*}$ meson trajectories [29] (left panel) and $\mathrm{\Sigma }$ and ${\mathrm{\Sigma }}^{*}$ trajectories [32] (right panel).

Figure 10

Total cross sections for the ${\pi }^{-}p\to K^{*0}\mathrm{\Lambda }$ based on the Regge approach without form factors. The data are taken from Ref. [24] (triangles) and Ref. [25] (circles).

Figure 11

Each contribution to the total cross sections for the ${\pi }^{-}p\to K^{*0}\mathrm{\Lambda }$ reaction given as a function of $s/s_{\mathrm{th}}$, based on a Regge approach. The dotted and dashed curves show the contributions of $K$ Reggeon exchange and $K^{*}$ Reggeon exchange, respectively. The dot-dot-dashed one draws the effect of $\mathrm{\Sigma }$ Reggeon exchange. The solid curve represents the total result. The experimental data are taken from Ref. [24] (triangles) and from Ref. [25] (circles).

Figure 12

Differential cross sections for the ${\pi }^{-}p\to K^{*0}\mathrm{\Lambda }$ reaction as functions of $\cos \theta$ at three different pion momenta (${\mathrm{P}}_{\text{lab}}$), based on a Regge approach. The experimental data are taken from Ref. [25]. The notations are the same as Fig. 11.

Figure 13

Differential cross sections for the ${\pi }^{-}p\to K^{*0}\mathrm{\Lambda }$ reaction as functions of $-t^{\prime }$ at four different pion momenta (${\mathrm{P}}_{\text{lab}}$), based on a Regge approach. The experimental data denoted by the squares are taken from Ref. [26], while those denoted by the stars are from Ref. [27]. Those designated by the circles are taken from Ref. [25]. The notations are the same as Fig. 11.

Figure 14

In the left panel, each contribution to the total cross sections for the ${\pi }^{-}p\to D^{*-}{\mathrm{\Lambda }}_c^{+}$ reaction is drawn as a function of $s/s_{\mathrm{th}}$ from a Regge approach. The dotted and dashed curves show $t$-channel contributions, i.e., those of $D$ Reggeon exchange and $D^{*}$ Reggeon exchange, respectively. The dot-dot-dashed curve depicts the contribution of ${\mathrm{\Sigma }}_c$ Reggeon exchange. The solid curve represents the full result of the total cross section. In the right panel, the total cross section for the ${\pi }^{-}p\to D^{*-}{\mathrm{\Lambda }}_c^{+}$ reaction (solid curve) is compared with that for the ${\pi }^{-}p\to K^{*0}\mathrm{\Lambda }$ one (dashed one). The experimental data for the ${\pi }^{-}p\to K^{*0}\mathrm{\Lambda }$ reaction are taken from Ref. [24] (triangles) and from Ref. [25] (circles).

Figure 15

Comparison of the differential cross section for the ${\pi }^{-}p\to D^{*-}{\mathrm{\Lambda }}_c^{+}$ with that for the ${\pi }^{-}p\to K^{*0}\mathrm{\Lambda }$ based on a Regge approach. The experimental data are taken from Ref. [25].