Decay angular distributions of $K^{*}$ and $D^{*}$ vector mesons in pion-nucleon scattering

The production mechanisms of open strangeness ($K^{*}$) and open charm ($D^{*}$) vector mesons in ${\pi }^{-}p$ scattering, namely, ${\pi }^{-}+p\to K^{*0}+\mathrm{\Lambda }$ and ${\pi }^{-}+p\to D^{*-}+{\mathrm{\Lambda }}_c^{+}$, are investigated within the modified quark-gluon string model. To identify the major reaction mechanisms, we consider the subsequent decays of the produced vector mesons into two pseudoscalar mesons, i.e., $K^{*}\to K+\pi$ and $D^{*}\to D+\pi$. We found that the decay distributions and density matrix elements are sensitive to the production mechanisms and can be used to disentangle the vector trajectory and pseudoscalar trajectory exchange models. Our results for $K^{*}$ production are compared with the currently available experimental data and the predictions for $D^{*}$ production process are presented as well. Our predictions can be tested at the present or planned experimental facilities.

Figure 1

Planar diagram decomposition for the reaction of ${\pi }^{-}+p\to D^{*-}+{\mathrm{\Lambda }}_c^{+}$.

Figure 2

Diagrammatic representation of the effective ${\pi }^{-}+p\to K^{*0}+\mathrm{\Lambda }$ and ${\pi }^{-}+p\to D^{*-}+{\mathrm{\Lambda }}_c^{+}$ reactions.

Figure 3

Unpolarized differential cross sections of (a) ${\pi }^{-}+p\to K^{*0}+\mathrm{\Lambda }$ and (b) ${\pi }^{-}+p\to D^{*-}+{\mathrm{\Lambda }}_c^{+}$ for the vector (solid curves) and pseudoscalar (dashed curves) Reggeon exchanges. The experimental data for ${\pi }^{-}+p\to K^{*0}+\mathrm{\Lambda }$ are from Ref. [26].

Figure 4

The spin-density matrix elements ${\rho }_{\lambda {\lambda }^{\prime }}^0$ defined in Eq. (13) as functions of $(t_{\max }-t)$ for $K^{*-}$ production at $p_{\pi }^{}=6$ GeV/$c$ [panels (a)–(d)] and for $D^{*-}$ production at $p_{\pi }^{}=15$ GeV/$c$ panels (e)–(h). The results for vector meson (V) and pseudoscalar (PS) Reggeon exchanges are in panels (a), (b), (e), and (f) and panels (c), (d), (g), and (h), respectively. The results in panels (a), (c), (e), and (g) were obtained in the $s$ frame, while those in panels (b), (d), (f), and (h) were obtained in the $t$ frame.

Figure 5

The same as in Fig. 4 but for ${\rho }_{\lambda {\lambda }^{\prime }}^{+}$.

Figure 6

Spin-density matrix elements for $K^{*0}$ production in the $s$ frame. Panels (a), (b), and (c) correspond to ${\rho }_{00}^0, \mathrm{Re}{\rho }_{10}^0$, and ${\rho }_{1-1}^0$ matrix elements, respectively. The vector and pseudoscalar Reggeon exchange models are depicted by the solid and dashed curves, respectively. The experimental data are from Ref. [26].

Figure 7

The same as in Fig. 6 but in the $t$ frame.

Figure 8

Angular distributions $\frac{2}{3}W\left(\mathrm{\Theta }\right)$ of Eq. (20) for $K^{*}$ and $D^{*}$ excitations are shown in the upper and lower panels, respectively. Panels (a), (b), (e), and (f) are for $\frac{2}{3}{W}^0\left(\mathrm{\Theta }\right)$ and panels (c), (d), (g), and (h) are for $\frac{2}{3}{W}^{+}\left(\mathrm{\Theta }\right)$. The results are given in both the $s$ and $t$ frames. The vector and pseudoscalar Reggeon exchange cases are depicted by the solid and dashed curves, respectively. Calculation is done for $|t_{\max }-t|=0.1{\text{GeV}}^2$ at $p_{\pi }^{}=6$ GeV/$c$ for $K^{*}$ production and $p=15$ GeV/$c$ for $D^{*}$ production.

Figure 9

The same as in Fig. 8 but for the azimuthal angle distributions $\frac{4\pi }{3}W(\mathrm{\Theta }=\pi /2,\mathrm{\Phi })$ of Eq. (21).