Insights into the exotic charged states $Z_b(10610)$ and $Z_b(10650)$ from their photoproduction off nuclei

Abstract

The possibility to study the nature of the famous charged bottomonium-like states $Z_b(10610)$ and $Z_b(10650)$, which is by far the best known, from their inclusive photoproduction off nuclei near the kinematic threshold is investigated within the collision model based on the nuclear spectral function. The model accounts for $Z_b(10610)^{\pm}$ and $Z_b(10650)^{\pm}$ production in direct photon--nucleon interactions as well as four different scenarios for their intrinsic configurations: compact tetraquarks, molecules of the two open-beauty mesons and two mixtures of both of them for each of $Z_b$ state. We calculate within these scenarios the absolute and relative excitation functions on $^{12}$C and $^{184}$W nuclei at photon energies of 61--90 GeV, the absolute momentum differential cross sections and ratios of them for their production off these target nuclei at laboratory polar angles of 0$^{\circ}$--5$^{\circ}$ and for photon energy of 75 GeV as well as the A-dependences of the transparency ratios for the $Z_b(10610)^{\pm}$ mesons at photon energy of 75 GeV. We show that the absolute and relative observables considered reveal distinct sensitivity to the $Z_b(10610)^{\pm}$ and $Z_b(10650)^{\pm}$ internal structures. Therefore, they might be useful for the determination of these structures from the comparison of them with the experimental data from the future high-precision experiments at the upcoming experimental facilities, such as the planned high-luminosity electron-ion colliders in the United States and China.

Figures (12)

• Figure 1: (Color online.) Excitation functions for the production of $Z_b(10610)^{\pm}$ (left panel) and $Z_b(10650)^{\pm}$ (right panel) mesons off $^{12}$C from the direct processes (1), (2) proceeding on an off-shell target nucleons and on a free ones being at rest. The curves are calculations in the scenarios, in which the $Z_b(10610)^{\pm}$ and $Z_b(10650)^{\pm}$ are treated as a purely compact four quark (4$q$) states, as a purely molecular states, or as a hybrid states: mixtures of the non-molecular (compact) and molecular (non-compact) components, in which there are 50% of the 4$q$ components and 50% molecular components, as well as 25% and 75% of the nonmolecular and molecular states. The left and right arrows indicate the threshold energies for the $Z_b(10610)^{\pm}$ and $Z_b(10650)^{\pm}$ photoproduction on a free nucleons in reactions (1), (2).
• Figure 2: (Color online.) Excitation functions for the production of $Z_b(10610)^+$ (left panel) and $Z_b(10610)^-$ (right panel) mesons off $^{184}$W , respectively, from the direct processes (1) and (2) proceeding on an off-shell target nucleons and on a free ones being at rest. The curves and the arrows denote the same as in Fig. 1 for the $Z_b(10610)^{\pm}$.
• Figure 3: (Color online.) The same as in Fig. 2, but for the $Z_b(10650)^{\pm}$ mesons.
• Figure 4: (Color online.) Ratios between the $Z_b(10610/10650)^{\pm}$ production cross sections on $^{12}$C, shown in Fig. 1 and calculated in the compact tetraquark scenarios and in the hybrid pictures for them, in which there are 50% of the 4$q$ components and 50% molecular components; in the hybrid pictures for them, in which there are 50% of the 4$q$ components and 50% molecular components, as well as 25% and 75% of the nonmolecular and molecular states; in the hybrid pictures for them, in which there are 25% of the 4$q$ components and 75% molecular components, as well as in the molecular scenarios for an off-shell target nucleons, as functions of photon energy.
• Figure 5: (Color online.) Ratios between the $Z_b(10610/10650)^{+}$ (left panel) and between the $Z_b(10610/10650)^-$ (right panel) production cross sections on $^{184}$W, shown in Figs. 2, 3, as functions of photon energy. The curves denote the same as in Fig. 4.