Pseudotensor meson family

The pseudoscalar tensor states, ${\pi }_2$, ${\eta }_2$, and $K_2$, are systematically studied through the Okubo-Zweig-Iizuka- allowed two-body strong decays, including both the observed states reported by the Particle Data Group and the predicted states. Phenomenological analysis combined with the experimental data not only can test the assignments to these discussed states, but it can also predict more abundant information on their partial decay widths, which is helpful in the experimental study of these observed and predicted pseudotensor states.

Figure 1

The analysis of the Regge trajectories for the ${\pi }_2$, ${\eta }_2$, and $K_2$ states. Slopes of the trajectories are 1.22, 1.18, and $1.71/1.75{\mathrm{GeV}}^2$ for the ${\pi }_2$, ${\eta }_2$, and $K_2$ states, respectively. Here, open circle and filled circle denote the theoretical and experimental values, respectively. In addition, the meson names written in red are the states still absent in experiment, where we predict their masses via the analysis of the Regge trajectories. In Ref. [9], Bugg also presented Regge trajectories with the average slope (see Fig. 1 in Ref. [9] for more details), which is slightly different from our present analysis.

Figure 2

The plots in $(J,M^2)$ for the $\pi /{\pi }_2/{\pi }_4$ and $\eta /{\eta }_2/{\eta }_4$ mesons. Here, open circle and filled circle are the theoretical and experimental values, respectively.

Figure 3

The OZI-allowed two-body decay modes of the ${\pi }_2$, ${\eta }_2$, and $K_2$ states. Here, $\omega$, $\rho$, and ${\eta }^{\prime }$ denote $\omega (782)$, $\rho (770)$, and ${\eta }^{\prime }(958)$, respectively. The OZI-allowed two-body decays are marked by $\surd$. ${\pi }_2^1/{\eta }_2^1/K_2^1$, ${\pi }_2^2/{\eta }_2^2/K_2^2$, ${\pi }_2^3/{\eta }_2^3/K_2^3$, ${\pi }_2^4/{\eta }_2^4/K_2^4$, ${\pi }_2^5/{\eta }_2^5/K_2^5$, and ${\pi }_2^6/K_2^6$ correspond to ${\pi }_2(1670)/{\eta }_2(1645)/K_2(1770)$, ${\pi }_2(1880)/{\eta }_2(1870)/K_2(1820)$, ${\pi }_2(2005)/{\eta }_2(2030)/K_2(2200)$, ${\pi }_2(2100)/{\eta }_2(2250)/K_2(2250)$, ${\pi }_2(2285)/{\eta }_2(2480)/K_2(2560)$, and ${\pi }_2(2540)/K_2(2610)$, respectively. In addition, we mark these predicted states in the first column with the yellow background.

Figure 4

The $R$ dependence of the calculated partial and total decay widths of ${\pi }_2(1670)$. Here, the horizontal dot-dashed line with band is the experimental total width from Ref. [62]. All results are in units of MeV. The vertical yellow bands denote the allowed $R$ value range, where the theoretical result overlaps with the experimental data in Ref. [63].

Figure 5

The $R$ dependence of the calculated partial and total decay widths of ${\pi }_2(2005)$. Here, the dot-dashed line with the horizontal band is the experimental total width from Ref. [47]. All obtained partial and total decay widths are in units of MeV.

Figure 6

The $R$ dependence of calculated partial and total decay widths of ${\pi }_2(2100)$. Here, the dot-dashed line with the horizontal band is the experimental total width from Ref. [61]. The green band corresponds to the range of the $R$ value, where the experimental data can be fitted with our theoretical results. All obtained partial and total decay widths are in units of MeV.

Figure 7

The $R$ dependence of the partial and total decay widths of ${\pi }_2(2285)$. Here, the dot-dashed line with the horizontal band is the experimental total width from Ref. [3]. The vertical band denotes that the theoretical result overlaps with the experimental data when taking the corresponding $R$ range. All results are in units of MeV.

Figure 8

The $R$ dependence of calculated partial and total decay widths of ${\pi }_2(2540)$. Here, the dot-dashed line with the horizontal band is the predicted total decay width corresponding to the $R=5.06–5.2{\mathrm{GeV}}^{-1}$ range. Here, all results are in units of MeV.

Figure 9

The $R$ dependence of calculated partial and total decay widths (in units of MeV) of ${\eta }_2(1645)$. Here, the dot-dashed line with the horizontal is the experimental width from Ref. [65]. The vertical band corresponds to the $R$ range, where the theoretical total decay width overlaps with the experimental data.

Figure 10

The $R$ dependence of calculated partial and total decay widths of ${\eta }_2(2030)$. Here, the dot-dashed line with the horizontal band denotes the experimental width from Ref. [4].

Figure 11

The variation of calculated partial and total decay widths of ${\eta }_2(2250)$ in the $R$ value. Here, the dot-dashed line with the horizontal band is the experimental total width from Ref. [76]. All decay widths are in units of MeV. The vertical band means that the range of the theoretical result overlaps with the experimental data.

Figure 12

The $R$ dependence of calculated partial and total decay widths of ${\eta }_2(2480)$ (in units of MeV).

Figure 13

The $\theta$ dependence of calculated partial and total decay widths of ${\eta }_2(1870)$. The dot-dashed line with the horizontal band denotes the experimental width from Ref. [68]. Here, we fix $R=2.5{\mathrm{GeV}}^{-1}$ for ${\eta }_2(1870)$.

Figure 14

The $R$ dependence of calculated partial and total decay widths of $K_2(1770)$ (in units of MeV). Here, the dot-dashed line with the error band denotes the experimental width of $K_2(1770)$ in Ref. [82].

Figure 15

The $R$ dependence of calculated partial and total decay widths of $K_2(1820)$ (in units of MeV). Here, the dot-dashed line with the error band is the experimental width of $K_2(1820)$ in Ref. [82].

Figure 16

The three-dimensional (left panel) and contour (right panel) plots of the total decay width of $K_2(2200)$ (the first row), $K_2(2250)$ (the second row) depending on the $R$ and ${\theta }_{K(2)}$ values.

Figure 17

The three-dimensional (left panel) and contour (right panel) plots of the total decay widths of $K_2(2560)$ (the first row), $K_2(2610)$ (the second row) depending on the $R$ and ${\theta }_{K(3)}$ values.