Analyzing ${\eta }^{\prime }$ photoproduction data on the proton at energies of 1.5–2.3 GeV

The recent high-precision data for the reaction $\gamma p\to p{\eta }^{\prime }$ at photon energies in the range 1.5–2.3 GeV obtained by the CLAS Collaboration at the Jefferson Laboratory have been analyzed within an extended version of the photoproduction model developed previously by the authors based on a relativistic meson-exchange model of hadronic interactions [Phys. Rev. C 69, 065212 (2004)]. The ${\eta }^{\prime }$ photoproduction can be described quite well over the entire energy range of available data by considering $S_{11},P_{11},P_{13}$, and $D_{13}$ resonances, in addition to the t-channel mesonic currents. The observed angular distribution is due to the interference between the t-channel and the nucleon s- and u-channel resonance contributions. The $j=3/2$ resonances are required to reproduce some of the details of the measured angular distribution. For the resonances considered, our analysis yields mass values compatible with those advocated by the Particle Data Group. We emphasize, however, that cross-section data alone are unable to pin down the resonance parameters and it is shown that the beam and/or target asymmetries impose more stringent constraints on these parameter values. It is found that the nucleonic current is relatively small and that the $\mathit{NN}{\eta }^{\prime }$ coupling constant is not expected to be much larger than 2.

Figure 1

Diagrams contributing to $\gamma p\to {\eta }^{\prime }p$. Time proceeds from right to left. The intermediate baryon states are denoted N for the nucleon and R for the $S_{11},P_{11},P_{13}$, and $D_{13}$ resonances. The intermediate mesons in the t-channel are ρ and ω. The external legs are labeled by the four-momenta of the respective particles and the labels s, u, and t of the hadronic vertices correspond to the off-shell Mandelstam variables of the respective intermediate particles. The three diagrams in the lower part of the diagram are transverse individually; the three diagrams in the upper part are made gauge invariant by an appropriate choice for the contact current depicted in the top-right diagram. The nucleonic current (nuc) referred to in the text corresponds to the top line of diagrams; the meson-exchange current (mec) and resonance current contributions correspond, respectively, to the leftmost diagram and the two diagrams on the right of the bottom line of diagrams.

Figure 2

(Color online) Differential cross section for $\gamma p\to p{\eta }^{\prime }$ according to the mechanisms shown in Fig. 1 as a function of the ${\eta }^{\prime }$ emission angle ${\theta }_{{\eta }^{\prime }}$ in the center-of-momentum frame of the system. As indicated in the legend, the curves correspond to the fit results of Tables (dash-double-dotted), (dotted lines), (dashed), (solid), and (dash-dotted). The numbers ($T\gamma ,W$) in parentheses are the incident photon energy $T_{\gamma }$ and the corresponding s-channel energy $W=\sqrt{s}$, respectively, in GeV. The data are from Ref. 11.

Figure 3

(Color online) Differential cross sections and the dynamical content of the present model corresponding to the fit result of Table . The dash-dotted curves correspond to the mesonic current contribution; the dashed curves to the $S_{11}$ resonance current and the dotted curves to the $P_{11}$ resonance. The dot-double-dashed curves correspond to the $P_{13}$ resonance current, whereas the dash-double-dotted curves show the $D_{13}$ resonance contribution. The solid curves correspond to the total current. The nucleonic current contribution (long-dashed curves) is very small and cannot be seen on the present scale.

Figure 4

(Color online) Same as in Fig. 3 for the fit result of Table . The nucleonic current contribution (long-dashed curves) is very small and cannot be seen on the present scale.

Figure 5

(Color online) Same as in Fig. 3 for the fit result of Table .

Figure 6

(Color online) Same as in Fig. 3 for the fit result of Table . The nucleonic current contribution (long-dashed curves) is negligible and cannot be seen on the present scale.

Figure 7

(Color online) Same as in Fig. 3 for the fit result of Table .

Figure 8

(Color online) Total cross section for $\gamma p\to p{\eta }^{\prime }$ as a function of the total energy of the system, $W=\sqrt{s}$. The panels from top to bottom correspond to the fit results of Tables , as indicated. The overall total cross sections (solid lines) are broken down according to their dynamical contributions, with line styles defined in Fig. 3. The two dashed vertical lines are placed to guide the eye through the two bump positions in all panels.

Figure 9

(Color online) Fit result with no resonances. $g_{\mathit{NN}{\eta }^{\prime }}=2.10$ and ${\Lambda }_v=1264$ MeV. See the legend to Fig. 3.

Figure 10

(Color online) Photon beam and target nucleon asymmetries ${\Sigma }_B$ (top panel) and ${\Sigma }_T$ (bottom), respectively, for $\gamma p\to p{\eta }^{\prime }$ as a function of the ${\eta }^{\prime }$ emission angle ${\theta }_{{\eta }^{\prime }}$ in the center-of-momentum system. See the legend to Fig. 2 for the meaning of the different curves.