Hara's Theorem Research Articles

Hyperon weak radiative decay * *Supported by the National Natural Science Foundation of China (11425525, 11521505), DFG and NSFC funds to the Sino-German CRC 110 “Symmetries and the Emergence of Structure in QCD” (NSFC) (11261130311), Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030302), National Key Basic Research Program of China (2015CB856700); Q.W. is also supported by the research

We revisit the hyperon weak radiative decays in the framework of the non-relativistic constituent quark model. This study confirms the nonlocal feature of the hyperon weak radiative transition operators, which are dominated by the pole terms, and an overall self-consistent description of the available experimental data for the Cabibbo-favored hyperon weak radiative decays is presented. It provides a natural mechanism for evading the Hara theorem, where sizeable parity-violating contributions can come from the intermediate orbital excitations. Cancellations between pole terms also explain the significant SU(3) flavor symmetry breaking manifested by the experimental data. We also discuss several interesting selection rules arising from either the electromagnetic or the weak interaction vertices. These features suggest nontrivial relations among various hyperon decays.

Revisiting Weak Radiative Decays of Hyperons

Triggered by experimentally driven renewed interest in hyperon properties we address the subject of weak radiative hyperon decays (WRHD). We start with the issue of Hara's theorem and briefly discuss the question of its possible evasion. Then, we give a short review of the story of vector-meson-dominance (VMD) approach to WRHD. We stress the shift from the Hara's-theorem-violating to Hara's-theorem-satisfying version of the VMD approach that did occur over time. Finally, spurred by a recent theoretical paper, we discuss the pole model description of WRHD, putting special attention to the issue of the contributions from the intermediate $\Lambda(1405)$ state. We point out that the measurement of the $\Lambda \to n \gamma$ decay asymmetry could resolve the encountered ambiguities and definitely answer the question of whether Hara's theorem is violated or not.

Weak radiative hyperon decays

The problem of weak radiative hyperon decays (WRHD) is reviewed. With the rcent measurement of the Ξ 0 → Λ γ asymmetry confirming Hara's theorem, implications from its violation in low-energy theoretical approaches are discussed. It is shown how an underlying symmetry link should be formulated for a successful description of both nonleptonic and radiative weak hyperon decays. The sign of the Ξ 0 → Λ γ asymmetry and the overall size of parity-violating WRHD amplitudes together lead to the resolution of the old S:P problem in nonleptonic decays.

Electroweak radiative corrections to parity-violating electroexcitation of theΔ

We analyze the degree to which parity-violating (PV) electroexcitation of the $\Delta(1232)$ resonance may be used to extract the weak neutral axial vector transition form factors. We find that the axial vector electroweak radiative corrections are large and theoretically uncertain, thereby modifying the nominal interpretation of the PV asymmetry in terms of the weak neutral form factors. We also show that, in contrast to the situation for elastic electron scattering, the axial $N\to\Delta$ PV asymmetry does not vanish at the photon point as a consequence of a new term entering the radiative corrections. We argue that an experimental determination of these radiative corrections would be of interest for hadron structure theory, possibly shedding light on the violation of Hara's theorem in weak, radiative hyperon decays.

Parity-violating photoproduction of pi(+/-) on the delta resonance.

We analyze the real-photon asymmetry A(gamma)(+/-) for the parity-violating (PV) pi(+/-) production on the Delta resonance via the reactions (-->)gamma + p --> Delta(+) --> pi(+) + n and (-->)gamma + d --> Delta(0) + p --> pi(-) + p + p. This asymmetry is nonvanishing due to a PV gamma N Delta coupling constant, d(Delta)(+/-). We argue that an experimental determination of this coupling would be of interest for hadron dynamics, possibly shedding light on the S-wave/ P-wave puzzle in the hyperon nonleptonic decays and the violation of Hara's theorem in weak radiative hyperon decays.

Reply to “Comment on ‘Hara’s theorem in the constituent quark model’ ”

In the preceding Comment, it is alleged that a ``hidden loophole'' in the proof of Hara's theorem has been found, which purportedly invalidates the conclusions of the paper commented upon. I show that there is no such loophole in the constituent quark model, and that the ``counterexample'' presented in the Comment is not gauge invariant.

Comment on “Hara’s theorem in the constituent quark model”

It is pointed out that current conservation alone does not suffice to prove Hara's theorem as it was claimed recently. By explicit calculation we show that the additional implicit assumption made in such "proofs" is that of a sufficiently localized current.

Weak radiative hyperon decays and vector meson dominance

We study the question whether the phenomenologically successful VMD approach to weak radiative hyperon decays can be made consistent with Hara's theorem and still yield the pattern of asymmetries exhibited by experimental data. It appears that an essential ingredient which governs the pattern of asymmetries is the off-shell behaviour of the input electromagnetic 1/2^- 1/2^+ \gamma couplings. Although this behaviour can be chosen in such a way that the experimentally observed pattern is obtained, and yet Hara's theorem satisfied, at the same time the approach yields a definite prediction for the size of weak meson-nucleon coupling constants. Comparison with experiment reveals then another conflict.

Generalized Gordon identities, Hara theorem and weak radiative hyperon decays

It is shown that an alternative form of the parity-nonconserving (PNC) transition electromagnetic current resolves partly a puzzle with the Hara theorem. Its new formulation has allowed PNC weak radiative hyperon transitions of charged hyperons Σ +⇒ p+ γ and Ξ −⇒ Σ −+ γ revealing hitherto the unseen transition toroid dipole moment.

Hara's theorem, quark model, and $\gamma _5$ -dependent renormalization constants

We discuss the applicability of $\gamma_5$ -dependent field renormalization as a means of renormalizing away the apparent violation of Hara's theorem observed in the quark model. It is pointed out that a result totally analogous to the violation of Hara's theorem is predicted by the quark model also for neutral baryons. For neutral baryons, however, such a result cannot be renormalized away. This proves that $\gamma _5$ -dependent renormalization does not provide a proper way for a hadron-level understanding of the violation of Hara's theorem observed in the quark model.

Weak radiative hyperon decays, Hara’s theorem, and the diquark

Weak radiative hyperon decays are discussed in the diquark-level approach. It is pointed out that in the general diquark formalism one may reproduce the experimentally suggested pattern of asymmetries, while maintaining Hara's theorem in the SU(3) limit. At present, however, no detailed quark-based model of parity-violating diquark-photon coupling exists that would have the necessary properties.

Hara's theorem, quark model, and

We discuss the applicability of gamma_5-dependent field renormalization as a means of renormalizing away the apparent violation of Hara's theorem observed in the quark model. It is pointed out that a result totally analogous to the violation of Hara's theorem is predicted by the quark model also for neutral baryons. For neutral baryons, however, such a result cannot be renormalized away. This proves that gamma_5-dependent renormalization does not provide a proper way for a hadron-level understanding of the violation of Hara's theorem observed in the quark model.

Hara’s theorem and W—exchange in hyperon weak radiative decays

We reconsider Hara's theorem in its relation to the well-known properties of beta-decay. All assumptions necessary for the theorem to be true are explicitly formulated. Further, we study the W-exchange contribution to weak radiative decays and show that it does not violate Hara's theorem. However, this contribution reveals the essential role of particle mixing in symmetry considerations and some peculiar features of gauge-invariant amplitudes under perturbative expansion. Together they explain an effect, which was treated as contradicting Hara's theorem, without any violation. The properties of W-exchange we describe here may have more general importance and should be taken into account in further detailed calculations of weak processes.

Hara's theorem in the constituent quark model.

We show that the parity-violating electromagnetic matrix elements describing the hyperon decay in the nonrelativistic constituent quark model obey Hara{close_quote}s theorem in first-order perturbation theory, i.e., to {ital O}({ital G}{sub {ital F}}), where {ital G}{sub {ital F}}{approx_equal}10{sup {minus}5}{ital M}{sub {ital N}}{sup {minus}2} is the Fermi weak interaction coupling constant and {ital M}{sub {ital N}} is the nucleon mass. Particular emphasis is put on questions of gauge invariance and of threshold behavior. We discuss our results and compare them with the literature. {copyright} {ital 1996 The American Physical Society.}

Hyperon weak radiative decays in chiral perturbation theory.

We investigate the leading-order amplitudes for weak radiative decays of hyperons in chiral perturbation theory. We consistently include contributions from the next-to-leading order weak-interaction Lagrangian. It is shown that due to these terms Hara's theorem is violated. The data for the decay rates of the charged hyperons can be accounted for. However, at this order in the chiral expansion, the four decay rates of the neutral hyperons satisfy relations which are in disagreement with the data. The asymmetry parameters for all the decays cannot be accounted for without higher-order terms. We briefly comment on the effect of the 27-plet part of the weak interaction.

The puzzle of the quark model: Weak radiative hyperon decays

Weak radiative hyperon decays present us with a long-standing puzzle, namely the question of validity of a hadron-level theorem proved by Hara. We briefly discuss the conflict between expectations based on Hara's theorem and experiment as well as the way in which the quark model evades the theorem. Violation of Hara's theorem in the quark model is traced back to the issue of hadron compositeness and the nonequivalence of standard ways of imposing gauge-invariance condition at quark and hadron levels. This suggests that our understanding of nonlocal composite nature of hadrons may require some important change.

Comment of a recent critique of Hara's theorem for radiative hyperon decay

Contrary to a recent assertion, infrared sungularities arising from internal bremsstrahlung in radiative hyperon decays do not invalidate Hera's theorem which states that the asymmetry parameters inΣ+ →pγ and Ξ− → Σ−γ vanish in the exact flavor SU(3) limit.

Comments on the symmetry relations in the hyperon radiative decays

We demonstrate that in general Hara's theorem which gives various symmetry relations for the hyperon radiative decays is not valid. The new relations we derive are different from those given by Hara. But for the Σ +→P γ decay, the asymmetry parameter is still zero in the exact SU(3) limit.

Four-quark operators in hyperon radiative decays and Hara's theorem

We demonstrate that in the effective Hamiltonian for the process s+u..-->..u+d+..gamma.., one can identify two types of local four-quark operators; type I operators violate Hara's theorem and type II respect it. By an explicit calculation we demonstrate that the quark-quark bremsstrahlung process generates both types of operators but only type I survive in the SU(3) limit.