Spin-Density Matrix Elements for $\gamma p\to K^{*0}{\Sigma }^{+}$ at $E_{\gamma }=1.85–3.0\mathrm{GeV}$ with Evidence for the $\kappa (800)$ Meson Exchange

The exclusive reaction $\gamma p\to K^{+}{\pi }^{-}{\Sigma }^{+}$ was measured for the first time using linearly polarized photons at beam energies from 1.85 to 2.96 GeV. Angular distributions in the rest frame of the $K^{+}{\pi }^{-}$ system were fitted to extract spin-density matrix elements of the $K^{*0}$ decay. The measured parity spin asymmetry shows that natural-parity exchange is dominant in this reaction. This result clearly indicates the need for $t$-channel exchange of the $\kappa (800)$ scalar meson.

Figure 1

(a) Scatter plot of the missing mass of the $K^{+}{\pi }^{-}$ system versus the invariant mass of the $K^{+}{\pi }^{-}$ system; (b),(c) projected spectra for the invariant mass and missing mass distributions, respectively; (d) missing mass of the $K^{+}$ (with a ${\pi }^{-}$ detected), and the lower dashed histogram indicates the final even selection within $3\sigma$ of the ${\Sigma }^{+}$ peak and the $K^{*0}$ peak; (e) missing mass distribution with solid arrows around the signal region ($K^{*0}$ peak) and dashed arrows showing the outside of the sideband regions; (f) same as (b), but with a cut on the ${\Sigma }^{+}$ peak after the sideband background subtraction, and the overlaid dashed line shows the estimated $Y^{*}$ background.

Figure 2

Decay angular distributions of $\cos {\theta }_{K^{+}}$, ${\varphi }_{K^{+}}$, $(\varphi -\Phi {)}_{K^{+}}$, and ${\Phi }_{K^{+}}$ in the GJ frame for the sum of vertical polarization and horizontal polarization after acceptance correction. The dotted lines show Monte Carlo data using the measured spin-density matrix elements, while the overlaid black histograms indicate the $Y^{*}$ background yield from a Monte Carlo simulation.

Figure 3

Decay angular distributions in the helicity frame. Notations are the same as in Fig. 2.

Figure 4

Parity spin asymmetry ($P_{\sigma }=2{\rho }_{1-1}^1-{\rho }_{00}^1$) in the helicity frame. The data point is averaged over photon energies from 1.85 to 2.96 GeV. The solid (dashed) line is the result of model I (model II) of Ref. [15] at $E_{\gamma }=2.5\mathrm{GeV}$. Model I has almost no contribution from $\kappa$ exchange, whereas model II includes substantial $\kappa$ exchange.