Nonleptonic Hyperon Decays Research Articles

Nonleptonic Hyperon Decays in a Current-Current Quark Model

The symmetric quark model is used to provide an explanation of the $S$- and $P$-wave non-leptonic hyperon decays. The current-algebra approach, applied to the current-current weak Hamiltonian constructed of Bose-type quark fields, leads to a remarkable agreement with experiment.

“Ur-citon”: An Attempt for Unified Theory of Hadrons*

A theoretical scheme for unified treatment of the world of all hadrons is presented, which includes heuristically the successes of the quark model without the well-known difficulties regarding spin-statistics connection and binding problem. Our essential idea exists in the following: Introducing the operator ψA(p,ξ), called “ur-citon” which transforms similarly to the quark, depends on the internal Lorentz variables ξ, and is quantized through Bose-type commutation relations; we consider the “inner Fock expansion” of the general “inner state vector”. Then the expansion coefficients, which satisfy the “generalized Bargmann-Wigner equations,” are considered to represent our hadron fields, and are “second-quantized” following the prescription of the usual quantum field theory. In our theory the level scheme of mesons and baryons is given through the system of two and three three-dimensional harmonic oscillators, respectively, contrasting with one and two oscillators in the quark model. For the baryons this difference makes no detectable results at present, so our scheme shares the success with the usual quark model. For the mesons a degree of success seems to be much reinforced in our theory, providing an explanation of the “anomalous fine structure” and a possible solution for the A2-splitting problem. A general scheme for getting various kinds of effective vertices among hadrons is investigated also from the same unified view-point. Then it is useful to use a diagram, called “ur-citon diagram,” which is written by lines with an arrow representing a flow of ur-citons. A tentative application to the electromagnetic form factors of nucleons is shown to lead to a satisfactory result which reproduces the famous experimental behavior, the scaling law and the dipole-like behavior. Weak interactions among hadrons and leptons are, similarly to the usual theory, assumed to be given by a “current-current” like interaction in our scheme, where its parts relevant to hadrons are treated by our ur-citon scheme. Then we can derive rigorously the phenomenological rule “octet dominance” for the non-leptonic interaction. Moreover, as a result of detailed application to the non-leptonic hyperon decay it is shown that our theory with only one parameter reproduces the characteristic experimental behavior of both the S-wave and P-wave decays.

Explanation for nonleptonic decays of hyperons

On the basis of Okubo's dispersion approach, the resonance contribution to the current algebra result for nonleptonic decays of hyperons is calculated via Regge theory. A four parameter best-fit solution to both s and p-wave amplitudes is found to be in very good agreement with experiment. Our result provides a uniform explanation of puzzling features of previous work.

Final-State Interactions in Nonleptonic Hyperon Decays

The effects of final-state interactions on nonleptonic hyperon decay amplitudes are evaluated within the current-algebra framework of partially conserved axial-vector currents. Good agreement with experimental amplitudes is obtained for both $S$- and $P$-wave decays.

Once-Subtracted Dispersion Relations, Current Algebra, and Nonleptonic Weak Decays of Hyperons

Nonleptonic weak decays of hyperons and the ${K}_{1}\ensuremath{\rightarrow}2\ensuremath{\pi}$ decay are carefully analyzed using current algebra, partial conservation of axial-vector current, and once-subtracted dispersion relations, a method suggested by Okubo, Mathur, and Marshak. We have calculated the dispersion integral by assuming it to be saturated by the low-mass intermediate states of the nucleon octet, of the ${\frac{3}{2}}^{+}$ decuplet of $\ensuremath{\Delta}(1236)$, and of the ${\mathrm{\textonehalf{}}}^{\ensuremath{-}}$ ${\mathrm{SU}}_{3}$ singlet ${Y}_{0}^{*}(1405)$, in the case of hyperon decays, and by the intermediate states of vector mesons and a possible ${0}^{+}$ scalar-meson nonet, in the case of ${K}_{1}\ensuremath{\rightarrow}2\ensuremath{\pi}$ decay. The matrix element of the parity-violating weak Hamiltonian density between two baryons (which is required to evaluate the hyperon decay amplitudes) is related to the ${K}_{1}\ensuremath{\rightarrow}2\ensuremath{\pi}$ decay amplitude by the ${K}_{1}$ tadpole mechanism. With pseudovector ${\mathrm{SU}}_{3}$-symmetric coupling among the nucleon and pseudoscalar-meson octets, we are able to obtain a good fitting of all the hyperon decay amplitudes in terms of four parameters. We also find that the corrections to the soft-pion values are very important not only for $P$-wave hyperon decay amplitudes, but also for $S$-wave amplitudes. They are also extremely important for ${K}_{1}\ensuremath{\rightarrow}2\ensuremath{\pi}$ decays. Furthermore, we find that, contrary to the findings of Hara and Nambu, there is no evidence for the concept of a "universal parityconserving spurion" in hyperon and ${K}_{1}\ensuremath{\rightarrow}2\ensuremath{\pi}$ weak decays.

On Nonleptonic Hyperon Decays. I

Nonleptonic hyperon decays are studied in the framework of new s-u symmetry and absence rule for an octet spurion. It is shown that the Lee-Sugawara relation is derived from the symmetry instead of R (or RP) reflection for parity conserving decay amplitudes, and from the absence rule in t channel for parity violating decay amplitudes, and that the characteristic properties of decay amplitudes especially appearing in Σ-decay modes are well reproduced.

Correspondence between the Three-Triplet Model and the Quartet Model in Nonleptonic Hyperon Decays

Correspondence between the Three-Triplet Model and the Quartet Model in Nonleptonic Hyperon Decays

Urbaryon Rearrangement Diagram and Nonleptonic Hyperon Decays

Nonleptonic hyperon decays are investigated from the standpoint of urbaryon rear­ rangement diagram. It is shown that duality assures the Lee-Sugawara relation of both S-wave and P-wave amplitudes of nonleptonic hyperon decays under simple assumptions that the H-type diagram is dominant in S-wave decays and that the Z-type diagram is domi­ nant in P-wave decays. The cluster model is discussed in connection with the assumptions for explaining the main dynamical properties of S-wave and P-wave decays. It is found that the characteristics of S-wave decays can be understood by setting a constraint to the t-channel and that those of the P-wave decays can be understood by setting the constraint to the s-channel: A short content of this article has already been published. [H. Noda and F. Toyoda, Prog. Theor. Phys. 44 (1970), 811].

Intermediate W bosons, gauge fields, and the nonleptonic weak decays

Following the analysis of Nishijima and Sato, we use the chiral symmetric gauge field model to compute the s-wave amplitudes of the nonleptonic weak decays. It is pointed out that the weak interaction Lagrangian which has been derived from the assumption of octet W bosons is consistent with experiment. The p-wave amplitudes of the nonleptonic hyperon decay are obtained by using the sum rule that has been derived by the author. The result for both s- and p-wave amplitudes, which is a theoretical prediction with no adjustable parameter, is in fair accord with the experimental data.

Asymptotic SU(3) symmetry: Broken SU(3) and relations between baryon mass differences and non-leptonic hyperon decay amplitudes

The technique of asymptotic SU(3) symmetry is extended to the non-vanishing equal-time commutators between vector charges and the time-derivatives of other vector charges. Relations are obtained between the mass splittings in the 1 2 + baryon octet and the s-wave amplitudes for non-leptonic hyperon decays. Numerical results agree reasonably well with experimental data.

Answer to "Comments on `Duality and Nonleptonic Hyperon Decay' "

A recent result on duality in nonleptonic hyperon decay is clarified.Received 10 June 1970DOI:https://doi.org/10.1103/PhysRevD.2.1354©1970 American Physical Society

Comments on "Duality and Nonleptonic Hyperon Decay"

It is shown that the results of Nussinov and Rosner, for $S$-wave hyperon decay, do depend upon assuming current algebra and partially conserved axial-vector current, contrary to the claim made by them.

Analysis of Hyperon Nonleptonic Decay Amplitudes

Hyperon nonleptonic decay amplitudes are analyzed including relative phases and signs under the assumption of CP-invariance. Magnitudes of S- and P-wave amplitudes and their relative phases are evaluated, by taking account of the final state interactions. In A- and E­ decays, the Lll=1/2 rule holds in good accuracy. The relative sign of the amplitude A-7mco to A-7prc- is likely to be minus than plus, and the P-wave amplitudes of .s+ -'mrc+ and .s+ -7prco seem to be of equal sign. Both are consistent with the signs predicted by the Lll = 1/2 rule. In .s+-decay, the large phase shift difference between the !=1/2 and 3/2 S-wave states leads to IS(..r++)/S(.J:o+)j>O.l6, and it is found that sc.s++) is mainly imaginary. No evidence of large violation of CP is found in any processes.

Nonleptonic Hyperon Decays and Breaking of Chiral $SU(3) \otimes SU(3)$

Nonleptonic decays of hyperons are discussed in connection with the breaking of chiral SU(3) ⊗SU(3). We assume an effective ∂µJµ7(x) interaction of nonleptonic decays, which is reduced to HW(x) = -iG[Q7(x0)+Q57(x0), m0(S0(x)+λS8(x))]. The amplitudes of the decays calculated in hard-pion limit give a good agreement with experiment both for S-waves and P-waves. In addition, it is shown that the f/d ratio of scalar spurion is -3.06, which is very close to that of mass-splitting -3.05, and λ= 2.01. Therefore one may identify m0(S0(x)+λS8(x)) as a mass operator, and then the strength of weak ∂µJµ7(x) interaction is estimated to be G = 0.232 ×10-5.

Sum rule for nonleptonic hyperon decay

A simple sum rule is derived which relates the p-wave amplitudes to those of the s-wave of the non-leptonic hyperon decay.

Nonleptonic Hyperon Decays

Suzuka and Sugawara's theory of $S$-wave nonleptonic hyperon decay is reviewed to see to what extent their theory tests current algebra and the current\ifmmode\times\else\texttimes\fi{}current form of interaction. The only argument for the current\ifmmode\times\else\texttimes\fi{}current form in nonleptonic decays that it is all compelling is the vanishing of the $S$-wave amplitude $A({{\ensuremath{\Sigma}}_{+}}^{+})$ for the decay ${\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}n+{\ensuremath{\pi}}^{+}$. For the $P$-wave decay, to which the soft-pion formalism is inapplicable, an octet pole model is used. To fit the empirical $P$-wave amplitudes, strong-coupling shifts are required in both the $S$ and the $P$ waves. Including $\mathrm{SU}(3)$ symmetry breaking leads to parity-violating Born terms in the $S$ waves; to estimate the parity-violating spurion coupling, the kaon tadpole model and ${K}_{2}\ensuremath{\pi}$ decay rate are used. If pionic and kaonic strong-coupling constants are suppressed by $\frac{2}{3}$ and $\frac{1}{3}$, all the $S$- and $P$-wave amplitudes are given within 20%, but $A({{\ensuremath{\Sigma}}_{+}}^{+})$ now does not precisely vanish. If $A({{\ensuremath{\Sigma}}_{+}}^{+})=0$ exactly is insisted on, then the suppression of pionic strong-coupling constants by $\frac{2}{3}$ and $\frac{1}{3}$ is necessary.

Parity-Conserving Nonleptonic Decays of Hyperons and theSU(3)-Symmetry Breaking of the Strong Interaction

Implications of the similarity between the vertices lJ8B8II8 of the SU (3) ·breaking strong coupling and the parity-conserving nonleptonic hyperon decays are investigated. It is noted that, where the structure of the strong vertices is determined so as to be consistent with the P-wave decay amplitudes of hyperons, three or more strong-coupling constants can be re­ latively SU (3) -symmetric if the 'renormalized' F/ D-ratio is properly redefined. Dependence of the strong-coupling constants and the 'renormalized' Fj D-ratio on the SU (3)-breaking parameter is presented by setting the 'bare' F/ D ratio to be 2/3.

Investigation of Nonleptonic Hyperon Decays and Baryon β-Decays Based on the Quartet Model

The correspondence between the phenomenological laws for nonleptonic hyperon decays and the quartet model is investigated. It is shown that the S-wave decays can be explained by the single-urbaryon transition with the derivative type coupling, while the P-wave decays can be explained by the two-urbaryon transition. The quartet model is applied further to the baryon a-decays and it succeeds in describing the G A/Gv-ratio of the neutron a-decay and the F/D-ratio of the axial-vector coupling in a compatible way with the nonleptonic hyperon decays.

Weak-Interaction Theories ofCPNonconservation Applied to Hyperon Nonleptonic Decay

Possible $\mathrm{CP}$ violation in hyperon nonleptonic decay is investigated in the framework of several current-current weak-interaction theories which have recently been proposed. Of those studied, only the neutral-current models of Das and Oakes lead to unambiguous results. The Das model is extraordinary in that it predicts a maximal $\mathrm{CP}$ violation in the $\ensuremath{\Sigma}_{+}^{}{}_{}{}^{+}$ decay mode which, unfortunately, the final-state interactions conspire to imitate even if $\mathrm{CP}$ is conserved. This same model suggests a $\mathrm{CP}$-violating effect in the $\ensuremath{\Sigma}_{\ensuremath{-}}^{}{}_{}{}^{\ensuremath{-}}$ mode, which is roughly a 2\ifmmode^\circ\else\textdegree\fi{} departure from the final-state-interaction correction of 7\ifmmode^\circ\else\textdegree\fi{} to $\ensuremath{\Delta}$.

Nonleptonic Hyperon Decays and StaticSU(6) as aRest-Condition

It is shown that a new treatment of nonleptonic hyperon decays in SU(6) along the viewpoint proposed recently by the present author leads to a satisfactory understanding of the P-wave decays as well as the S-wave decays, deriving the Lee-Sugawara relation for both cases.