Nonleptonic Hyperon Decays Research Articles

Weak hyperon decays in heavy baryon chiral perturbation theory: Renormalization and applications

The complete renormalization of the weak Lagrangian to chiral order ${q}^{2}$ in heavy baryon chiral perturbation theory is performed using heat kernel techniques. The results are compared with divergences appearing in the calculation of Feynman graphs for the nonleptonic hyperon decay $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Lambda}}p{\ensuremath{\pi}}^{\ensuremath{-}}$ and an estimate for the size of the counterterm contributions to the s-wave amplitudes in nonleptonic hyperon decays is given.

Hyperon nonleptonic decays in chiral perturbation theory reexamined

We recalculate the leading nonanalytic contributions to the amplitudes for hyperon nonleptonic decays in chiral perturbation theory. Our results partially disagree with those calculated before, and include new terms previously omitted in the P-wave amplitudes. Although these modifications are numerically significant, they do not change the well-known fact that good agreement with experiment cannot be simultaneously achieved using one-loop S- and P-wave amplitudes.

Chiral perturbation theory for [formula omitted] hyperon decays

We study the |ΔI| = 3 2 amplitudes of hyperon non-leptonic decays of the form B → B′ π in the context of chiral perturbation theory. The lowest-order predictions are determined in terms of only one unknown parameter and are consistent within errors with current data. We investigate the theoretical uncertainty of these predictions by calculating the leading non-analytic corrections. We also present an estimate for the size of the S-wave Λ and Ξ decays which vanish at leading order. We find that the corrections to the lowest-order predictions are within the expectations of naive power counting and, therefore, that this picture can be tested more accurately with improved measurements.

A detailed determination of the a priori mixing angles in non-leptonic decays of hyperons

Non-leptonic decays of hyperons can provide a detailed determination of the a priori mixing angles that appear in physical hadrons in the approach in which non-perturbative flavour and parity violations are present in tiny pieces of the hadron mass operator. The determination of such angles in these decays will provide a benchmark to test their necessary universality-like property in other types of decays. Our main result is that the magnitudes of the a priori mixing angles can be determined quite accurately.

A priori mixed hadrons, weak radiative and non-leptonic decays of hyperons

A priori mixings of eigenstates in physical states are quantum mechanical effects well known in several realms of physics. The possibility that such effects are also present in particle physics, in the form of flavour and parity mixings, is studied. Applications to weak radiative and non-leptonic decays of hyperons are discussed.

Non-leptonic hyperon decays in chiral perturbation theory

The non-leptonic hyperon decays are analyzed up to one-loop order including all counterterms in the framework of heavy baryon chiral perturbation theory. We use the exchange of the spin-\(\frac{3}{2}\) decuplet resonances as an indication of which low-energy constants contribute significantly to these investigated processes. We choose four independent decay amplitudes that are not related by isospin relations in order to perform a fit for the pertinent low-energy constants and find a satisfactory fit both for s- and p-waves. The chiral corrections to the lowest order forms for the s-waves are moderate whereas there are significant modifications of the p-wave amplitudes.

Non-leptonic hyperon decays in chiral perturbation theory

The non-leptonic hyperon decays are analyzed up to one-loop order including all counterterms in the framework of heavy baryon chiral perturbation theory. We use the exchange of the spin-3/2 decuplet resonances as an indication of which low-energy constants contribute significantly to these investigated processes . We choose four independent decay amplitudes that are not related by isospin relations in order to perform a fit for the pertinent low-energy constants and find a satisfactory fit both for s- and p-waves. The chiral corrections to the lowest order forms for the s-waves are moderate whereas there are significant modifications of the p-wave amplitudes.

|ΔS|=1 hadronic weak decays of hyperons in a soliton model

Abstract We study the parity violating hyperon non-leptonic weak decays in the three flavor Skyrme model. We follow the approach in which the symmetry breaking terms in the action are diagonalized exactly within the collective coordinate approximation. We show that although this method introduces some configuration mixing, the ΔI =1/2 rule is numerically well satisfied. In addition, and in contrast to previous calculations, we show that not only the relative amplitudes are in good agreement with the empirical values but also their absolute values. The issue of whether the strong interaction enhancement factors should be included in soliton calculations is also addressed.

Isospin mixing and model dependence

We show that recent calculations of \Delta I=3/2 effects in nonleptonic hyperon decay induced by m_d-m_u\neq 0 are subject to significant model dependence.

Role of(3*,3)operators in the chiral symmetry approach to nonleptonic decays andCPviolation

We study the kaon-pole diagrams which involve the nonvanishing tadpole transition {l_angle}0{vert_bar}O{sub 6+i7}{vert_bar}{bar K}{sup 0}{r_angle} , where the operator O belongs to the (3{sup {asterisk}},3) representation of chiral SU(3){times}SU(3). As is well known, the pole contribution exactly cancels the direct contribution to K-2{pi} and s-wave nonleptonic hyperon decay in the SU(3) and chiral limits. It is shown that there are additional contributions which vanish in the SU(3) limit, these being of order (m{sub K}{sup 2}{minus}m{sub {pi}}{sup 2})/m{sub K}{sup 2} or (m{sub B{sup {prime}}}{minus}m{sub B})/m{sub K}{sup 2}. The contribution of such corrections to direct CP violation in K{r_arrow}2{pi} and hyperon decays is calculated, which could in some cases be a substantial fraction of the standard model predictions for direct CP violation in these transitions. {copyright} {ital 1997} {ital The American Physical Society}

Instantons and nonleptonic hyperon decays.

The instanton-induced term is included in an analysis of nonleptonic strangeness-changing hyperon decays. The same type of analysis has led previously to a reasonable qualitative, and to some extent quantitative, description of the decay amplitudes. The instanton contributions do not improve old results. Data favor a very small instanton influence.

Spin-flavor structure of large Nc baryons.

The spin-flavor structure of large ${\mathit{N}}_{\mathit{c}}$ baryons is described in the 1/${\mathit{N}}_{\mathit{c}}$ expansion of QCD using quark operators. The complete set of quark operator identities is obtained, and used to derive an operator reduction rule which simplifies the 1/${\mathit{N}}_{\mathit{c}}$ expansion. The operator reduction rule is applied to the axial vector currents, masses, magnetic moments, and hyperon nonleptonic decay amplitudes in the SU(3) limit, to first order in SU(3) breaking, and without assuming SU(3) symmetry. The connection between the Skyrme and quark operator representations is discussed. An explicit formula is given for the quark model operators in terms of the Skyrme model operators to all orders in 1/${\mathit{N}}_{\mathit{c}}$ for the two flavor case.

On the gluon dipole penguin contribution to nonleptonic hyperon decays

We discuss the effect of the gluon dipole penguin operator in the amplitudes for nonleptonic hyperon decays. Making explicit use of chiral symmetry, we clarify the circumstances under which direct and tadpole contributions could cancel, leading to a suppressed contribution.

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.

Quark diagrams and the Delta I=1/2 rule.

Nonleptonic decays of hyperons are analyzed on the basis of the quark-diagram scheme. It is shown that the external $W$-emission amplitudes and the internal $W$-emission amplitudes lead to the breaking of the $\ensuremath{\Delta}I=\frac{1}{2}$ rule. A sum rule among the decay amplitudes which include the $\ensuremath{\Delta}I=\frac{3}{2}$ effects is derived.

Nonrealitivistic chiral expansion and nonleptonic decays of octet and decuplet baryons

We discuss the chiral lagrangian for J P = 1 2 + octet and J P = 3 2 + decuplet baryons in the language of the heavy particle effective theory. We show that the effective theory qualitatively reproduces the Pauli amplitudes for the nonleptonic hyperon decays, calculated recently by Trofimenkoff. We discuss the relation of our results to nonrelativistic SU(6). We argue that we can consistently classify the meson-baryon interaction terms in lowest order in the momentum expansion according to their transformation properties under nonrelativistic SU(6). Nevertheless, the theory as a whole remains explicitly Lorentz invariant. We explain why this does not run afoul of the theorems concerning interacting relativistic SU(6) theories. We use this SU(6) classification to discuss the relation between the nonleptonic Ω − decays and the nonleptonic decays of the octet baryons. We find that the Ω − decays cannot be explained by any interaction term transforming simply under SU(6) because the nonleptonic Ω − decays do not display the pronounced ΔI = 1 2 enhancement seen in the octet hyperon decays. Any explanation of the Ω − decays requires a fine tuning of the parameters in the effective theory. We speculate that this problem may point to a flow in the basic assumption that ΔI = 1 2 four-quark operators, universally enhanced by QCD, are the dominant mechanism behind the ΔS = 1 nonleptonic decays.

Rescattering effects and the constant of weak pion-nucleon coupling

Renormalization of the weak pion-nucleon coupling constant ƒ π NN due to rescattering of the emitted π-meson is considered. The mechanism controlling this renormalization involves strong emission of the π-meson followed by its P-odd rescattering on the nucleon. This mechanism is shown to suppress the ƒ π NN value. The suppression factor depends upon the form factor in the strong πNN vertex. For realistic values of the cut-off parameter in this vertex the ƒ π NN coupling constant proves to be diminished by a factor of ∼4. The resulting value of ƒ π NN calculated in the quark model with current quark masses is compatible with experimental bounds. So the rescattering mechanism removes the disagreement between the (large) theoretical value of ƒ π NN and the (small) experimental limit without deteriorating the dynamic enhancement of the ΔT = 1 2 amplitude in nonleptonic hyperon decays.

Strong evidence for a new strange matrix element

I show that there exists a four quark operator O s involving strangequarks whose matrix elements 〈nπ 0| O s|p〉 and 〈n| O s|p〉 may be computed as they are related by SU (3) symmetry to the weak nonleptonic hyperon decays. The matrix elements are large as a consequence of the ΔI = 1 2 rule, or octet enhancement. This computation provides the strongest evidence yet for large strange matrix elements in nonstrange particle states.

Hyperon decays and quark-quark correlations

The nonleptonic weak Hamiltonian strongly favours the annihilation and creation of correlated quark pairs in spin zero and colour antitriplet states. It is demonstrated that bothS- andP-wave nonleptonic hyperon decays are well described by this mechanism if supplemented by factorization contributions. Apart from the use of mass values and the π-nucleon coupling constant, the results are obtained in a parameter free way. Since the diquark properties applied are identical to the ones used in the calculation ofK→2π decays and the long range contribution to theKL−KS mass difference, a coherent physical picture of dominant nonperturbative effects in the low energy domain is reached.

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.