CP violation in the hyperon decays $Σ\to Nπ$

TL;DR

This work evaluates CP violation in hyperon decays $Σ\to Nπ$ by first updating SM expectations using a chiral-Lagrangian approach and data-driven isospin decompositions, then explores two new-physics avenues that could boost CP-odd observables: (i) enhanced chromomagnetic-penguin operators constrained by kaon data, and (ii) a THDM+D dark-matter framework with additional four-quark operators. The study shows that NP can increase CP asymmetries in $Σ\to Nπ$ by up to an order of magnitude relative to SM predictions, with several channels yielding effects potentially observable at BESIII and future facilities such as PANDA and the Super Tau-Charm Facility. The results emphasize that kaon-sector constraints play a crucial role in delimiting NP contributions and that upcoming precision measurements of $Σ$ CP asymmetries can provide key tests of strange-quark CP violation beyond kaons. Overall, the paper identifies concrete experimental targets and interprets current data within both SM and beyond-SM contexts, highlighting the interface between hyperon CP violation and new physics.

Abstract

The study of $CP$ violation in hyperon transitions has a long history. In the early 2000s the HyperCP experiment made a major effort to seek $CP$-odd signals in the decay sequence $Ξ^-\toΛπ^-$ and $Λ\to pπ^-$, which motivated more searches. Most recently the BESIII and LHCb Collaborations have acquired or improved the upper bounds on $CP$ violation in a variety of hyperon nonleptonic processes, including $Σ^+\to nπ^+$ and $Σ^+\to pπ^0$. These measurements have not reached the standard-model level yet, but have stimulated a renewed interest in $CP$-violating new physics in strange-quark decay beyond what is constrained by the parameters $\varepsilon$ and $\varepsilon^\prime$ from the kaon sector. In this paper, after updating the standard-model expectations for $CP$-odd observables in the modes $Σ^\pm\to Nπ$, we revisit new-physics scenarios that could enhance the corresponding quantities in $Λ\to Nπ$ and $Ξ\toΛπ$ and apply them to the $Σ^\pm$ modes. We find that the $CP$ asymmetries in the latter can be significantly increased over the standard-model expectations, at levels which may be tested in the ongoing BESIII experiment and in future endeavors such as PANDA and the Super Tau Charm Facility.

Figures (5)

• Figure 1: Leading-order diagrams for the SM contributions to (a) S- and (b) P-wave $\mathit\Sigma\to N\pi$ decay. Each hollow square symbolizes a coupling from ${\cal L}_{\Delta S=1}^{\tt SM}$ in eq. (\ref{['Lw']}). In this and the next figure, each solid (dashed) line represents a spin-1/2 baryon (pseudoscalar meson), each thick dot a coupling from ${\cal L}_{\rm s}$ in eq. (\ref{['Lstrong']}), and $\mathfrak B=N,\mathit\Lambda,$ or $\mathit\Sigma$.
• Figure 2: The predicted $\hat{A}_{\mathit\Sigma^+\to n\pi^+}$ and $\hat{A}_{\mathit\Sigma^+\to p\pi^0}$ in the SM (red) and in the new-physics scenarios (blue) dealt with in sections \ref{['cmo']} ( CMO) and \ref{['dmmodel']} ( 4q), compared to the corresponding 1$\sigma$ (black) intervals of the BESIII findings cited in eq. (\ref{['ASigma-data']}), the statistical and systematical errors having been summed in quadrature.
• Figure 3: Leading-order diagrams for the new contributions to (a) S- and (b) P-wave $\mathit\Sigma\to N\pi$ decay. Each hollow square symbolizes a coupling from $\mathfrak L_\chi^{\tt CMO}$ in eq. (\ref{['Lgnew']}) or ${\cal L}_\chi^{\rm new}$ in eq. (\ref{['Lchi']}).
• Figure 4: Top: the distributions of $CP$ asymmetries $\hat{A}_{\mathit\Sigma^+\to n\pi^+}^{\rm new}$, $\hat{A}_{\mathit\Sigma^+\to p\pi^0}^{\rm new}$, and $\hat{A}_{\mathit\Sigma^-\to n\pi^-}^{\rm new}$ in connection with the sample absolute-values of Yukawa coupling $\mathbb Y_{dd}$ fulfilling the requirements specified in the text. Bottom: the corresponding $\hat{B}_{\mathit\Sigma^+\to n\pi^+}^{\rm new}$, $\hat{B}_{\mathit\Sigma^+\to p\pi^0}^{\rm new}$, and $\hat{B}_{\mathit\Sigma^-\to n\pi^-}^{\rm new}$.
• Figure 5: The predicted $\hat{A}_{\mathit\Lambda\to p\pi^-}$ and $\hat{A}_{\mathit\Xi^0\to\mathit\Lambda\pi^0}$ (left panel) and $\hat{A}_{\mathit\Lambda\to p\pi^-}\!+\!A_{\mathit\Xi^-\to\mathit\Lambda\pi^-}$ (right panel) in the SM (red) and in the new-physics scenarios (blue) dealt with in sections \ref{['cmo']} ( CMO) and \ref{['dmmodel']} ( 4q), compared to the 1$\sigma$ intervals of the corresponding data cited in eq. (\ref{['AL-AX-data']}).