Off-shell Chiral Dynamics in the $Λ(1405)$ Resonance and $K^-p$ Femtoscopic Correlations

Abstract

We present the first systematic investigation of the $S=-1$ meson--baryon interaction within a fully off-shell covariant unitarized chiral effective field theory framework up to next-to-leading order. In particular, we perform a detailed comparison with the widely used on-shell approximation. We find that the resulting scattering observables are very similar, thereby confirming the validity of key results obtained within the on-shell scheme. A notable advantage of the off-shell treatment, however, is the absence of unphysical left-hand cuts induced by the on-shell approximation. Employing the off-shell amplitudes, we compute the femtoscopic correlation functions for $K^-p$ and $π^\pmΣ^\mp$ pairs. The $K^-p$ correlation functions are found to be consistent with previously published results based on the on-shell approximation, with marginal differences attributed to slight variations in the descriptions of the scattering data. The $π^\pmΣ^\mp$ correlation functions are predicted for the first time, and are expected to provide valuable constraints on the nature of the $Λ(1405)$ resonance and the coupled-channel chiral dynamics of the $K^-p$ system.

Figures (8)

• Figure 1: Global fit results for $K^-p$ scattering and subthreshold dynamics. The first six panels (a)--(f) present the comparison between experimental cross sections for various $S=-1$ channels $K^-p\rightarrow\{K^-p,\bar{K}^0n,\pi^-\Sigma^+,\pi^0\Sigma^0,\pi^+\Sigma^-,\pi^0\Lambda\}$Humphrey:1962zzKim:1965zzdSakitt:1965khKittel:1966zzEvans:1983hzCiborowski:1982et and the U$\chi$EFT results at both WT and NLO (including both off-shell and on-shell cases) with uncertainty bands estimated by the EFT Bayesian truncation Furnstahl:2015rhaMelendez:2017phjMelendez:2019izc. The final four panels (g)--(j) illustrate the real and imaginary parts of the subthreshold $K^-p$ elastic amplitudes compared to data from Ref. Bazzi:2011zj. Panels (g) and (h) show the off-shell results where the dotted lines represent our LO calculations performed using the WT parameter (paras) sets, while panels (i) and (j) provide the corresponding on-shell non-smooth amplitudes for comparison. The smooth behavior of the full off-shell amplitudes, characterized by the absence of unphysical left-hand cut interferences, reveals that the two-pole structure of the $\Lambda(1405)$ is robust.
• Figure 2: Pole positions of the $\Lambda(1380)$ and $\Lambda(1405)$ in the complex energy plane, obtained from NLO, LO, and WT schemes with both off-shell (OFF) and on-shell (ON) schemes. The dashed ellipses serve as visual guides to indicate the two-pole cluster structure.
• Figure 3: $K^-p$ CFs and the impact of off-shell dynamics for $R = 1.0$ fm. (a)--(b): Off-shell versus on-shell comparison at fixed chiral order, showing effective reabsorption of off-shell effects at WT but noticeable deviations at NLO. (c)--(d): Channel-by-channel contributions to the total CFs for the NLO off-shell and on-shell cases, demonstrating that the $K^-p$ single-channel contributions already exhibit a marked discrepancy even in the vicinity of the threshold. The shaded error bands for the CFs in panels (a)–(d) reflect the uncertainties originating from the channel weights $w_j$Encarnacion:2024jge.
• Figure 4: Comparison of the $K^-p$ single-channel CF contributions between NLO off-shell and on-shell schemes, alongside the on-shell KP formula results with ERE; the results show that the near-threshold discrepancy between the off-shell and on-shell CFs arises solely from the different scattering lengths $a_{K^-p}$ rather than explicit off-shell effects. The shaded error bands for the CFs arise from the uncertainties of the $a_{K^-p}$ in Table \ref{['tab:akp_fits']}.
• Figure 5: The $\pi^{\pm}\Sigma^{\mp}$ CFs with NLO-OFF and NLO-ON for $C_{\pi^+\Sigma^-}(p)$ (a) and $C_{\pi^-\Sigma^+}(p)$ (b). Panels (c) and (d) regroup the same curves by scheme to highlight the fine structure between the two channels.