Recoil polarization observables in the electroproduction of $K$ mesons and $\Lambda$'s from the proton

A model developed previously to investigate the electromagnetic production of strangeness from the proton is used to investigate single and double recoil polarization observables in the reaction $ep\to e^{\prime }{K}^{+}\Lambda$ in the relativistic impulse approximation. The formalism is based on a tree-level, effective Lagrangian model, which incorporates a variety of baryon resonances with spins up to $\frac{5}{2}$ and the two kaon resonances, $K^{☆}\left(892\right)$ and $K1\left(1270\right)$. The parameters of the model were fit to a large pool of photoproduction data from the CLAS, GRAAL, SAPHIR, and LEPS collaborations and to CLAS data for the virtual photoproduction structure functions ${\sigma }_U,{\sigma }_T,{\sigma }_L,{\sigma }_{TT},{\sigma }_{LT}$, and ${\sigma }_{L{T}^{\prime }}$. Using two different versions of this model, results are presented for three recoil polarization asymmetries that have been measured recently at CLAS. A new fit is then presented which incorporates the new polarization data in the fitted data set. Results obtained with this new fit are presented for six recoil polarization asymmetries and compared with results from one of the previous fits.

Figure 1

Contributions to the amplitude for the reaction $\gamma p\to K^{+}\Lambda$ in the (a) $s$ channel, (b) $u$ channel, and (c) $t$ channel.

Figure 2

$P_y^0$ vs $W$ for $E_{\mathrm{Lab}}=5.499\mathrm{GeV}$, and (a) $cos{\theta }_K=-0.725$, (b) $cos{\theta }_K=-0.217$, (c) $cos{\theta }_K=0.106$, (d) $cos{\theta }_K=0.305$, (e) $cos{\theta }_K=0.706$, (f) $cos{\theta }_K=0.910$. In each panel, the solid, dot-dashed, and dotted curves were obtained as explained in the text. All curves have been averaged over the angle $\varphi$ and were obtained using the fit B described in the text. Data are from Ref. [2].

Figure 3

$P_y^0$ vs $W$ for $E_{\mathrm{Lab}}=5.499\mathrm{GeV},-q^2=1.90$ ${\mathrm{GeV}}^2$, and (a) $cos{\theta }_K=-0.725$, (b) $cos{\theta }_K=-0.217$, (c) $cos{\theta }_K=0.106$, (d) $cos{\theta }_K=0.305$, (e) $cos{\theta }_K=0.706$, (f) $cos{\theta }_K=0.910$. In each panel, the solid curve has been averaged over the angle $\varphi$, while the dash-dotted curve was obtained with $\varphi ={30}^{\circ }$. Both curves were obtained with the fit B described in the text. Data are from Ref. [2].

Figure 4

$P_y^0$ vs $W$ for $E_{\mathrm{Lab}}=5.499\mathrm{GeV},-q^2=1.90{\mathrm{GeV}}^2$, and (a) $cos{\theta }_K=-0.725$, (b) $cos{\theta }_K=-0.217$, (c) $cos{\theta }_K=0.106$, (d) $cos{\theta }_K=0.305$, (e) $cos{\theta }_K=0.706$, (f) $cos{\theta }_K=0.910$. In each panel, the solid curve was obtained with fit A and the dash-dotted curve with fit B as described in the text. All curves have been averaged over the angle $\varphi$ as described in the text. Data are from Ref. [2].

Figure 5

$P_y^0$ vs $cos{\theta }_K$ for $E_{\mathrm{Lab}}=5.499\mathrm{GeV}$ and (a) $W=1.633\mathrm{GeV},-q^2=2.11$ ${\mathrm{GeV}}^2$, (b) $W=1.863\mathrm{GeV},-q^2=2.08$ ${\mathrm{GeV}}^2$,(c) $W=2.063\mathrm{GeV},-q^2=2.01$ ${\mathrm{GeV}}^2$, (d) $W=2.274\mathrm{GeV},-q^2=1.90$ ${\mathrm{GeV}}^2$, (e) $W=2.475\mathrm{GeV},-q^2=1.75$ ${\mathrm{GeV}}^2$, (f) $W=2.724\mathrm{GeV},-q^2=1.52$ ${\mathrm{GeV}}^2$. In each panel, the solid curve was obtained with fit A and the dash-dotted curve with fit B as described in the text. All curves have been averaged over the angle $\varphi$ as described in the text. Data are from Ref. [2].

Figure 6

$P_y^0$ vs $-q^2$ for $E_{\mathrm{Lab}}=5.499\mathrm{GeV},W=2.0625\mathrm{GeV}$, and (a) $cos{\theta }_K=-0.725$, (b) $cos{\theta }_K=-0.217$, (c) $cos{\theta }_K=0.106$, (d) $cos{\theta }_K=0.305$, (e) $cos{\theta }_K=0.706$, (f) $cos{\theta }_K=0.910$. In each panel, the solid curve was obtained with fit A and the dash-dotted curve with fit B as described in the text. All curves have been averaged over the angle $\varphi$ as described in the text.

Figure 7

$P_z^{\prime }$ vs $cos{\theta }_K$ for $E_{\mathrm{Lab}}=5.754\mathrm{GeV}$ and (a) $W=1.753\mathrm{GeV},-q^2=2.61$ ${\mathrm{GeV}}^2$, (c) $W=1.985\mathrm{GeV},-q^2=2.56$ ${\mathrm{GeV}}^2$, (e) $W=2.314\mathrm{GeV},-q^2=2.41$ ${\mathrm{GeV}}^2$. $P_x^{\prime }$ vs $cos{\theta }_K$ for $E_{\mathrm{Lab}}=5.754\mathrm{GeV}$ and (b) $W=1.753\mathrm{GeV},-q^2=2.61$ ${\mathrm{GeV}}^2$, (d) $W=1.985\mathrm{GeV},-q^2=2.56$ ${\mathrm{GeV}}^2$, (f) $W=2.314\mathrm{GeV},-q^2=2.41$ ${\mathrm{GeV}}^2$. In each panel, the solid curve was obtained with fit A and the dash-dotted curve with fit B as described in the text. All curves have been averaged over the angle $\varphi$ as described in the text. Data are from Ref. [1].

Figure 8

$P_z^{\prime }$ vs $-q^2$ for $E_{\mathrm{Lab}}=5.754\mathrm{GeV},W=1.99\mathrm{GeV}$, and (a) $cos{\theta }_K=-0.25$, (c) $cos{\theta }_K=0.43$, (e) $cos{\theta }_K=0.90$. $P_x^{\prime }$ vs $-q^2$ for $E_{\mathrm{Lab}}=5.754\mathrm{GeV},W=1.99\mathrm{GeV}$, and (b) $cos{\theta }_K=-0.25$, (d) $cos{\theta }_K=0.43$, (f) $cos{\theta }_K=0.90$. In each panel, the solid curve was obtained with fit A and the dash-dotted curve with fit B as described in the text. All curves have been averaged over the angle $\varphi$ as described in the text. Data are from Ref. [1].

Figure 9

$P_y^0$ vs $W$ for $E_{\mathrm{Lab}}=5.499\mathrm{GeV},-q^2=1.90$ ${\mathrm{GeV}}^2$, and (a) $cos{\theta }_K=-0.725$, (b) $cos{\theta }_K=-0.217$, (c) $cos{\theta }_K=0.106$, (d) $cos{\theta }_K=0.305$, (e) $cos{\theta }_K=0.706$, (f) $cos{\theta }_K=0.910$. In each panel, the solid curve was obtained with the new fit and the dash-dotted curve with fit B as described in the text. All curves have been averaged over the angle $\varphi$ as described in the text. Data are from Ref. [2].

Figure 10

$P_y^0$ vs $cos{\theta }_K$ for $E_{\mathrm{Lab}}=5.499\mathrm{GeV}$ and (a) $W=1.633\mathrm{GeV},-q^2=2.11$ ${\mathrm{GeV}}^2$, (b) $W=1.863\mathrm{GeV},-q^2=2.08$ ${\mathrm{GeV}}^2$, (c) $W=2.063\mathrm{GeV},-q^2=2.01$ ${\mathrm{GeV}}^2$, (d) $W=2.274\mathrm{GeV},-q^2=1.90$ ${\mathrm{GeV}}^2$, (e) $W=2.475$ GeV, $-q^2=1.75$ ${\mathrm{GeV}}^2$, (f) $W=2.724$ GeV, $-q^2=1.52$ ${\mathrm{GeV}}^2$. In each panel, the solid curve was obtained with the new fit and the dash-dotted curve with fit B as described in the text. All curves have been averaged over the angle $\varphi$ as described in the text. Data are from Ref. [2].

Figure 11

$P_z^{\prime }$ vs $cos{\theta }_K$ for $E_{\mathrm{Lab}}=5.754$ GeV and (a) $W=1.753$ GeV, $-q^2=2.61$ ${\mathrm{GeV}}^2$, (c) $W=1.985$ GeV, $-q^2=2.56$ ${\mathrm{GeV}}^2$, (e) $W=2.314$ GeV, $-q^2=2.41$ ${\mathrm{GeV}}^2$. $P_x^{\prime }$ vs $cos{\theta }_K$ for $E_{\mathrm{Lab}}=5.754$ GeV and (b) $W=1.753$ GeV, $-q^2=2.61$ ${\mathrm{GeV}}^2$, (d) $W=1.985$ GeV, $-q^2=2.56$ ${\mathrm{GeV}}^2$, (f) $W=2.314$ GeV, $-q^2=2.41$ ${\mathrm{GeV}}^2$. In each panel, the solid curve was obtained with the new fit and the dash-dotted curve with fit B as described in the text. All curves have been averaged over the angle $\varphi$ as described in the text. Data are from Ref. [1].

Figure 12

$P_x^0$ vs $cos{\theta }_K$ for $E_{\mathrm{Lab}}=5.754$ GeV, $\varphi ={30}^{\circ }$, and (a) $W=1.753$ GeV, $-q^2=2.61$ ${\mathrm{GeV}}^2$, (c) $W=1.985$ GeV, $-q^2=2.56$ ${\mathrm{GeV}}^2$, (e) $W=2.314$ GeV, $-q^2=2.41$ ${\mathrm{GeV}}^2$. $P_x^{\prime }$ vs $cos{\theta }_K$ for $E_{\mathrm{Lab}}=5.754$ GeV, $\varphi ={30}^{\circ }$, and (b) $W=1.753$ GeV, $-q^2=2.61$ ${\mathrm{GeV}}^2$, (d) $W=1.985$ GeV, $-q^2=2.56$ ${\mathrm{GeV}}^2$, (f) $W=2.314$ GeV, $-q^2=2.41$ ${\mathrm{GeV}}^2$. In each panel, the solid curve was obtained with the new fit and the dash-dotted curve with fit B as described in the text.

Figure 13

$P_y^0$ vs $cos{\theta }_K$ for $E_{\mathrm{Lab}}=5.499$ GeV, $\varphi ={30}^{\circ }$, and (a) $W=1.633$ GeV, $-q^2=2.11$ ${\mathrm{GeV}}^2$, (c) $W=2.063$ GeV, $-q^2=2.01$ ${\mathrm{GeV}}^2$, (e) $W=2.475$ GeV, $-q^2=1.75$ ${\mathrm{GeV}}^2$. $P_y^{\prime }$ vs $cos{\theta }_K$ for $E_{\mathrm{Lab}}=5.754$ GeV, $\varphi ={30}^{\circ }$, and (b) $W=1.633$ GeV, $-q^2=2.11$ ${\mathrm{GeV}}^2$, (d) $W=2.063$ GeV, $-q^2=2.01$ ${\mathrm{GeV}}^2$, (f) $W=2.475$ GeV, $-q^2=1.75$ ${\mathrm{GeV}}^2$. In each panel, the solid curve was obtained with the new fit and the dash-dotted curve with fit B as described in the text.

Figure 14

$P_z^0$ vs $cos{\theta }_K$ for $E_{\mathrm{Lab}}=5.754$ GeV, $\varphi ={30}^{\circ }$, and (a) $W=1.753$ GeV, $-q^2=2.61$ ${\mathrm{GeV}}^2$, (c) $W=1.985$ GeV, $-q^2=2.56$ ${\mathrm{GeV}}^2$, (e) $W=2.314$ GeV, $-q^2=2.41$ ${\mathrm{GeV}}^2$. $P_z^{\prime }$ vs $cos{\theta }_K$ for $E_{\mathrm{Lab}}=5.754$ GeV, $\varphi ={30}^{\circ }$, and (b) $W=1.753$ GeV, $-q^2=2.61$ ${\mathrm{GeV}}^2$, (d) $W=1.985$ GeV, $-q^2=2.56$ ${\mathrm{GeV}}^2$, (f) $W=2.314$ GeV, $-q^2=2.41$ ${\mathrm{GeV}}^2$. In each panel, the solid curve was obtained with the new fit and the dash-dotted curve with fit B as described in the text.