Electromagnetic production of $K\Sigma$ on the nucleon near threshold

Photo- and electroproduction of $K\Sigma$ have been investigated near their production thresholds by using an effective Lagrangian approach. For this purpose, the background amplitude is constructed from suitable Feynman diagrams, whereas the resonance terms are calculated by means of the Breit–Wigner form of multipoles. Experimental data available in the proton channels $(K^{+}{\Sigma }^0$ and $K^0{\Sigma }^{+})$ with energies up to 50 MeV above the thresholds have been utilized to extract the unknown parameters. In these proton channels the calculated observables fit nicely to the experimental data, whereas in the neutron channels $(K^{+}{\Sigma }^{-}$ and $K^0{\Sigma }^0)$ the predicted observables contain some uncertainties due to the the uncertainties in the values of helicity photon couplings. To this end, new $K^0{\Sigma }^{+}$ photoproduction data are urgently required. The present analysis indicates the validity of the $P_{\Lambda }=-\frac{1}{3}{P}_{\Sigma }$ relation derived a long time ago. In the electroproduction sector the present analysis confirms the smooth transition between photoproduction and low $Q^2$ electroproduction data. The effect of new Crystal Ball data is shown to be mild at the backward angles. It is also found that the electroproductions of $K^0{\Sigma }^{+}$ and $K^0{\Sigma }^0$ are practically not the suitable reactions for investigating the $K^0$ charge form factor, since the effect is small.

Figure 1

Hadronic and electromagnetic coupling constants in the hyperon resonance intermediate state of $K\Sigma$ photoproductions. Whereas the hadronic coupling constants are related through Eq. (1), the electromagnetic coupling constants of the charged $\Sigma$ production is different from that of the neutral $\Sigma$ production.

Figure 2

Contribution of the background, $N\left(1710\right)P_{11},N\left(1720\right)P_{13},N\left(1700\right)D_{13}$, and $\Delta \left(1700\right)D_{33}$ resonance amplitudes to the total cross section of the $\gamma +N\to K\Sigma$ processes in four isospin channels.

Figure 3

Total cross section obtained in the present work (solid lines) compared with the results of Kaon-Maid [13] (dashed-dotted lines) and chiral perturbation theory (CHPT) [11] (dashed lines) as well as the available experimental data from the SAPHIR collaboration (open circles [41] and solid triangle [51]), and the CLAS collaboration (solid squares [42]). In the case of the $K^0{\Sigma }^0$ and $K^{+}{\Sigma }^{-}$ channels (right panels), the uncertainties of the present calculations, due to the uncertainties in the helicity photon couplings of the resonances given in Table 2, are indicated by the shaded green areas. If these uncertainties are excluded, the result is shown by the solid lines. Note that both the present work and Kaon-Maid do not include the total-cross-section data shown in this figure in the fitting database. The CHPT uses the leading coupling constants predicted by SU(3) as the input for calculating this cross section.

Figure 4

Comparison between angular distributions of the $\gamma +p\to K^{+}+{\Sigma }^0$ differential cross section obtained from the present and Kaon-Maid [13] models with experimental data from the SAPHIR (open circles [41]), CLAS (solid squares [43], solid circles [42], and solid triangles [49]), and Crystal Ball (open squares [58]) collaborations. The corresponding total c.m. energy $W$ (in GeV) is shown in each panel. Except for the new Crystal Ball data, all experimental data displayed in this figure were used in the fit to obtain the solid line.

Figure 5

Angular distribution of the $\gamma +p\to K^0+{\Sigma }^{+}$ differential cross sections. Notation of the curves is as in Fig. 4. Experimental data at $W=1720$ MeV are from the SAPHIR Collaboration [51].

Figure 6

Variation in the differential cross section of the $\gamma +p\to K^0+{\Sigma }^{+}$ process as a result of 20% variation of the $r_{K_{1}K\gamma }$ values. Note that the variation is indicated by the green shaded area. Solid lines indicate the cross section calculated without this variation. Experimental data are the same as in Fig. 5.

Figure 7

As in Fig. 5 but for the $\gamma +n\to K^{+}+{\Sigma }^{-}$ channel. The shaded areas display the uncertainties of the present calculations due to the uncertainties in the helicity photon couplings as in Fig. 3.

Figure 8

As in Fig. 7 but for the $\gamma +n\to K^0+{\Sigma }^0$ channel.

Figure 9

Recoil polarization in the $\gamma +p\to K^{+}+{\Sigma }^0$ process as a function of kaon scattering angle. Solid squares display the new CLAS data [43], whereas open circles exhibit the SAPHIR data [41]. Notation of the curves is as in Fig. 4. The inset shows a comparison between the previous calculation with Kaon-Maid and experimental data for the $\gamma +p\to K^{+}+\vec{\Lambda }$ process [9].

Figure 10

Differential cross section for the $\gamma p\to K^{+}{\Sigma }^0$ channel. Solid and dashed curves are obtained from the calculations with excluding and including the new Crystal Ball data [58] in the database of the present analysis, respectively. Dash-dotted curves represent the predictions of Kaon-Maid [13]. Experimental data are from the SAPHIR (open circles [41]), CLAS (solid squares [43], solid circles [42]), and Crystal Ball (open squares [58]) collaborations. The corresponding value of $cos\theta$ is given in each panel.

Figure 11

$Q^2$ dependence of the resonance multipoles for the nucleon resonances used in the present analysis.

Figure 12

Separated differential cross sections for kaon electroproduction $e+p\to e^{\prime }+K^{+}+{\Sigma }^0$ as a function of kaon scattering angles at $W=1.725$ GeV and for two different values of $Q^2$ (the values are shown in the top panels). Experimental data are from the CLAS collaboration [50]. Notation of the curves is as in Fig. 4. Note that ${\sigma }_i\equiv d{\sigma }_i/d\Omega$, where $i=\mathrm{U},\mathrm{TT}$, and LT. Predictions of Kaon-Maid in the top and bottom panels have been renormalized by a factor of $\frac{1}{10}$ in order to fit on the scale.

Figure 13

As in Fig. 12, but for separated transverse (T) and longitudinal (L) differential cross sections at $W=1.75$ GeV and $Q^2=1.0$ ${\mathrm{GeV}}^2$. Note that all experimental data shown in this Figure [50] are not used in the fit. Solid and open circles indicate two different methods of the ${\sigma }_{\mathrm{L}}\text{−}{\sigma }_{\mathrm{T}}$ separation, which are slightly shifted for the sake of visibility. Further explanation of the data can be found in Ref. [50] as well as in the JLab Experiment CLAS Database [67]. In the lower panel, the prediction of Kaon-Maid has been renormalized by a factor of $\frac{1}{3}$ to fit on the scale.

Figure 14

Comparison between new electroproduction data at $W=1.75$ GeV and $Q^2=0.036$ ${\mathrm{GeV}}^2$ from MAMI [63] with photoproduction data from the SAPHIR [41], CLAS [42], and Crystal Ball [58] collaborations, along with the prediction of the present work (solid line) and Kaon-Maid (dash-dotted line). The prediction of Kaon-Maid has been renormalized by a factor of $\frac{1}{2}$ to fit on the scale. Note that all data shown in this figure are not used in the fitting process since the corresponding energies are higher than the upper energy limit. Furthermore, the predicted differential cross sections are calculated for the electroproduction case $(Q^2=0.036$ ${\mathrm{GeV}}^2)$.

Figure 15

As in Fig. 14 but for the virtual photon momentum transfer squared $Q^2$ distribution calculated with $W=1.75$ GeV, $cos\theta =0.35,\epsilon =0.4$, and $\Phi =0^{\circ }$. See Sec. VI of Ref. [9] for a detailed explanation of the electroproduction parameters. The inset shows a comparison between Kaon-Maid and the result of the present work for higher $Q^2$ values.

Figure 16

Longitudinal differential cross section of (a) the neutral kaon electroproduction $e+p\to e^{\prime }+K^0+{\Sigma }^{+}$ and (b) $e+n\to e^{\prime }+K^0+{\Sigma }^0$, as a function of the virtual photon momentum squared $Q^2$ at $W=1.72$ GeV and for the kaon scattering angle $87.{13}^{\circ }$. Solid lines show the calculation with a $K^0$ form factor obtained in the LCQ model [73] while dashed lines are obtained by using the QMV model [74, 75]. The dash-dotted lines are obtained from a computation with the $K^0$ pole excluded.