Evidence for excitation of two resonance states in the isovector two-baryon system with a mass of 2.2 GeV/ $c^2$

We report on measurements of the differential cross section $d\sigma /d\mathrm{\Omega }$ and the first measurement of the analyzing power $A_y$ in the $\mathrm{\Delta }\left(1232\right)$ excitation energy region of the reaction $pp\to {\left\{pp\right\}}_s{\pi }^0$ where ${\left\{pp\right\}}_s$ is a ${}^{1}S_0$ proton pair. The experiment has been performed with the ANKE spectrometer at COSY-Jülich. The data reveal a peak in the energy dependence of the forward ${\left\{pp\right\}}_s$ differential cross section, a minimum at zero degrees of its angular distribution, and a large analyzing power. The results present a direct manifestation of two two-baryon resonance-like states with $J^P=2^{-}$ and $0^{-}$ and an invariant mass of $2.2\mathrm{GeV}/c^2$.

Figure 1

Contributions of the dominant ${}^{1}D_{2}p$ (dotted curves), ${}^{3}F_{3}d$ (dot-dashed curves), and ${}^{3}P_{2}d$ (dashed curves) amplitudes to the total unpolarized cross section of reaction (1) (solid curves) according to the said [10] partial wave analysis. The bold green curves correspond to the C500, and the thin magenta curves correspond to the SP96 solution.

Figure 2

The ANKE spectrometer setup (top view), showing the positions of the hydrogen cluster-jet target and the forward detector (FD).

Figure 3

Angular dependencies of the differential cross section $d\sigma /d\mathrm{\Omega }$ (left) and the analyzing power $A_y$ (right) at the beam energies $T_p$ equal to 353, 500, 550, 700, 800 MeV. The errors shown are purely statistical. The curves represent fitting equations (4) to the data. See supplemental material [35] for the numerical values of $d\sigma /d\mathrm{\Omega }$ and $A_y$.

Figure 4

Energy dependence of the leading amplitudes squared for reaction (1) according to the said SP96 [10] PWA calculations.

Figure 5

Energy dependencies of the parameters fitted for $d\sigma /d\mathrm{\Omega }$ and $A_y$: (a) forward cross section $d{\sigma }_0/d\mathrm{\Omega }$, (b) slope parameter $\kappa$, (c) maximal analyzing power $A_y^{\max }$. $•$—ANKE data (combined analysis of Refs. [30, 31] and present work), $▴$—WASA data [28]. The errors include statistical and systematic uncertainties from the normalization used to find luminosity and polarization. The curve approximating $d{\sigma }_0/d\mathrm{\Omega }$ is the Breit–Wigner fit in the range where the line is solid. The corridor shows the 68% confidence interval.

Figure 6

Energy dependencies of the amplitudes squared of the transitions (a) ${}^{3}P_2\to {}^{1}S_{0}d$, (b) ${}^{3}P_0\to {}^{1}S_{0}s$, and (c) their relative phase $\varphi$. The solid curves show the approximation of the $|M_d^P{|}^2$ values by Eq. (6) in panel (a) and of the $|M_s^P{|}^2$ values by the sum of resonance (6) and background (7) in panel (b). The dash-dotted curve in panel (c) presents the approximation of the $\varphi$ values by Eq. (8). The corridors show the 68% confidence interval. The experimental data are marked as in Fig. 5. Stars at the beam energy $T_p=1100\mathrm{MeV}$ correspond to the results of the fit by using $|M_d^P{|}^2$ extrapolation and $d\sigma /d\mathrm{\Omega }$ data [30], as described in the text. Empty triangles are excluded from the fit for the reason given in the text. The sources of errors are the same as in Fig. 5. The dotted line in panel (b) shows the background (7). The dotted curve in panel (c) shows the relative phase of the ${}^{3}P_0$ and ${}^{3}P_2$ amplitudes in the $pp\to pp$ scattering.

Figure 7

Contribution of the ${}^{3}F_{2}d$ wave amplitude to the two-amplitude (${}^{3}P_{0}s$, ${}^{3}P_{2}d$) model calculations. Dash-dotted curves show maximal upper and lower deviations of the calculated (a) $d{\sigma }_0/d\mathrm{\Omega }$, (b) $\kappa$, and (c) $A_y^{\max }$ caused by the presence of the ${}^{3}F_{2}d$ wave amplitude, as described in the text. Solid curves correspond to the results of the calculation without the ${}^{3}F_{2}d$ wave. The experimental data are marked as in Fig. 6.