Induced polarization of $\Lambda \left(1116\right)$ in kaon electroproduction

We have measured. the induced polarization of the $\Lambda$(1116) in the reaction $ep\to e^{\prime }{K}^{+}\Lambda$, detecting the scattered $e^{\prime }$ and $K^{+}$ in the final state along with the proton from the decay $\Lambda \to p{\pi }^{-}$. The present study used the CEBAF Large Acceptance Spectrometer (CLAS), which allowed for a large kinematic acceptance in invariant energy $W$ ($1.6\le W\le 2.7$ GeV) and covered the full range of the kaon production angle at an average momentum transfer $Q^2=1.90{\text{GeV}}^2$. In this experiment a 5.50-GeV electron beam was incident upon an unpolarized liquid-hydrogen target. We have mapped out the $W$ and kaon production angle dependencies of the induced polarization and found striking differences from photoproduction data over most of the kinematic range studied. However, we also found that the induced polarization is essentially $Q^2$ independent in our kinematic domain, suggesting that somewhere below the $Q^2$ covered here there must be a strong $Q^2$ dependence. Along with previously published photo- and electroproduction cross sections and polarization observables, these data are needed for the development of models, such as effective field theories, and as input to coupled-channel analyses that can provide evidence of previously unobserved $s$-channel resonances.

Figure 1

Kinematics for $K^{+}\Lambda$ electroproduction showing the angles and polarization axes in the c.m. reference frame.

Figure 2

Three-dimensional cut-away view of CLAS showing the drift chambers (R1, R2, and R3), Cherenkov counters (CC), time-of-flight system (TOF), and Electromagnetic calorimeters (EC). In this view, the beam enters the picture from the upper left corner and travels down the center of the detector. The detector is roughly 10 m in diameter.

Figure 3

Minimum $\Delta t$ (ns) vs $p$ (GeV) distributions for identified kaons (left) and protons (right). Plots (a) and (b) show the distributions without any cuts. Plots (c) and (d) show the same distributions for kaons and protons after applying the $\Lambda$ missing-mass and the $\pi$ missing-mass-squared cuts shown in Fig. 4.

Figure 4

(a) Reconstructed missing mass squared $M{M}^2\left(e^{\prime }{K}^{+}p\right) \left({\mathrm{GeV}}^2\right)$ vs baryon missing mass $MM\left(e^{\prime }{K}^{+}\right)$ (GeV). (b) Missing mass squared distribution $M{M}^2\left(e^{\prime }{K}^{+}p\right) \left({\mathrm{GeV}}^2\right)$. The red lines show the applied cut, which includes events with only a missing pion ($\Lambda$ events) and events with a missing pion plus a photon (${\Sigma }^0$ events). Negative values are due to finite resolution effects. (c) Hyperon missing mass $MM\left(e^{\prime }{K}^{+}\right)$ distribution after applying the $\pi$ missing-mass-squared cut. The red lines in this plot show the missing mass range over which the background-subtracted yields are integrated for the final $\Lambda$ sample selection. All plots require a detected proton.

Figure 5

Distribution of $K^{+}\Lambda$ events in $Q^2$ and $W$. The ${\mathcal{P}}_N^0$ values are measured for $W$ up to 2.7 GeV only and summed over the full $Q^2$ range.

Figure 6

Typical fits to the reconstructed hyperon mass spectra for different $W$ bins summed over $Q^2$ using Eq. (17). Panels (a)–(d) correspond to $cos{\theta }_K^{\mathrm{c}.\mathrm{m}.}=0.5$, 0.9, 0.1, and 0.9, respectively. The green curves correspond to the $\Lambda$ peak, the red curves to ${\Sigma }^0$ peak, the magenta curves to the hadron-misidentification background, and the blue curves to the total fit function.

Figure 7

Dependence of the acceptance factors on $W$ for forward-going (blue crosses) and backward-going (red circles) protons at $0.8<cos{\theta }_K^{\mathrm{c}.\mathrm{m}.}<1$ with respect to the $\widehat{t},\widehat{n}$, and $\widehat{l}$ polarization axes.

Figure 8

$W$ averaged ${\mathcal{P}}_L^0$ (blue circles) and ${\mathcal{P}}_T^0$ (red squares) values vs $cos{\theta }_K^{\mathrm{c}.\mathrm{m}.}$ summed over $Q^2$. The dashed lines represent the lowest total point-to-point systematic uncertainty from Table 3.

Figure 9

Induced $\Lambda$ polarization ${\mathcal{P}}_N^0$ vs $Q^2$ for different $cos{\theta }_K^{\mathrm{c}.\mathrm{m}.}$ and $W$ bins. The solid red lines are fits to a constant, and the error bars are statistical only. The results show no significant dependence on $Q^2$ within our statistical uncertainties.

Figure 10

Induced $\Lambda$ polarization ${\mathcal{P}}_N^0$ vs $cos{\theta }_K^{\mathrm{c}.\mathrm{m}.}$ for $W$ from 1.6125 to 1.8875 GeV at an average $Q^2$ of $1.90 {\mathrm{GeV}}^2$. The black circles are the results of this analysis and the blue crosses are the CLAS photoproduction results from Ref. [32]. All data points show statistical uncertainties only. The overlaid curves correspond to RPR-2007 [13] (green long dash), RPR-2011 [14] (red solid), Extended Kaon-Maid [52] (blue dot-dash), and Maxwell [8, 9] (magenta thick solid) model predictions, respectively.

Figure 11

Same as Fig. 10 except for $W$ from 1.9125 to 2.275 GeV.

Figure 12

Same as Fig. 10 except for $W$ from 2.325 to 2.675 GeV.

Figure 13

Induced $\Lambda$ polarization ${\mathcal{P}}_N^0$ vs $W$ for our seven $cos{\theta }_K^{\mathrm{c}.\mathrm{m}.}$ bins at an average $Q^2$ of $1.90 {\mathrm{GeV}}^2$. The symbols and curves are the same as Fig. 10 with additional curves RPR-2011NoRes (red short dash) and RPR-2011NoL (red dots) [51].