Hyperon non-leptonic decays in relativistic Chiral Perturbation Theory with resonances

Abstract

Motivated by recent experimental advances in the corresponding measurements, non-leptonic hyperon decays are calculated, for the first time in a relativistic manner, in Chiral Perturbation Theory at next-to-leading order (NLO). On the one hand, relativistic loop corrections are computed explicitly based on the ground-state octet and decuplet fields. On the other hand, the NLO weak-transition low-energy constants are estimated by resonance saturation, inspired by the non-relativistic tree-level computation of Ref. [1]. In particular, the $1/2^-$ and the (excited) $1/2^+$ resonance octets are utilized. The remaining unknown parameters are fitted to the decay amplitudes. A good combined fit to both $s$- and $p$-wave amplitudes is achieved with the caveat of not being very tightly constrained. The role of the resonances is found to be crucial. Consequences for further investigations and open questions are addressed.

Figures (7)

• Figure 1: Tree-level diagrams including resonances. The dashed, solid and wiggle lines correspond to meson, ground-state octet baryon ($B$) and $1/2^{\pm}$ baryon resonances ($R_{+}, \ R_{-}$), respectively. The box depicts the weak interaction mediated by the LECs $h_{D,F}$ and $w_{d,f}$ ($BR_{-}$), $d^*, f^*$ ($BR_{+}$) for the LO (\ref{['eq:weaklag']}) and resonance (\ref{['eq:weak-s-res-L']}, \ref{['eq:weak-p-res-L']}) Lagrangians, respectively. Diagrams (d) and (e) for $R_-$ and diagram (a) contribute to the s-wave amplitude. Diagrams (d) and (e) for $R_+$ together with diagrams (b) and (c) contribute to the p-wave.
• Figure 2: Loop diagrams contributing to the s-wave amplitude. The types of lines and LECs are the same as in Fig. \ref{['fig:tree-diags']}, except for the double line, representing states from the baryon decuplet ($T$), mediated by $h_C$ from (\ref{['eq:weaklag']}).
• Figure 3: Loop diagrams that contribute to the p-wave amplitude. The types of lines are the same as in Figs. \ref{['fig:tree-diags']}-\ref{['fig:s-wave-diags']}.
• Figure 4: Results of the combined fit to the s- and p-wave amplitudes via the isospin amplitudes $L_{2\Delta I, 2I}$. The theoretical error, $\sigma(\mathcal{M})_{\rm theory}$, is defined in Eq. \ref{['eq:theo_err']}. The error $\sigma(\mathcal{M})_{\rm corr}$ corresponds to the 1$\sigma$ error propagated from the fitted LECs including the correlation coefficients and the uncertainty in the LEC $\mathcal{H}$ given in Table \ref{['tab:strong_LECs']}.
• Figure 5: Size comparison of $l_{\rm expt}$ to the various LO and NLO contributions to the physical amplitudes, corresponding to the values in the bottom half of Table \ref{['tab:iso-fit-comb-res']}.