Theoretical study of $\Lambda$ resonances from an analysis of Crystal Ball $K^{-}p\to {\pi }^0{\Sigma }^0$ reaction data with center-of-mass energies of 1536–1676 MeV

With an effective Lagrangian approach, we analyze the $K^{-}p\to {\pi }^0{\Sigma }^0$ reaction to study the $\Lambda$ hyperon resonances by fitting the Crystal Ball data on differential cross sections and ${\Sigma }^0$ polarization with the center-of-mass energies of 1536–1676 MeV. Besides well-established Particle Data Group (PDG) four-star $\Lambda$ resonances around this energy range, the $\Lambda \left(1600\right){\frac{1}{2}}^{+}$ resonance, listed as a three-star resonance in the PDG data, is found to be definitely needed. In addition, there is strong evidence for the existence of a new $\Lambda \left({\frac{3}{2}}^{+}\right)$ resonance around 1680 MeV.

Figure 1

Feynman diagrams for $K^{-}p\to {\pi }^0{\Sigma }^0$: (a) $t$-channel $K^{*}$ exchange, (b) $u$-channel proton exchange, and (c) $s$-channel $\Lambda$ and its resonances exchanges.

Figure 2

The differential cross sections from Ref. [12], the VA group [10], and the UCLA group [11] of the CB Collaboration at similar beam momenta.

Figure 3

The total cross sections from Ref. [12], the VA group [10], and the UCLA group [11].

Figure 4

Fit compared with the differential cross-section data from Refs. [10, 11, 12]. The dashed lines show results with the inclusion of only five four-star $\Lambda$ resonances in the $s$ channel; the blue solid lines represent the results of including an additional $\Lambda \left({\frac{1}{2}}^{+}\right)$ resonance.

Figure 5

The most favored fit (red solid lines) to the differential cross-section data from Refs. [10, 11, 12], and the corresponding prediction to the polarizations compared with the data of Refs. [10, 11]. As a comparison, fits by dropping the ${\frac{3}{2}}^{+}$ resonance or by replacing it with $\Lambda \left(1690\right){\frac{3}{2}}^{-}$ are shown with blue dashed and black dot-dashed lines, respectively.

Figure 6

Fits compared with the differential cross-section data of Refs. [10, 11, 12] and the polarization data of Refs. [10, 11]. The dashed lines represent the results with four-star resonances only, the blue solid lines stand for the results when adding the three-star $\Lambda \left(1600\right){\frac{1}{2}}^{+}$ resonance, and the green solid lines show the results of the most favored solution.

Figure 7

Fits compared with the differential cross-section data of Refs. [10, 11, 12] and the polarization data of Refs. [10, 11]. The dashed lines represent the results with four-star resonances only, the blue solid lines stand for the results when adding the three-star $\Lambda \left(1600\right){\frac{1}{2}}^{+}$ resonance, and the green solid lines show the results of our most favored solution.