Non-leptonic Hyperon Decay Amplitudes Research Articles

Skyrme model and nonleptonic hyperon decays

This report is an attempt to explain both s- and p-wave nonleptonic hyperon decays by means of the QCD enhanced effective weak Hamiltonian supplemented by the SU(3) Skyrme model used to estimate nonperturbative matrix elements. The model has only one free parameter, namely, the Skyrme charge $e$, which is fixed through the experimental values of the octet-decuplet mass splitting $\Delta $ and the axial coupling constant $g_{A}$. Such a dynamical approach produces nonleptonic hyperon decay amplitudes that agree with experimental data reasonably well.

Strong isospin mixing effects on the extraction of [formula omitted] non-leptonic hyperon decay amplitudes

The existence of isospin admixtures in the physical Λ, π 0 complicates the extractionof ΔI = 3 2 non-leptonic hyperon decay amplitudes from experimental data, allowing contributions associated with large ΔI = 1 2 amplitudes to appear in the (nominally) ΔI = 3 2 amplitudes obtained ignoring these admixtures. We show how to correct for this effect to leading order in m d − m n and extracted the true ΔI = built 3 2 amplitudes. The resulting corrections are modest (<25%) for s-waves, but extremely large, ≌100% and ≌ 400% for Λ and Ξ p-wave, respectively.

Comparison of theoretical and experimental nonleptonic hyperon decay amplitudes

It is shown that fitting Pauli amplitudes instead of Dirac amplitudes reduces substantially the mismatch in fits to experiment of theoretical parity-violating and parity-conserving nonleptonic hyperon decay amplitudes for massless pions obtained from current algebra and PCAC, effective chiral lagrangians, or lowest order chiral perturbation theory.

Non-leptonic hyperon decays in the chiral bag model

ΔS=1 non-leptonic hyperon decay amplitudes are calculated within a recently developed scheme, whose theoretical support is the chiral bag model. This model is not only used to describe baryons, also to incorporate the weak interactions via SU(2) L⊗U(1) local gauge invariance of its lagrangian. The large sensitivity to the pion energy dependence of the S waves is pointed out. Experimental amplitudes are well reproduced for a bag radius of ∼0.65 fm.

?T=3/2 amplitudes of nonleptonic hyperon decays

It is pointed out that the usual factorization approximation for the ΔT=3/2 part of the effective weak Hamiltonian has to be modified by including theK−π pole terms for thep-wave nonleptonic hyperon decay amplitudes.

Evidence for Corrections to Soft-PionS-Wave Nonleptonic Hyperon-Decay Amplitudes

Evidence is found for corrections to the soft-pion $S$-wave nonleptonic hyperon-decay amplitudes from the observed deviation from the generalized Lee-Sugawara relation $2A({\ensuremath{\Xi}}_{\ensuremath{-}}^{\ensuremath{-}})+A({\ensuremath{\Lambda}}_{\ensuremath{-}}^{0})+{(\frac{3}{2})}^{\frac{1}{2}}A({\ensuremath{\Sigma}}_{\ensuremath{-}}^{\ensuremath{-}})=0$. These corrections, assumed to come from the low-lying ${\mathrm{\textonehalf{}}}^{\ensuremath{-}}$ excited baryon intermediate states, are estimated experimentally with use of the expressions suggested by the quark model and are found to reduce significantly the soft-pion results.

Direct quark-model calculation of weak nonleptonic matrix elements

It is shown how wave-packet techniques developed by Donoghue and Johnson may be utilized to calculate parity-violating nonleptonic hyperon decay amplitudes directly---without the use of current algebra and PCAC (partial conservation of axial-vector current).

Non-leptonic hyperon decays and harmonic oscillator quark model for baryons

Non-leptonic hyperon decay amplitudes have been calculated using the Weinberg-Salam model with QCD corrections. Baryon states have been described using the harmonic oscillator (Isgur-Karl) model. The results agree with experiments and with the results obtained previously using the MIT bag model for baryons. It seems that the theoretical predictions are practically quark-model independent.

Calculation of non-leptonic hyperon decay amplitudes without arbitrary parameters

Non-leptonic hyperon decay amplitudes are calculated starting from the Weinberg-Salam model and employing the QCD renormalized effective weak Hamiltonian which includes the effects of SU(4) symmetry breaking. The amplitudes are described through the commutator approximation (s-wave), the ground-state pole approximation (p-wave) and separable contributions. Values of all parameters are taken from either experiments or theoretical estimates. Such a no-parameter approach works well for s-wave amplitudes, reproducing their relative signs and absolute magnitudes. For p-wave amplitudes the relative signs are correctly reproduced, while some magnitudes are too small. The importance of separable contributions and of the so-called “penguin” terms is explicitly shown.

The magnitude of the parity-violating nucleon-pion couplingN 0-, and final-state interactions

The purpose of this letter is to present a new estimate for the magnitude ot the parity-violating amplitude ~ pT:(henceforth denoted by N~ based on the inclusion of final-state interactions. I t is important to know the magnitude of iV ~ because pion exchange contributes to the long-range par t of the weak parity-violating internucleon potential which manifests itself in parity-violating nuclear transitions (~). In a previous paper (2) TROFIMENKOFF and the author showed that the inclusion of final-state interactions in nonleptonic hyperon decay amplitudes led to a good fit of Sand P-wave amplitudes to experiment, in contrast to the mediocre fit obtained in the conventional current-algebra-PCAC method. Our conclusion in this letter is that the inclusion of final-state interactions, which has been shown (2) both to be essential and to lead to a much improved agreement with experiment for nonleptonic hyperon decays, significantly modiiics the older estimate for N ~ based on the current-algebraPCAC method (3.4). We now briefly review our method for including the effect of final-state interactions on parity-violating nonleptonie hyperon decays and the parity-violating AS----0 process j~--~pT:-. Our notation here is identical with that of ref. {2). This paper (2) should be referred to for general orientation and also specific results. The matrix element T for the parity-violating processes a ~ f l + ~(c) (we are t reat ing both AS = 0 and AS : 1 amplitudes here, because we shall later relate the AS = 0 to the AS-----1 amplitudes) with corresponding momenta P~-+P~-~-k and masses M ~ M~ + m can be wri t ten as

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.

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.

Phenomenological Chiral Model for Nonleptonic Hyperon Decays

The $S$- and $P$-wave nonleptonic hyperon decay amplitudes are calculated using a chiral-invariant effective Lagrangian. This reproduces the current-algebra results in a very simple way, the baryon pole diagram arising without any ambiguity whatsoever. As is well known, this leaves us with the wrong ratio of $S$- to $P$-wave amplitudes. It is noted that one way out of this dilemma is to add another term to the effective Lagrangian which vanishes in the limit of zero pion four-momentum, and hence contributes to the physical answer without contributing to the current-algebra result. The addition of the ${K}^{*}$ pole diagram leaves us with a rough three-parameter fit to all the amplitudes plus the $K\ensuremath{\rightarrow}2\ensuremath{\pi}$ amplitudes.

Decuplet Poles in the Tadpole Model for Nonleptonic Hyperon Decays

Using a previously discussed dynamical model, we show that the baryon octet and decuplet poles alone lead to a simple explanation of the observed parity-violating nonleptonic hyperon decay amplitudes, essentially without involving any unknown parameters, provided that the strong interactions are $\mathrm{SU}(3)$-invariant.

Currents with irregular charge-conjugation properties and the non-leptonic hyperon decays

The non-leptonic hyperon decay amplitudes are investigated under the assumption that the weak hadronic current in the CP-invariant current × current non-leptonic Hamiltonian belongs to an octet representing a mixture of a “regular” and an “irregular” octet with respect to charge-conjugation and that the irregular octet, like the regular one, belongs to the (8, 1) representation of SU(3) × SU(3). The results obtained suggest that the vanishing of the s-wave amplitude A( Σ + +), for the Σ + → n + π + decay may be connected with the presence of irregular currents and independent of the assumption that the ΔT = 1 2 transitions predominate. The relation between reduced matrix elements leading to A( Σ + +) = 0 simultaneously ensures the validity of the ΔT = 1 2 rule in Λ and Σ decays and predicts a violation of this rule for Ξ-decay.

Current Algebra ofSU(6)Wand Nonleptonic Hyperon Decays

The parity-violating and parity-conserving parts of the nonleptonic hyperon decay amplitudes are studied in the framework of the group ${\mathrm{SU}(6)}_{W}$. Describing the decay in terms of the usual weak Hamiltonian ${H}_{w}$ bilinear in Cabibo currents by the amplitude $〈{B}_{2}M|{H}_{w}(0)|{B}_{1}〉$, the meson $M$ is contracted from the final state, the partially conserved axial-vector-current hypothesis is introduced and the meson is taken off the mass shell. The amplitude is then evaluated at an arbitrary point off the mass shell of the meson, assuming the quark model for the currents and a single-particle pole approximation. The nine $S$-wave and twelve $P$-wave decays of the baryons in the 56-dimensional representation of ${\mathrm{SU}(6)}_{W}$ are found to be determined by four parameters, one of which relates the $S$- and $P$-wave decays. A new $P$-wave sum rule for the baryon octet decays $8\sqrt{3}P({{\ensuremath{\Xi}}_{\ensuremath{-}}}^{\ensuremath{-}})=3P({{\ensuremath{\Sigma}}_{0}}^{+})+3\sqrt{3}P({{\ensuremath{\Lambda}}_{\ensuremath{-}}}^{0})\ensuremath{-}(\frac{5}{\sqrt{2}})P({{\ensuremath{\Sigma}}_{+}}^{+})$ is found, as well as new sum rules relating the ${\ensuremath{\Omega}}^{\ensuremath{-}}$ decay to the decays of the baryon octet. With the latter result, the nonleptonic decay rates of the ${\ensuremath{\Omega}}^{\ensuremath{-}}$ are calculated from experimental octet decay amplitudes.

A New Triangle Relation for Nonleptonic Hyperon Decay Amplitudes as a Consequence of the Octet Spurion and theRSymmetry

A triangle relation TΛ=2TΞ-+√3TΣ0 is obtained for the nonleptonic decay amplitudes of Λ→p+π-, Σ+→p+π0 and Ξ-→Λ+π-. This relation is shown to be in excellent agreement with the experiment especially when γΣ+→p+π0>0. The assumptions are the octet spurion hypothesis and the R symmetry.