Production of the ${\eta }_1(1855)$ through kaon induced reactions under the assumptions that it is a molecular or a hybrid state

By the reaction of kaon interacting with a proton, we investigate the production of the newly observed ${\eta }_1(1855)$ predicted in the picture of the $K{\overline{K}}_1(1400)$ molecular state and hybrid state. The total and differential cross sections of the concrete $K^{-}p\to {\eta }_1(1855)\mathrm{\Lambda }$ reaction are calculated. Taking the partial decay width of the ${\eta }_1$ to $K{\overline{K}}^{*}$ as 0.9 MeV and 98.1 MeV, the minimum cross section of the ${\eta }_1(1855)$ production via the $K^{-}p$ reaction can reach up 0.59 nb and 63.8 nb at the center of mass energies $W\simeq 3.5\mathrm{GeV}$, respectively. The differential cross sections for the ${\eta }_1(1855)$ production at the different center of mass energies are also available. Furthermore, we present the Dalitz processes of $2\to 3$ and $2\to 4$, and initially discuss the feasibility of finding out the ${\eta }_1(1855)$ in experiments like J-PARC.

Figure 1

Schematic diagram for the $t$-channel contribution to the $K^{-}p\to {\eta }_1(1855)\mathrm{\Lambda }$ reaction.

Figure 2

The energy dependence of the total cross section for production of the ${\eta }_1(1855)$ through $t$ channel with cutoff ${\mathrm{\Lambda }}_t=1.6\pm 0.3\mathrm{GeV}$. The full (red) and dashed (blue) lines are the corresponding results when the partial width of ${\eta }_1$ decay into $K{K}^{*}$ is taken as 0.9 MeV and 98.1 MeV, respectively. The bands stand for the error bar of the cutoff ${\mathrm{\Lambda }}_t$.

Figure 3

The differential cross section $d\sigma /d\cos \theta$ of the ${\eta }_1(1855)$ production at different c.m. energies $W=3.5\mathrm{GeV}$, 3.6 GeV, 4, 6 GeV and 8 GeV. Here, the notation is the same as that in Fig. 2.

Figure 4

The $t$-distribution for the $K^{-}p\to {\eta }_1(1855)\mathrm{\Lambda }$ reaction at different c.m. energies $W=3.5\mathrm{GeV}$, 3.6 GeV and 4 GeV. Here, the notation is the same as that in Fig. 2.

Figure 5

Same as Fig. 4 except that the c.m. energy is expanded to 6 GeV, 8 GeV and 10 GeV.

Figure 6

The limiting value of $|t{|}_{\min }$ as a function of $W$.

Figure 7

The invariant mass distribution $d{\sigma }_{K^{-}p\to {\eta }_1\mathrm{\Lambda }\to K{\overline{K}}^{*}\mathrm{\Lambda }}/d{M}_{K{\overline{K}}^{*}}$ reaction at different c.m. energies $W=3.5\mathrm{GeV}$, 3.6 GeV, 4 GeV, 6 GeV and 8 GeV for the partial decay width ${\mathrm{\Gamma }}_{{\eta }_1\to K{\overline{K}}^{*}}=0.90\mathrm{MeV}$. Here, the cutoff ${\mathrm{\Lambda }}_t$ is taken as 1.3 GeV.

Figure 8

Same as Fig. 7 except that the ${\mathrm{\Gamma }}_{{\eta }_1\to K{\overline{K}}^{*}}$ is taken as 98.1 MeV.