Weak Radiative Decays of Hyperons: Quark Model and Nonlocality

It is proved that symmetry structure of the parity-violating amplitudes of weak radiative hyperon decays in the Vector-Meson Dominance (VMD) approach, and the violation of Hara's theorem in particular, are also obtained when direct coupling e_q bar {q}γ _μ q A^μ of photon to quarks is used in place of VMD (with calculations performed in the limit of static quarks). Thus, violation of Hara's theorem in VMD-based models does not result from the lack of gauge invariance. It is further shown that, in the static limit of the quark model, the current-algebra commutator term in the parity-violating amplitudes of nonleptonic hyperon decays and the parity-violating Σ⁺ → p γ decay amplitude are proportional to each other. As a result, Hara's theorem may be satisfied in this limit if and only if the contribution from the current-algebra commutator in nonleptonic hyperon decays is zero. Violation of Hara's theorem is traced back to the nonlocality of quark model states in the static limit. It is argued that the ensuing intrinsic baryon nonlocality does not have to be unphysical. It is stressed that the measurement of the Ξ⁰ → Λ γ asymmetry will provide very important information concerning the presence or absence of nonlocal features in parity-violating photon coupling to baryons at vanishing photon momentum. If the Ξ⁰ → Λ γ asymmetry is found negative, Hara's theorem is satisfied but the gauge-invariant quark model machinery predicting its violation must miss some contribution, or be modified. If experiment confirms positive Ξ⁰ → Λ γ asymmetry, then, most likely, Hara's theorem is violated. Although positive Ξ⁰ → Λ γ asymmetry admits of the possibility that Hara's theorem is satisfied, this alternative is in disagreement with hints suggested by the similarity of photon and vector-meson couplings and the observed size of parity-violating nuclear forces.