Differential photoproduction cross sections of the ${\Sigma }^0\left(1385\right)$, $\Lambda \left(1405\right)$, and $\Lambda \left(1520\right)$

We report the exclusive photoproduction cross sections for the ${\Sigma }^0\left(1385\right)$, $\Lambda \left(1405\right)$, and $\Lambda \left(1520\right)$ in the reactions $\gamma +p\to K^{+}+Y^{*}$ using the CLAS detector for energies from near the respective production thresholds up to a center-of-mass energy $W$ of $2.85$ GeV. The differential cross sections are integrated to give the total exclusive cross sections for each hyperon. Comparisons are made to current theoretical models based on the effective-Lagrangian approach and fit to previous data. The accuracy of these models is seen to vary widely. The cross sections for the $\Lambda \left(1405\right)$ region are strikingly different for the ${\Sigma }^{+}{\pi }^{-}$, ${\Sigma }^0{\pi }^0$, and ${\Sigma }^{-}{\pi }^{+}$ decay channels, indicating the effect of isospin interference, especially at $W$ values close to the threshold.

Figure 1

Sample fit results of the strong final state of $K^{+}\Lambda {\pi }^0$. The events are plotted versus the missing mass off the $K^{+}$, which is equivalent to the invariant mass of the $\Lambda {\pi }^0$ system. The data are shown by the black crosses, while the ${\Sigma }^0\left(1385\right)$ signal MC and the $K^{*+}\Lambda$ background are shown by the red crosses and green circles, respectively. The sum of the MC templates is shown by the solid magenta lines, while the vertical dashed lines show the fit ranges.

Figure 2

Fit result to the strong final state of ${\Sigma }^{+}{\pi }^{-}$ before MC iteration, for $W=2.5$ GeV, $\cos {\theta }_{K^{+}}^{\mathrm{c}.\mathrm{m}.}=0.35$. The data are the black crosses. (a) The initial fit. Each MC template is shown by a different color, as well as the Breit-Wigner function for the $Y^{*}\left(1670\right)$. The sum of the fit is shown in cyan. (b) Same as in panel (a), but after two iterations of the $\Lambda \left(1405\right)$ template to match the data.

Figure 3

Differential cross section for $\gamma p\to K^{+}{\Sigma }^0\left(1385\right)$ for the indicated 100-MeV-wide bins in $W$ (GeV). The CLAS results are the filled blue points, with error bars that show the combined statistical- and signal-channel fit (see Fig. 1) uncertainties. The green hollow points are from LEPS [24]. The solid red lines are the model prediction of Ref. [10].

Figure 4

Differential cross section for $\gamma p\to K^{+}{\Sigma }^0\left(1385\right)$ with possible extrapolations in a single $W$ bin for $2.05\le W\le 2.15$ GeV. Some of the nine curves lie on top of each other. See text for discussion.

Figure 5

Total cross section of the ${\Sigma }^0\left(1385\right)$ as a function of $E_{\gamma }$, showing at each $E_{\gamma }$ the collection of alternative extrapolations of the differential cross sections tested. The lower black points show the summed unextrapolated data. The large red points show the averaged extrapolated values.

Figure 6

Total cross section for $\gamma p\to K^{+}{\Sigma }^0\left(1385\right)$ as a function of photon energy $E_{\gamma }$. The small blue points are the summed contribution from the measured range of angles in CLAS. The large red points are the extrapolated total cross sections using the method discussed in the text. The four dark brown square data points with cross-like error bars are bubble chamber data from Refs. [5, 6, 7]. The solid black curve shows the model of Ref. [10].

Figure 7

Comparison of the two ${\Sigma }^{+}{\pi }^{-}$ channels for the $\Lambda \left(1520\right)$ with $2.45\le W\le 2.55$ GeV. The gray band is the estimated systematic discrepancy between measurements using the two reconstructed final states. Note the logarithmic vertical scale.

Figure 8

Comparison of the three $\Sigma \pi$ decay modes for the $\Lambda \left(1520\right)$ in two energy bins at 8 $2.05\le W\le 2.15$ GeV and 8 $2.45\le W\le 2.55$ GeV as a function of center-of-mass kaon angle. For clarity, the data have been shifted slightly to prevent overlaps.

Figure 9

Differential cross section for $\gamma p\to K^{+}\Lambda \left(1520\right)$ with fit results to a single $W$ bin for $2.75\le W\le 2.85$ GeV. The various curves represent possible extrapolations to obtain the total cross section. Some of the nine curves lie on top of each other.

Figure 10

Differential cross section for $\gamma p\to K^{+}\Lambda \left(1520\right)$ for nine bins in center-of-mass energy $W$ (GeV). The solid blue circular points are the CLAS results. The lowest $W$ bin is 30 MeV wide, while the others are all 100 MeV wide. The lowest $W$ bin has a 36% systematic uncertainty in addition to the global 11.6% systematic uncertainty (Table 1) of the other bins. LEPS results are shown by the various colored hollow square points [13]. The hollow circular points show separate LEPS results [14]; in the lowest $W$ bin they are for $W=2.01$ GeV (red), $2.03$ GeV (blue), and $2.05$ GeV (green). The black dashed curve is the model calculation by He et al. [19], while the red solid curve is the model calculation by Nam et al. [16].

Figure 11

Total cross section of $\Lambda \left(1520\right)$ as a function of $E_{\gamma }$. The small blue points are the CLAS data summed over the acceptance of the detector, while the larger solid red points show the extrapolation over all space. The error bars are the combined statistical and extrapolation uncertainties. The dashed black curve is a calculation by He et al. [19] and the solid red curve is a calculation by Nam et al. [16]. The green hollow squares are measurements by SAPHIR [20], and the green hollow circles are measurements from LAMP2 [12].

Figure 12

Comparison of the two ${\Sigma }^{+}$ decay modes for the $\Lambda \left(1405\right)$ with $2.45\le W\le 2.55$ GeV. The gray band is the estimated systematic discrepancy between measurements using the two reconstructed final states. The points have been shifted for visual clarity.

Figure 13

Differential cross sections for $\gamma p\to K^{+}{Y}^{*}$ in the $\Lambda \left(1405\right)$ mass region from threshold to $1.5$ $\mathrm{GeV}/c^2$ for each of the three $\Sigma \pi$ charge states. The ranges of center-of-mass energies $W$ (GeV) are indicated. The ${\Sigma }^{+}{\pi }^{-}$ channel is shown as red circles and solid lines, the ${\Sigma }^0{\pi }^0$ channel is shown as blue squares and a dashed line, and the ${\Sigma }^{-}{\pi }^{+}$ channel is shown as green triangles and a dot-dashed line. The curves are simply spline fits to guide the eye.

Figure 14

Differential cross sections for $\gamma p\to K^{+}{Y}^{*}$ in the $\Lambda \left(1405\right)$ mass region for each of the three $\Sigma \pi$ charge states. The ranges of center-of-mass energies $W$ (GeV) are indicated. Same as previous figure, but on a linear vertical scale to emphasize the differences in lower $W$.

Figure 15

Differential cross sections for $\gamma p\to K^{+}{Y}^{*}$ for the $\Lambda \left(1405\right)$ mass region in the indicated 100-MeV-wide bins in $W$ (GeV). The CLAS data (solid blue points) have been summed over the three $\Sigma \pi$ decay modes. The error bars combine statistical and systematic fitting uncertainties. The forward-most datum in the lowest $W$ bin used an estimated value for the ${\Sigma }^0{\pi }^0$ cross section. The green hollow circle points are from Ref. [24]. The red curves are from Ref. [39], based on the model of Ref. [27] discussed in the text, while the flat dashed magenta line in the $W=2.0$ GeV panel is the prediction from Ref. [28].

Figure 16

Total cross section of $\Lambda \left(1405\right)$ mass region versus $E_{\gamma }$. The small blue points show the summed measured data from the CLAS detector, while the large red points show the extrapolation to all angles. The error bars are combined statistical and fitting uncertainties. The vertical dashed line shows the reaction threshold. The black curves are a calculation by Nam et al. based on Ref. [27], with the variable $g_{K^{*}N{\Lambda }^{*}}$ set to 0 (solid), $+3.18$ (dotted), or $-3.18$ (dashed).

Figure 17

Comparison of differential cross sections of the ${\Sigma }^0\left(1385\right)$ (black circles), $\Lambda \left(1405\right)$ (blue triangles), and $\Lambda \left(1520\right)$ (red squares) as a function of kaon production angle $\cos {\theta }_{K^{+}}^{\mathrm{c}.\mathrm{m}.}$ for each 100 MeV wide bin in energy $W$ (GeV). For the $\Lambda \left(1520\right)$ the threshold bin has $2.02\le W\le 2.05$ GeV.

Figure 18

Comparison of total cross sections for the ${\Sigma }^0\left(1385\right)$ (black circles, solid line), $\Lambda \left(1405\right)$ (blue triangles, dashed line), and $\Lambda \left(1520\right)$ (red squares, dot-dashed line) vs $E_{\gamma }$. The points for the $\Lambda \left(1405\right)$ and $\Lambda \left(1520\right)$ have been offset by 20 MeV for visual clarity. The open green circles and open magenta squares are the ground state $\Lambda$ and ${\Sigma }^0$ total cross sections, respectively, from Ref. [34].