Nucleon resonances in $\gamma p\to K^{*+}\mathrm{\Lambda }$

The high-precision cross section data for the reaction $\gamma p\to K^{*+}\mathrm{\Lambda }$ reported by the CLAS Collaboration at the Thomas Jefferson National Accelerator Facility have been analyzed based on an effective Lagrangian approach in the tree-level approximation. Apart from the $t$-channel $K,\kappa ,K^{*}$ exchanges, the $s$-channel nucleon ($N$) exchange, the $u$-channel $\mathrm{\Lambda },\mathrm{\Sigma },{\mathrm{\Sigma }}^{*}\left(1385\right)$ exchanges, and the generalized contact term, the contributions from the near-threshold nucleon resonances in the $s$ channel are also taken into account in constructing the reaction amplitude. It is found that to achieve a satisfactory description of the differential cross section data, at least two nucleon resonances should be included. By including the $N\left(2060\right){5/2}^{-}$ resonance, which is responsible for the shape of the angular distribution near the $K^{*}\mathrm{\Lambda }$ threshold, and one of the $N\left(2000\right){5/2}^{+}, N\left(2040\right){3/2}^{+},N\left(2100\right){1/2}^{+},N\left(2120\right){3/2}^{-}$ and $N\left(2190\right){7/2}^{-}$ resonances, one can describe the cross section data quite well, with the fitted resonance masses and widths compatible with those advocated by the Particle Data Group. The resulted predictions of the beam, target, and recoil asymmetries are found to be quite different from various fits, indicating the necessity of the spin observable data for $\gamma p\to K^{*+}\mathrm{\Lambda }$ to further pin down the resonance contents and associated parameters in this reaction.

Figure 1

Status of theoretical description of the differential cross sections for $\gamma p\to K^{*+}\mathrm{\Lambda }$ at selected energies in the near-threshold region. The numbers in parentheses denote the photon laboratory incident energy (left number) and the total center-of-mass energy of the system (right number). The blue dashed lines represent the results from Ref. [18], and the black solid lines denote the results from model I of our present work, which will be discussed later. The scattered symbols are the most recent data from CLAS Collaboration [9].

Figure 2

Generic structure of the $K^{*}$ photoproduction amplitude for $\gamma N\to K^{*}\mathrm{\Lambda }$. Time proceeds from left to right.

Figure 3

Differential cross sections for $\gamma p\to K^{*+}\mathrm{\Lambda }$ as a function of $cos\theta$ in the center-of-mass frame in the near threshold region. The black solid lines correspond to the fit result including the $N\left(2000\right)5/2^{+}$ and $N\left(2040\right)3/2^{+}$ resonances with ${\chi }^2/N=2.50$. The blue dashed lines represent the results from model V with ${\chi }^2/N=2.18$. The scattered symbols are the most recent data from CLAS Collaboration [9]. The numbers in parentheses denote the photon laboratory incident energy (left number) and the total center-of-mass energy of the system (right number), in MeV.

Figure 4

Differential cross sections for $\gamma p\to K^{*+}\mathrm{\Lambda }$ as a function of $cos\theta$ in the center-of-mass from models I (black solid lines), II (green dash-double-dotted lines), III (black solid lines), IV (red dash-dotted lines), and V (cyan dotted lines). The scattered symbols denote the CLAS data [9]. The photon incident energy binning is 100 MeV. The numbers in parentheses denote the centroid value of the photon laboratory incident energy (left number) and the corresponding total center-of-mass energy of the system (right number), in MeV.

Figure 5

Differential cross sections for $\gamma p\to K^{*+}\mathrm{\Lambda }$ as a function of $cos\theta$ in the center of mass from model I (black solid lines). The scattered symbols denote the CLAS data [9]. The blue dashed, green dash-double-dotted, and magenta dash-dotted lines represent the individual contributions from $K,N\left(2060\right){5/2}^{-}$, and $N\left(2000\right){5/2}^{+}$ exchanges, respectively. The photon incident energy binning is 100 MeV. The numbers in parentheses denote the centroid value of the photon laboratory incident energy (left number) and the corresponding total center-of-mass energy of the system (right number), in MeV.

Figure 6

Total cross sections with individual (resonance, Born term, $K$) contributions for $\gamma p\to K^{*+}\mathrm{\Lambda }$. The panels from top to bottom correspond to the results of modes I–V, as indicated. The data are from CLAS [9] but not included in the fit.

Figure 7

Same as in Fig. 6 for model I. The blue dash-dotted line corresponds to the results with resonance $N\left(2060\right){5/2}^{-}$ switched off, while the green dashed line to those with $N\left(2000\right){5/2}^{+}$ switched off. The black solid line is the results of model I shown in Fig. 6.

Figure 8

Same as in Fig. 6 for model IV, except that it has been artificially forced to better reproduce the measured differential cross section at $W=2.217$ GeV (red solid line). The black dashed line is the results of model IV shown in Fig. 6.

Figure 9

Photon beam asymmetries as functions of cosine of the $K^{*}$ emission angle $\theta$ in the center-of-mass system at two energies for the $\gamma p\to K^{*+}\mathrm{\Lambda }$ reaction. The numbers in parentheses denote the photon laboratory incident energy (left number) and the total center-of-mass energy of the system (right number), in MeV. The blue double-dash-dotted curve, green dashed curve, black solid curve, cyan dash-dotted curve, and orange dash-double-dotted curve represent the predictions corresponding to the models I–V, respectively.

Figure 10

Same as in Fig. 9 for target nucleon asymmetries.

Figure 11

Same as in Fig. 9 for recoil $\mathrm{\Lambda }$ asymmetries.