Alternative Form of the Parity-Violating Current for the Hyperon Weak Radiative Decays and Hara Theorem

TL;DR

This paper proposes an alternative formulation of the parity-violating current in hyperon radiative decays, resolving previous contradictions with experimental data and suggesting the presence of transition toroid dipole moments.

Contribution

It introduces an alternative form of the parity-violating current that reformulates Hara's theorem, allowing nonzero asymmetries in hyperon decays and highlighting the role of toroid dipole moments.

Findings

Reformulated Hara's theorem to allow nonzero asymmetry in hyperon decays.

Identified the significance of toroid dipole moments in weak radiative transitions.

Reproduced Vasanti's formula at the quark level.

Abstract

It is shown that upon considering an alternative form of a parity-violating part of the transition electromagnetic current it is possible to reformulate Hara theorem in a way that it does not forbid any more nonzero asymmetry in the hyperon weak radiative decays $\Sigma^{+} \to p+\gamma$ and $\Xi^{-} \to \Sigma^{-}+\gamma$ in the limit of exact $SU(3)_{f}$ symmetry thus resolving a contradiction with the data and maybe revealing hitherto unseen transition toroid dipole moments. A result is consistent with the traditional one on the single-quark weak radiative transition models. We have also reproduced Vasanti formula at the quark level. As for two-quark weak radiative transitions we have found that the important part of it contains also a toroid dipole moment contribution which seems to be an intrinsic reason of the apparent contradiction between the Hara theorem conclusion and quark model results for hyperon weak radiative decays.