Weak Radiative Decays of Hyperons: Quark Model and Nonlocality

It is proved that symmetry structure of the parity-viol. (p.v.) amplitudes of weak radiative hyperon decays in the VMD approach, and the violation of Hara's theorem in particular, are also obtained when direct coupling e_q \bar{q}\gamma_{\mu}q A^{\mu} of photon to quarks is used in place of VMD. 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 CA commutator term in the p.v. amplitudes of nonleptonic hyperon decays (NLHD) and the parity-violating \Sigma ^+ \to p \gamma 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 CA commutator in NLHD 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 \Xi ^0 \to \Lambda \gamma asymmetry will provide very important information concerning the presence or absence of nonlocal features in p.v. photon coupling to baryons at vanishing photon momentum. If the \Xi ^0 \to \Lambda \gamma 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 \Xi ^0 \to \Lambda \gamma asymmetry, then, most likely, Hara's theorem is violated. Although positive \Xi ^0 \to \Lambda \gamma 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 p.v. nuclear forces.