Strangeness-changing Current Research Articles

Allomorphic corrections to semileptonic processes

The notion of allomorphic corrections to $S$-matrix elements for semileptonic processes, which by definition are absent in the lowest nontrivial order of perturbation theory, is introduced and analyzed. The complete fourth-order allomorphic corrections to the leptonic weak currents are calculated in an arbitrary gauge model of weak and electromagnetic interactions, treating the strong interactions (assumed mediated purely by gauge vector gluons) to all orders. These results are used to analyze the induced leptonic pseudoscalar current in charged-pion decay, and it is shown that weak restrictions on particle masses suffice to preserve the $V\ensuremath{-}A$ structure at the leptonic vertex to $O(\ensuremath{\alpha}{G}_{F})$. A preliminary discussion of the allomorphic corrections to hadronic weak currents is presented in the context of neutral-kaon decay (${K}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}$). It is shown that in theories in which the kaon field dimensionality is two or less, the usual suppression mechanisms involving charmed quarks probably do not suffice to remove induced neutral, strangeness-changing currents in $O(\ensuremath{\alpha}{G}_{F})$.

Current-current sugawara form and pion-kaon scattering lengths

It is shown that theSU2 ×SU2 invariant pion-kaon Lagrangians constructed by using the matrix method of Gursey, or the covariant derivative method of Weinberg, or by reduction from anSU3 ×SU3 invariant Lagrangian for the pseudoscalar meson octet, respectively, do not all give the same result. It is further shown that only the pion-kaon Lagrangian obtained by using the matrix method can be expressed in general in the current-current Sugawara form in terms of the vector and the axial vector pion currents and the strangeness-changing currents. The origin of this discrepancy is due to a pion-kaon interaction term that is itselfSU2 ×SU2 invariant and hence may be multiplied by an arbitrary parameter without spoiling theSU2 ×SU2 invariance of the Lagrangian. The matrix method, or equivalently the current-current Sugawara form, and the reduction method prescribe definite, though different, values for this parameter, whereas the covariant derivative method leaves the parameter undetermined. Since the pionkaon scattering lengths depend on the value of this parameter, it is possible, in principle, to distinguish the various alternatives experimentally, if the pion-kaon scattering lengths can be measured to an accuracy of the order of (10 ÷ 20) percent. In particular, such a measurement would provide a direct test of the current-current Sugawara form for theSU2 ×SU2 invariant pion-kaon Lagrangian.

Unified theory of weak and electromagnetic interactions with rule

An SU(2) ⊗ U (1) gauge theory of weak and electromagnetic interactions satisfying the ΔI = 12 rule is proposed, which has the following characteristic: (i) A neutral boson Z, coupling to the neutral strangeness-changing current is used in addition to the usual charged ones, to give the ΔI = 12 rule in the standard fashion. Couplings are chosen such that the Z decouples from the observed leptons, in order to agree with experiment. (ii) It is assumed that the |ΔY| = 2 transitions due to neutral vector-boson exchange cancel the |ΔY| = 2 contributions due to charged vector-boson exchange. This constraints the Cabibbo angle in a manner consistent with experiment.

Recent Applications of KN Forward Dispersion Relations and Sum Rules

AbstractRecent applications of kaon‐nucleon forward dispersion relations, superconvergence relations, finite energy sum rules, derivative sum rules, and the Adler‐Weisberger sum rule are reviewed. These dispersion relations and sum rules have been used for the determination of the KNA and KN coupling constants, the phases of the kaon‐nucleon forward scattering amplitudes, and the Regge pole parameters, and have allowed tests of the PCAC hypothesis for strangeness‐changing currents. They also provide important constraints which help to resolve ambiguities in the phenomenological analysis of the scattering data. A critical comparison of various methods which have been proposed is given, the theoretical predictions are compared with experiment when possible, and our present knowledge of the kaon‐nucleon interaction parameters is summarized. Some new results are presented.

Renormalization of the K_{e3} Form Factor

The renormalization of the ${K}_{e3}$ form factor by the strong SU(3)-nonconserving interaction is calculated from the Fubini-Furlan sum rule and an experimental determination of the derivative of the matrix element of the divergence of the strangeness-changing current. The calculated renormalization is in agreement with that determined from measurements of $\mathrm{ft}$ values in Fermi nuclear $\ensuremath{\beta}$ transitions and of the absolute rate for ${K}^{+}\ensuremath{\rightarrow}{e}^{+}{\ensuremath{\pi}}^{0}\ensuremath{\nu}$.

Partially Conserved Currents and Weak Form Factors

A modification of the Goldberger-Treiman relations (for ${G}_{A}$ and for the induced pseudoscalar ${G}_{P}$) is obtained by assuming, in addition to the hypothesis of partially conserved axial-vector currents, that the matrix element of the axial-vector current between two nucleon states is dominated by the ${A}_{1}(1080)$ and $\ensuremath{\pi}$. This yields a more detailed structure of the weak form factors. The result is discussed. Extending this line of thought to the case of strangeness-changing currents, which we assume to be "partially conserved," we obtain corresponding expressions for the strangeness-changing induced scalar and pseudoscalar form factors. A relation is obtained relating the induced scalar coupling to the ${K}_{l3}$ form-factor ratio $\ensuremath{\xi}=\frac{{f}_{\ensuremath{-}}(0)}{{f}_{+}(0)}$. These results are useful in a detailed study of the Cabibbo theory. A value for the ${K}_{l3}$ parameter $\ensuremath{\xi}$ is obtained by combining our results with the soft-pion current-algebra result of Callen and Treiman. It ranges from -0.15 to -0.10, depending on the experimental value of $\frac{{f}_{K}}{{f}_{\ensuremath{\pi}}}$.

Meson baryon sum rules

The PCAC consistency condition, the Adler-Weisberger sum rule and the dispersion superconvergent sum rule have been saturated with resonance contributions only. Strangeness-changing currents and strangeness-conserving currents have been considered and compared. The results obtained also support PCAC for the strangeness conserving current. While in theπN case PCAC and the Adler-Weisberger sum rule are almost saturated with the famous N 33 * resonance only, in the KN caseY 1 * (1385),Y 0 * (1405) andY 0 * (1520) seem to be sufficient. The superconvergent sum rule works very well in the case ofπN scattering, including the contribution of twelve resonances. For KN scattering it can be neither established nor disapproved.

Neutral Semileptonic Decays ofKMesons

The question of the existence of neutral leptonic currents coupled to the neutral strangeness-changing current is discussed in the light of recent experimental limits on ${{K}_{2}}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ and ${{K}_{2}}^{0}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}$ decay rates.

On the existence of weakly interacting charge-retention currents

Cross sections and cross-section ratios of strangeness conserving reactions and expressions for ratios and branching ratios of strangeness changing decays are presented, which can serve as tests of the existence of weakly interacting nucleon and lepton currents of the charge-retention variety, and of the selection rules which govern them. The calculations are principally based on two interaction models within the framework of isospace; as to the nucleon-lepton inteaction, one model is charge-independent while the other involves only neutral currents in addition to charge-exchange currents. The strangeness changing currents are assumed to obey the ΔI = 1 2 rule.

Violation of conservation of strangeness-changing current

Violation of conservation of strangeness-changing current

Universal theory of semi-weak interactions

A universal theory of semi-weak interactions is proposed on the basis of a new baryon-lepton symmetry principle and the conservation of a new quantum numberX, the « weak hypercharge ». The universality of the theory is achieved by coupling two intermediate charged vector bosons of different mass andX assignment to the strangeness-conserving and strangeness-changing currents. Acceptance of the conserved vector current hypothesis for strangeness-conserving processes leads to definite statements concerning the fields describing the electron and muon neutrinos, the (ΔQ/ΔS) properties of the strangeness-changing current and the existence of neutrino flip. The more striking experimental predictions of the theory (e.g., neutrino flip accompanied by hyperon production) are discussed in some detail. Alternative formulations of the theory are examined and it is shown that very little flexibility is allowed within the framework of a dynamical baryon-lepton symmetry principle.

Remarks on strangeness non-conserving weak leptonic interactions

The possibility that both the leptonic currents and the vector K- π resonance, M, couple with the same strangeness changing currents is discussed. The magnitude of renormalized coupling constant and the form factors of K μ3 -decay are discussed. A reasonable consistency with the present experimental situations with regard to the leptonic strangeness changing processes and to the K- π resonance is indicated.

A model for the K μ3 and K e3 decay modes

We propose a model for the K μ3 and K e3 decay modes based on the analytic properties of the invariant form factors and on the notion of a “partially conserved” strangeness-changing current. While the expressions we derive for the K μ3, K e3 branching ratio and the various spectra involve an arbitrary parameter, the observed large branching ratio of K μ3 to K e3, of the order of unity, leads to very definite predictions about the pion energy spectra in the two decay modes. If the model is successful, these decay modes present a good test of the intermediate vector boson hypothesis for weak interactions, provided the vector boson is not much heavier than the K-meson.