Role of $Σ(1660)$ in the $K^- p \toπ^0π^0Σ^0$ reaction

TL;DR

The paper uses an effective Lagrangian approach to study the role of the $\Sigma(1660)$ (with $J^P=1/2^+$) in near-threshold $K^-p$ reactions, modeling an $s$-channel $\Sigma(1660) \to \pi^0\Lambda(1405) \to \pi^0\pi^0\Sigma^0$ pathway alongside a non-resonant $u$-channel background. A combined fit to $K^-p \to \pi^0\pi^0\Sigma^0$ and $K^-p \to \pi^0\Lambda(1405)$ data yields a consistent set of couplings, notably $g_{\Sigma^*\bar{K}N}g_{\Sigma^*\pi\Lambda^*}=1.81\pm0.10$, and predicts a notable low-energy structure in the two-body channel and a non-negligible branching fraction for $\Sigma(1660)\to \pi^0\Lambda(1405)$, supporting the resonance’s existence. The results emphasize the importance of the $\Sigma(1660)$ in these reactions and motivate future high-precision measurements to pin down its properties and couplings. The work also provides a methodological framework for extracting resonance information from multi-channel hadronic processes near threshold.

Abstract

The processes of $K^-p \to π^0 π^0 Σ^0$ and $K^- p \to π^0 Λ(1405)$ are studied within the effective Lagrangian approach. In addition to the ``background" contribution from the $u$-channel nucleon pole term, contribution from the $Σ(1660)$ resonance with spin-parity $J^P=1/2^+$ is also considered. For the $K^-p \to π^0 π^0 Σ^0$ reaction, we perform a calculation for the total and differential cross sections by considering the contribution from the $Σ(1660)$ intermediate resonance decaying into $π^0 Λ(1405)$ with $Λ(1405)$ decaying into $π^0 Σ^0$. With our model parameters, the available experimental data on both the $K^-p \to π^0 π^0 Σ^0$ and $K^- p \to π^0 Λ(1405)$ reactions can be fairly well reproduced. It is shown that we really need the contribution from the $Σ(1660)$ resonance, and that these experimental measurements could be used to determine some properties of the $Σ(1660)$ resonance.

Figures (6)

• Figure 1: Scattering mechanisms of the $K^-p\rightarrow\pi^0\pi^0\Sigma^0$ reaction. It consists of $s$-channel $\Sigma(1660)$ resonance (a), and $u$-channel nucleon pole term (b). We also show the definition of the kinematical variables ($p_1$, $p_2$, $p_3$, $p_4$, $p_5$, $k$, $k_p$, $q$) used in the calculation.
• Figure 2: Definition of the three-body phase space in the $K^-p\rightarrow\pi^0\pi^0\Sigma^0$ reaction.
• Figure 3: Scattering mechanisms for the $K^-p \to \pi^0\Lambda(1450)$ reaction. (a): $s$-channel, (b): $u$-channel.
• Figure 4: Total cross section for the $K^-p \rightarrow \pi^0\pi^0\Sigma^0$ reaction. The experimental data are taken from Ref. CrystallBall:2004ovf.
• Figure 5: Differential cross sections of $K^-p\rightarrow\pi^0\pi^0\Sigma^0$ reaction for the $p_{K^-}=518$ MeV (upper left), 687 MeV (upper right), 714 MeV (lower left) and 750 MeV (lower right). The experimental data are taken from Ref. CrystallBall:2004ovf.