${\eta }^{\prime }$ and $\eta$ mesons with connection to anomalous glue

A review of the present understanding of ${\eta }^{\prime }$ and $\eta$ meson physics and these mesons as a probe of gluon dynamics in low-energy QCD is presented. Recent highlights include the production mechanism of $\eta$ and ${\eta }^{\prime }$ mesons in proton-nucleon collisions from threshold to high energy, the ${\eta }^{\prime }$ effective mass shift in the nuclear medium, searches for possible $\eta$ and ${\eta }^{\prime }$ bound states in nuclei, as well as precision measurements of $\eta$ decays as a probe of light-quark masses. Recent experimental data, theoretical interpretation of the different measurements, and the open questions and challenges for future investigation are discussed.

Figure 1

Gluonic intermediate states contribute to the ${\eta }^{\prime }$. The ${\eta }^{\prime }$ mixes a chirality-two quark-antiquark contribution and chirality-zero gluonic contribution.

Figure 2

Coupling of the axial-vector current through gluonic intermediate states. Gluon propagators are shown as wavy lines. Straight lines denote quark propagators.

Figure 3

Feynman diagrams for the triangle and box anomalies. The anomaly comes from the pointlike part of the quark loop with the quarks carrying maximum momentum in the loop.

Figure 4

World data for the total cross sections for $pp\to pp\eta$ (upper points) and $pp\to pp{\eta }^{\prime }$ (lower points); see the text. The solid curves are arbitrarily scaled $pp$ FSI predictions of Eq. (37). Adapted from [308].

Figure 5

Analyzing power for the $\overrightarrow{p}p\to pp\eta$ reaction at $Q=15\mathrm{MeV}$. Here ${\theta }_{\eta }$ is the polar angle for the emission of the $\eta$ meson in the center-of-mass system. Full circles represent WASA results ([28]). Triangles are early data from COSY-11 measured at $\mathcal{E}=10\mathrm{MeV}$ ([115]). The dotted line denotes the prediction based on pseudoscalar-meson exchange ([237]), whereas the dashed line represents the vector exchange model ([133]). The solid line is the partial-waves fit to the WASA data. Adapted from [28].

Figure 6

Dependence of the parameter $\alpha$ [Eq. (44)] on the kinetic energy $T$ of the mesons for ${\pi }^0$, $\eta$, $\omega$, and ${\eta }^{\prime }$. From [238].

Figure 7

Excitation spectrum of ${}^{11}\mathrm{C}$ measured in the ${}^{12}\mathrm{C}(p,d)$ reaction at a proton energy of 2.5 GeV. The horizontal axis is the excitation energy $E_{\mathrm{ex}}$ referring to the ${\eta }^{\prime }$ emission threshold $E_0=957.78\mathrm{MeV}$. The solid gray curve displays a fit with a third-order polynomial. The inset displays a momentum spectrum of the deuterons in the calibration $\mathrm{D}(p,d)p$ reaction at 1.6 GeV. From [285], [286].

Figure 8

Total cross section for the $\gamma {}^3\mathrm{He}\to \eta {}^3\mathrm{He}$ reaction. Data are from [255] (red points) and [254] (green down triangles). Solid (dashed) curves represent plane wave impulse approximation (PWIA) calculations with a realistic (isotropic) angular distribution for the $\gamma n\to n\eta$ reaction. Inset: Ratio of measured and PWIA cross sections. From [255].

Figure 9

World data on the $pd\to {}^3\mathrm{He}\eta$ reaction close to threshold ([83]; [215]; [84]; [86]; [13]; [216]; [281]; [257]; [23], [29]). Notice the sharp rise at threshold. Adapted from [29].

Figure 10

Ratio of $\eta$ to ${\pi }^0$ production in RHIC PHENIX data. From [31].

Figure 11

The ${\eta }^{\prime }{\pi }^{-}$ exotic partial wave $1^{-+}$ (upper data) is much enhanced compared to $\eta {\pi }^{-}$ (lower data) in exclusive production from 191 GeV ${\pi }^{-}$ scattering on a hydrogen fixed target. From [33].