Nucleon resonances with spin $3/2$ and $5/2$ in the isobar model for kaon photoproduction

We compare two different propagator and vertex factor formulations of spin-$3/2$ and $-5/2$ nucleon resonances by using isobar models for kaon photoproduction on the proton $\gamma +p\to K^{+}+\mathrm{\Lambda }$. All nucleon resonances listed in the Particle Data Group listing with spin up to $5/2$ and with at least a two-star rating are included in the model. The unknown coupling constants are extracted from fitting to around 7400 data points. It is found that the gauge-invariant formulation of the spin-$3/2$ and $-5/2$ interactions leads to a better agreement with experimental data. An extensive comparison of model calculation with experimental data and comparison with the previous analyses are presented. A short discussion on the cross section near the production threshold is also provided.

Figure 1

Kinematics of the kaon electroproduction process $e+p\to e^{\prime }+K^{+}+\mathrm{\Lambda }$. The process can be also considered as a virtual kaon photoproduction, i.e., kaon photoproduction by the virtual photon ${\gamma }_{\mathrm{v}}$.

Figure 2

Feynman diagrams for the elementary operator of the kaon electroproduction process $e+p\to e^{\prime }+K^{+}+\mathrm{\Lambda }$. The intermediate states in these diagrams are (a) the $s$-channel proton and nucleon resonances; (b) the $u$-channel $\mathrm{\Lambda }$, ${\mathrm{\Sigma }}^0$, and hyperon resonances; and (c) the $t$-channel kaon and kaon resonances.

Figure 3

Calculated total cross sections obtained from Kaon–Maid [3], models A, B, C, and D, compared with the experimental data from the CLAS Collaboration [41]. Note that the experimental data shown in this figure are not included in the fitting database.

Figure 4

Differential cross sections for the $\gamma +p\to K^{+}+\mathrm{\Lambda }$ channel as a function of the total c.m. energy $W$ for different values of the kaon c.m. angle. Experimental data are from the CLAS Collaboration (solid squares [41] and open squares [42]), LEPS Collaboration (solid triangles [43]), and Crystal Ball Collaboration (open circles [45]). Notation of the curves is as in Fig. 3.

Figure 5

As in Fig. 4, but for the angular distribution of differential cross section with different values of the total c.m. energy $W$.

Figure 6

$\mathrm{\Lambda }$ recoil polarization as a function of the total c.m. energy $W$ for different values of the kaon c.m. angle. Notation of the curves and experimental data is as in Fig. 4.

Figure 7

As in Fig. 6, but for the angular distribution of the $\mathrm{\Lambda }$ recoil polarization with different values of the total c.m. energy $W$.

Figure 8

Target asymmetry as functions of the total c.m. energy and kaon angles. Notation of the curves is as in Fig. 3. Experimental data are from the GRAAL Collaboration [46].

Figure 9

Photon asymmetry as functions of the total c.m. energy and kaon angles. Notation of the curves is as in Fig. 3. Experimental data are from the LEPS [43] (open circles) and GRAAL [46] (closed circles) collaborations.

Figure 10

As in Fig. 9, but for the beam-recoil double polarization observable $C_x$. Experimental data are from the CLAS Collaboration [47].

Figure 11

As in Fig. 9, but for the beam-recoil double polarization observable $C_z$. Experimental data are from the CLAS Collaboration [47].

Figure 12

As in Fig. 9, but for the beam-recoil double polarization observable $O_x$. Experimental data are from the GRAAL Collaboration [48].

Figure 13

As in Fig. 12, but for the beam-recoil double polarization observable $O_z$. Experimental data are from the GRAAL Collaboration [48].

Figure 14

Total cross section as in Fig. 3, but limited to the threshold region. The multipoles model is taken from Ref. [30], whereas the result of chiral perturbation theory ($\chi \mathrm{PT}$) is obtained from Ref. [55]. The solid inverted triangles display the SAPHIR data [49]. All data shown in this figure were not included in our fitting database.

Figure 15

As in Fig. 4, but limited to the threshold region. The solid inverted triangles display the SAPHIR data [49], which were not used in the fitting process.

Figure 16

As in Fig. 5, but limited to the threshold region. The solid inverted triangles display the SAPHIR data [49], which were not used in the fitting process.

Figure 17

The Breit–Wigner resonance masses obtained in the present work compared with those obtained by the Giessen model (Shklyar et al. [58]), the Bonn–Gatchina model (Anisovich et al. [59]), as well as those estimated by the PDG [7].

Figure 18

As in Fig. 17, but for the extracted nucleon resonance widths.

Figure 19

Comparison between differential cross sections obtained from the best model of the present work (Model D, solid lines), the Bonn–Gatchina partial wave analysis (dash-dotted lines) [59], and the ANL-Osaka dynamical coupled-channel analysis (dashed lines) [1]. Notation for experimental data is as in Fig. 4.

Figure 20

As in Fig. 19, but for the recoiled $\mathrm{\Lambda }$ polarization.

Figure 21

As in Fig. 19, but for the photon asymmetry.

Figure 22

As in Fig. 19, but for the target asymmetry.

Figure 23

As in Fig. 19, but for the photon-recoil double polarization $C_x$ and $C_z$.

Figure 24

As in Fig. 19, but for the photon-recoil double polarization $O_x$ and $O_z$.

Figure 25

Angular distribution of the CGLN amplitudes for different values of the total c.m. energy $W$. Solid lines indicate the result obtained from the present analysis, whereas the dashed and the dash-dotted lines are obtained from the Bonn–Gatchina and Kaon–Maid models, respectively.

Figure 26

Electric and magnetic multipoles of the nucleon resonances used in the present analysis. Notation of the curves is as in Fig. 25.