Beam-recoil polarization transfer in the nucleon resonance region in the exclusive $\overrightarrow{e}p\to e^{\text{'}}{K}^{+}\overrightarrow{\Lambda }$ and $\overrightarrow{e}p\to e^{\text{'}}{K}^{+}{\overrightarrow{\Sigma }}^0$ reactions at the CLAS spectrometer

Beam-recoil transferred polarizations for the exclusive $\overrightarrow{e}p\to e^{\text{'}}{K}^{+}\overrightarrow{\Lambda },{\overrightarrow{\Sigma }}^0$ reactions have been measured using the Continuous Electron Beam Accelerator Facility's large acceptance spectrometer (CLAS) at the Thomas Jefferson National Accelerator Facility. New measurements have been completed at beam energies of 4.261 and 5.754 GeV that span a range of momentum transfer $Q^2$ from 0.7 to 5.4 ${\mathrm{GeV}}^2$, invariant energy $W$ from 1.6 to 2.6 GeV, and the full center-of-mass angular range of the $K^{+}$ meson. These new data add to the existing CLAS $K^{+}\Lambda$ measurements at 2.567 GeV, and provide the first-ever data for the $K^{+}{\Sigma }^0$ channel in electroproduction. Comparisons of the data with several theoretical models are used to study the sensitivity to $s$-channel resonance contributions and the underlying reaction mechanism. Interpretations within two semiclassical partonic models are made to probe the underlying reaction mechanism and the $s\overline{s}$ quark-pair creation dynamics.

Figure 1

Tree-level diagrams contributing to the $\mathit{KY}$ reactions: (a) $s$-channel exchanges, (b) $t$-channel exchanges, and (c) $u$-channel exchanges.

Figure 2

Kinematics for $\mathit{KY}$ electroproduction defining the c.m. angles and coordinate systems used in the analysis. This figure shows a positive Φ angle.

Figure 3

Calculations of the depolarization factor $D(y)$ at 5.754 GeV using the MB model [42] in representative data sorts (a) summing over all $Q^2$ and $\cos {\theta }_K^{\mathrm{c}.\mathrm{m}.}$ and (b) summing over all $W$ and $\cos {\theta }_K^{\mathrm{c}.\mathrm{m}.}$.

Figure 4

Three-dimensional view of the CLAS detector with the different subsystems labeled. A single sector of the detector has been cut away to enable a view of the inner subsystems. The diameter of the CLAS detector is $~5$ m, and it is $~8$ m long.

Figure 5

Time difference $\delta t$ (ns) between the SC system and the flight time calculated for specific hadron-mass hypotheses plotted against the hadron momentum $P$ (GeV) for (a) ${\pi }^{+}$, (b) $K^{+}$, and (c) $p$ at 5.754 GeV. Each plot shows the timing cuts imposed upon the spectra for the given mass hypothesis.

Figure 6

$e^{\text{'}}{K}^{+}p$ final-state data from runs at 5.754 GeV. (a) Missing mass for $p(e,e^{\text{'}}{K}^{+})X$. (b) Missing mass squared for $p(e,e^{\text{'}}{K}^{+}p)X$. (c) ${\mathrm{MM}}^2(e^{\text{'}}{K}^{+}p)$ vs MM$(e^{\text{'}}{K}^{+})$ showing the cuts used to select the $K^{+}\Lambda$ and $K^{+}{\Sigma }^0$ event samples. (Units in GeV.)

Figure 7

Sample hyperon spectrum fit results using hyperon templates derived from Monte Carlo (Λ: green curve; ${\Sigma }^0$: red curve) and a third-order polynomial for the background (magenta curve). The smoothed templates have been allowed to shift along the mass axis and convoluted with a Gaussian to give the best ${\chi }^2$ per degree of freedom (${\chi }_{\nu }^2$) values for the fits. These distributions at 5.754 GeV are summed over all $W$ and $\cos {\theta }_K^{\mathrm{c}.\mathrm{m}.}$ for central $Q^2$ values as indicated. The blue curve shows the full fit result.

Figure 8

Ratio of the number of background counts to Λ counts in the Λ analysis mass window weighted by the uncertainty in the ratio for each of the kinematic bins in this analysis at 5.754 GeV.

Figure 9

Ratios of the number of counts in the ${\Sigma }^0$ analysis mass window for the data at 5.754 GeV. (a) ${\Sigma }^0/\Lambda$ ratio. (b) Background/${\Sigma }^0$ ratio.

Figure 10

Polarization ${\mathcal{P}}^{\text{'}}$ vs $W$ for the pion misidentification background in the $(x^{\text{'}},y^{\text{'}},z^{\text{'}})$ coordinate system for the data summed over all $Q^2$ and $d{\Omega }_K^{\mathrm{c}.\mathrm{m}.}$.

Figure 11

Distributions of the transferred Λ (a) and ${\Sigma }^0$ (b) polarization components ${\mathcal{P}}_{y^{\text{'}}}^{\text{'}}$ vs $Q^2$ for two of our analysis bins. The error bars represent the statistical uncertainties only.

Figure 12

Transferred Λ polarization components ${\mathcal{P}}^{\text{'}}$ with respect to the $(x^{\text{'}},z^{\text{'}})$ axes vs $\cos {\theta }_K^{\mathrm{c}.\mathrm{m}.}$ for three bin-averaged $W$/$Q^2$ values as indicated for a beam energy of 5.754 GeV. The curves are calculations from the MB isobar model [42] (solid, black), the GLV Regge model [51] (short dash, blue), and the RPR model [52] variant including a $P_{11}(1900)$ state (dot-dash, red) and a $D_{13}(1900)$ state (long dash, black).

Figure 13

Transferred Λ polarization components ${\mathcal{P}}^{\text{'}}$ with respect to the $(x,z)$ axes vs $\cos {\theta }_K^{\mathrm{c}.\mathrm{m}.}$ for three bin-averaged $W$/$Q^2$ values as indicated for a beam energy of 5.754 GeV. The model calculations are as indicated in Fig. 12.

Figure 14

Transferred Λ polarization components ${\mathcal{P}}^{\text{'}}$ with respect to the $(x^{\text{'}},z^{\text{'}})$ axes (upper left panels) and $(x,z)$ axes (upper right panels) vs $W$ (GeV) for $\langle Q^2\rangle =2.54\hspace{0.5em}\mathrm{GeV}{}^2$ for a beam energy of 5.754 GeV. The bin-averaged $\cos {\theta }_K^{\mathrm{c}.\mathrm{m}.}$ values for each $W$ point are shown in the lower plot. A fit to $\langle \cos {\theta }_K^{\mathrm{c}.\mathrm{m}.}\rangle$ is provided by a second-order polynomial in $W$ as indicated on the plot. The model calculations are as indicated in Fig. 12.

Figure 15

Transferred Λ polarization components ${\mathcal{P}}^{\text{'}}$ with respect to the $(x^{\text{'}},z^{\text{'}})$ axes (left panels) and $(x,z)$ axes (right panels) vs $Q^2$ (${\mathrm{GeV}}^2$) for $\langle W\rangle =1.99$ GeV and $\langle \cos {\theta }_K^{\mathrm{c}.\mathrm{m}.}\rangle =0.43$ for a beam energy of 5.754 GeV. The model calculations are as indicated in Fig. 12.

Figure 16

Transferred ${\Sigma }^0$ polarization components ${\mathcal{P}}^{\text{'}}$ with respect to the $(x^{\text{'}},z^{\text{'}})$ (left) and $(x,z)$ (right) axes vs $\cos {\theta }_K^{\mathrm{c}.\mathrm{m}.}$ at $\langle Q^2\rangle =2.5$ ${\mathrm{GeV}}^2$ and $\langle W\rangle =2.1$ GeV for a beam energy of 5.754 GeV. The curves are calculations from the MB isobar model [42] (solid, black), the GLV Regge model [51] (short dash, blue), and the RPR model [52] with a missing $P_{11}(1900)$ state (dot-dash, red) and a missing $D_{13}(1900)$ state (long dash, black).

Figure 17

Transferred ${\Sigma }^0$ polarization components ${\mathcal{P}}^{\text{'}}$ with respect to the $(x^{\text{'}},z^{\text{'}})$ (left) and $(x,z)$ (right) axes vs $W$ (GeV) at $\langle Q^2\rangle =2.5\hspace{0.5em}\mathrm{GeV}{}^2$ for a beam energy of 5.754 GeV. The bin-averaged $\cos {\theta }_K^{\mathrm{c}.\mathrm{m}.}$ value for each $W$ point is represented by a second-order polynomial in $W$. The model calculations are as indicated in Fig. 16.

Figure 18

Transferred ${\Sigma }^0$ polarization components ${\mathcal{P}}^{\text{'}}$ with respect to the $(x^{\text{'}},z^{\text{'}})$ (left) and $(x,z)$ (right) axes vs $Q^2$ (${\mathrm{GeV}}^2$) at $\langle W\rangle =2.09\hspace{0.5em}\mathrm{GeV}$ and $\langle \cos {\theta }_K^{\mathrm{c}.\mathrm{m}.}\rangle =0.36$ at a beam energy at 5.754 GeV. The model calculations are as indicated in Fig. 16.

Figure 19

Transferred Λ polarization components ${\mathcal{P}}^{\text{'}}$ with respect to the $(z^{\text{'}},z)$ axes vs $\cos {\theta }_K^{\mathrm{c}.\mathrm{m}.}$ for three bin-averaged $W$/$Q^2$ values as indicated for a beam energy of 4.261 GeV.

Figure 20

$R_{\mathrm{sum}}$ [defined in Eq. (34)] vs $\cos {\theta }_K^{\mathrm{c}.\mathrm{m}.}$ for the 4.261 and 5.754 GeV data along with our fits (heavy solid lines) and the error band resulting from the fit uncertainties (light solid lines). The dashed red line in the upper right panel indicates the result of removing the $x=1$ constraint in the fit.

Figure 21

Ratio of longitudinal to transverse structure functions at ${\theta }_K^{\mathrm{c}.\mathrm{m}.}=0^{°}$ vs. $Q^2$. The blue cross data points (about $Q^2=1.5\hspace{0.5em}{\mathrm{GeV}}^2$) are for $4.261\hspace{0.5em}\mathrm{GeV}$ and the red cross points (about $Q^2=2.5\hspace{0.5em}{\mathrm{GeV}}^2$) are for 5.754 GeV. The inner error bars on our points represent the statistical uncertainties arising from the fit and the outer error bars represent the combination of statistical and estimated systematic uncertainties. Data are from Mohring et al. [24] (solid circles), Bebek et al. [37] (solid squares), and Raue and Carman [23] (diamonds). All of the filled points are near a common value of $W\hspace{0.5em}\approx \hspace{0.5em}1.84$ GeV.

Figure 22

(a) A model of the reaction where a circularly polarized virtual photon strikes an oppositely polarized $u$ quark inside the proton. The spin of this quark flips, and the quark recoils from its neighbors. An $s\overline{s}$ quark pair is created from a $J^{\pi }=0^{-}$ two-gluon exchange (in lowest order) to produce the final-state $K^{+}$ and Λ hyperon. (b) A model of the reaction where an $s\overline{s}$ quark pair is produced from a circularly polarized real photon that hadronizes such that the $s$ quark in the Λ retains its full polarization after being “precessed” by a spin-orbit interaction, while the $\overline{s}$ quark ends up in the spinless kaon. In both pictures, the shaded band represents a spinless $u\text{−}d$ diquark system.