Partial Conservation Of Axial-vector Current Research Articles

Long-range effects in the weak parity-violating pion-nucleon coupling.

The weak parity-violating pion-nucleon coupling constant ${F}_{\ensuremath{\pi}}$ is calculated by using an approach based on PCAC (partial conservation of axial-vector current), current algebra, and dispersion relations. We find the result ${F}_{\ensuremath{\pi}}$=(2.1--5.5)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}7}$.

Decays of heavy unstable neutrino

It is shown that the branching fractions for the decay modes ${\ensuremath{\pi}}^{0}{\ensuremath{\nu}}_{a}$ and ${\ensuremath{\pi}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ of the heavy unstable neutrino ${\ensuremath{\nu}}_{3}$ are comparable with the ${\ensuremath{\pi}}^{+}{e}^{\ensuremath{-}}$ mode emphasized by Shrock. The required ${\ensuremath{\pi}}^{0}$ decay constant (${f}_{{\ensuremath{\pi}}^{0}}$) pertaining to the neutrino neutral-current matrix element between ${\ensuremath{\pi}}^{0}$ and the vacuum is evaluated using the Goldberger-Treiman relation and PCAC (partial conservation of axial-vector current).

Nearly massless pion in a modified bag model

The properties of the pions are studied in a modified bag model. The pion wave function is approximated by the projection of the qq-bar wave function in the bag that has zero center-of-mass motion. The parameters of the model are determined by the usual stability condition and the additional requirement that the pion mass m/sub ..pi../ approach zero in a manner consistent with the hypothesis of partially conserved axial-vector current (PCAC). This fixes the bag volume energy to be m/sub ..pi..//4. Static pion properties are in good agreement with data provided that quarks in the pion are correlated by a modulating function characterized by a correlation momentum p/sub c/approx.300 MeV/c. The bag-model and Nambu-Goldstone views of the pion are reconciled as a distinction is made between constituent and current quarks. Assuming their fields to be related by a transformation analogous to that of Nambu and Jona-Lasinio we calculate the vacuum expectation value of the current quark density to be 0.04 GeV/sup 3/, corresponding to a current quark mass of 5 MeV. We test our ideas by calculating, to first order of the gluon-exchange interaction, the pion decay constant and the vector and axial-vector form factors for pion radiative decay. Inmore » our model the pion decay constant satisfies the PCAC requirement that it has a finite value in the limit of zero-mass pion.« less

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).

Pion-pole term in electroproduction of off-mass-shell pions

The dependence of the invariant amplitudes for electroproduction of off-mass-shell pions on the pion Born term is investigated when current-algebra Ward identities and PCAC (partial conservation of axial-vector current) are used to determine pion electroproduction invariant amplitudes. We show that an amplitude satisfying the Ward identities can be constructed starting from the usual Born terms which do not satisfy them and that this same amplitude will be obtained for a large class of input Born terms.

Application of current algebra and partial conservation of axial-vector current to proton-antiproton annihilations

A soft-pion study using current algebra and the partially conserved axial-vector current (PCAC) hypothesis is made of the proton-antiproton annihilation process p-barp..-->..K/sup +/K/sup -/3..pi../sup 0/. Of the three neutral pions only two are considered as soft with the third pion forming part of the external final state. The differential rate for the process is normalized to the differential rate of the corresponding process without the soft pions. Theoretical predictions for the branching ratios at various antiproton momenta are compared with the existing experimental data.

Soft-pion emission in $$\bar pp$$ annihilations

Current algebra and partially conserved axial-vector current (PCAC) hypothesis are applied to study the proton-antiproton annihilation process\(\bar pp \to K^ + K^ - 4\pi ^0 \), treating all the emitted pions as soft. While the σ-terms are ignored, the double commutators giving rise to the divergence of axial-vector currents and representing π−π effects are retained. We express the rate for the process in a fully differential form in terms of the chosen variables and normalize it to the differential rate for the corresponding process without the soft pions. Branching ratios obtained after numerical integration of the expressions are given for various centre-of-mass energies and compared with the available experimental data.

Partially conserved axial-vector current condition in the quark model:GAGVfor vector mesons and theωρπcoupling constant

The PCAC (partially conserved axial-vector current) condition is implemented at the quark level for hadrons considered as bound states of constituent quarks. Using the Goldberger-Treiman relation and the $\ensuremath{\omega}\ensuremath{\rho}\ensuremath{\pi}$ coupling constant, it is shown that $\frac{{G}_{A}}{{G}_{V}}$ for the $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\rho}$ Gamow-Teller transition is lower than the quark-model prediction by 20%. This supports the current view that $\frac{{G}_{A}}{{G}_{V}}$ for bound quarks is reduced by confinement effects. With this reduction, the decay rates $\ensuremath{\Gamma}({D}^{*}\ensuremath{\rightarrow}D{\ensuremath{\pi}}^{0})$ are calculated and found to be more or less in agreement with measurements.

Current algebra and PCAC-application to p̄p→ K+K-π0π0π0

Current algebra and the partially conserved axial-vector current (PCAC) hypothesis are employed to arrive at the amplitude for the emission of three neutral soft pions in the annihilation process p-bar p to K+K-. All final-state pi - pi scattering effects coming out of the current-algebra approach are taken into account. The differential rate for the process is normalised to the rate of the original reaction without the soft pions. Branching ratios w(pp to K+K- pi 0 pi 0 pi 0)/w(pp to K+K-) are computed for different centre-of-mass energies. A comparison with the existing experimental data is made and the agreement is found to be reasonable.

Pionic decays and saturation of current-algebra sum rules in a nonrelativistic expansion of the quark shell model

Pionic decays of hadrons are calculated using a PCAC (partial conservation of axial-vector current) prescription and a quark shell model with quarks bound by a central potential, described by the Dirac equation. The Dirac Hamiltonian and operators are expanded in $\frac{v}{c}$, the internal quark velocity. Then, one finds an exact saturation of the current-algebra sum rules as defined in the SU(2) \ensuremath{\bigotimes} SU(2) symmetry of Gilman-Harari and Weinberg up to order $\frac{{v}^{4}}{{c}^{4}}$. The saturation is obtained without need of exotics, with the usual excitations of the ground state. The relation with the $P=\ensuremath{\infty}$ approach is clarified. The corrections found with respect to previous quark models in $L=2$ decays are discussed. They do not solve the problem of $\mathrm{SU}{(6)}_{W}$ coupling signs. Finally, the whole Weinberg scheme of linear SU(2) \ensuremath{\bigotimes} SU(2) symmetry is completed by the expression of the chiral-breaking part of the mass operator ${{m}_{4}}^{2}$.

Lie-algebra approach to symmetry breaking

A formal Lie-algebra approach to symmetry breaking is studied in an attempt to reduce the arbitrariness of Lagrangian (Hamiltonian) models which include several free parameters and/or ad hoc symmetry groups. From Lie algebra it is shown that the unbroken Lagrangian vacuum symmetry can be identified from a linear function of integers which are Cartan matrix elements. In broken symmetry if the breaking operators form an algebra then the breaking symmetry (or symmetries) can be identified from linear functions of integers characteristic of the breaking symmetries. The results are applied to the Dirac Hamiltonian of a sum of flavored fermions and colored bosons in the absence of dynamical symmetry breaking. In the partially reduced quadratic Hamiltonian the breaking-operator functions are shown to consist of terms of order ${g}^{2}$, $g$, and ${g}^{0}$ in the color coupling constants and identified with strong (boson-boson), medium strong (boson-fermion), and fine-structure (fermion-fermion) interactions. The breaking operators include a boson helicity operator in addition to the familiar fermion helicity and "spin-orbit" terms. Within the broken vacuum defined by the conventional formalism, the field divergence yields a gauge which is a linear function of Cartan matrix integers and which specifies the vacuum symmetry. We find that the vacuum symmetry is chiral SU(3)\ifmmode\times\else\texttimes\fi{}SU(3) and the axial-vector-current divergence gives a PCAC (partially conserved axialvector current)-like function of the Cartan matrix integers which reduces to PCAC for SU(2)\ifmmode\times\else\texttimes\fi{}SU(2) breaking. For the mass spectra of the nonets ${J}^{P}={0}^{\ensuremath{-}},\frac{1}{{2}^{+}},{1}^{\ensuremath{-}}$ the integer runs through the sequence 3,0, - 1, - 2, which indicates that the breaking subgroups are the simple Lie groups. Exact axial-vector-current conservation indicates a breaking sum rule which generates octet enhancement. Finally, the second-order breaking terms are obtained from the second-order spin tensor sum of the completely reduced quartic Hamiltonian. The breaking terms include the "anomalous" $^{*}F_{\ensuremath{\mu}\ensuremath{\nu}}{F}_{\ensuremath{\mu}\ensuremath{\nu}}$ term found by Schwinger, as well as fermion and boson helicity-breaking terms. Nonvanishing of the axial-vector-current divergence indicates the presence of solitons or, for electromagnetic coupling, of magnetic monopoles as the sources of strong fields.

Hyperon decays revisited

We examine the standard quantum-chromodynamics-inspired description of nonleptonic hyperon decays. We point out that the discrepancy between s- and p-wave amplitudes which emerged from a PCAC (partial conservation of axial-vector current) analysis cannot be cured by the inclusion of factorizable diagrams. We include anomalous contributions to the axial-vector current divergence which appear in the presence of the effective local Fermi interaction. Like factorizable diagrams, these preserve the successful results of PCAC for s-wave amplitudes, but are insufficient to give a quantitatively satisfactory description. We estimate the decay rates for ..cap omega../sup -/ ..-->.. ..xi..*..pi.. and ..xi../sup 0/l/sup -/..nu../sub l/ in view of further tests of the standard model.

Partial conservation of axial-vector current effects in the MIT bag model

We extend the calculations of the MIT-bag-model spectrum to include the pion-field exchange energy in a manner consistent with the ideas of partial conservation of axial-vector current. We find that this interaction energy is sufficient to destabilize the quark bag whose quantum numbers are those of the pion. The eta mass is also improved, while other features of the low-lying hadron mass spectrum are not significantly modified.

Constraints due to partial conservation of axial-vector current and charmed-baryon couplings

The PCAC (partial conservation of axial-vector current) consistency conditions are derived for inelastic processes involving charmed baryons. Numerical estimates of the conditions for the processes $\ensuremath{\pi}{C}_{0}\ensuremath{\rightarrow}\ensuremath{\pi}{C}_{0}$, $\ensuremath{\pi}{C}_{1}\ensuremath{\rightarrow}\ensuremath{\pi}{C}_{1}$, $\ensuremath{\pi}{C}_{0}\ensuremath{\rightarrow}\ensuremath{\pi}{C}_{1}$, and $\ensuremath{\pi}{C}_{0}\ensuremath{\rightarrow}\ensuremath{\pi}{C}_{1}^{*}$, determined with the help of observed charmed-baryon contributions, ared used in determining the pion-charmed-baryon coupling strengths. We find that the value of $\frac{{{g}_{\ensuremath{\pi}{C}_{1}{C}_{1}}}^{2}}{4\ensuremath{\pi}}$ agrees well with the previously determined values obtained with the potential-model calculations. The decay widths of ${C}_{1}$ and ${C}_{1}^{*}$ into ${C}_{0}\ensuremath{\pi}$ channel also compare well with the results of Lee, Quigg, and Rosner. We also note that the remaining couplings ${{g}_{\ensuremath{\pi}{C}_{1}{C}_{1}}}^{*}$ and ${g}_{\ensuremath{\pi}{C}_{1}^{*}{C}_{1}^{*}}$ have very small values and thus ${C}_{1}^{*}$ completely decouples from ${C}_{1}\ensuremath{\pi}$ and ${C}_{1}^{*}\ensuremath{\pi}$ channels.

Test of the soft-pion theorem in inclusive pion electroproduction

We show that the cross section of the deep-inelastic direct pion electroproduction in the central region can be deteermined by the use of the PCAC (partial conservation of axial-vector current) hypotheses and the light-cone current algebra in conjunction with the scaling in x for each value of x/sub B/, and that our result is consistent with the cross section of the inclusive reaction ..gamma../sub v/p ..-->.. ..pi../sup -/X.

Soft-pion emission inKp−interactions

Through use of PCAC (partially conserved axial-vector current) we calculate the amplitude for the emission of a single soft pion in the process $K^{\ensuremath{-}}p\ensuremath{\rightarrow}K^{\ensuremath{-}}p$. The ratio of cross sections $\frac{\ensuremath{\sigma}(K^{\ensuremath{-}}p\ensuremath{\rightarrow}K^{\ensuremath{-}}p{\ensuremath{\pi}}^{0})}{\ensuremath{\sigma}(K^{\ensuremath{-}}p\ensuremath{\rightarrow}K^{\ensuremath{-}}p)}$ is computed for various incoming kaon momenta. The agreement between theoretical and experimental results is reasonably good.

Sum rules for weakNNπamplitudes and theoretical descriptions of nonleptonic hyperon decays

The sum rule based on current algebra predicts the $p\ensuremath{\rightarrow}n+{\ensuremath{\pi}}^{+}$ amplitude to be $A({p}_{+}^{+})=\ensuremath{-}\ensuremath{\alpha}3.02\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}(\ensuremath{\hbar}=c=1)$. The weak-interaction-model-dependent parameter $\ensuremath{\alpha}$ can have the same value $\ensuremath{\alpha}=\frac{tan{\ensuremath{\theta}}_{c}}{\sqrt{2}}$ for the Weinberg-Salam as for the Cabibbo model if the observed $|\ensuremath{\Delta}\stackrel{\ensuremath{\rightarrow}}{I}|= 2$, $|\ensuremath{\Delta}S|=1$ enhancement is explained by using PCAC (partially conserved axial-vector current). When the Melosh transformation is used with the soft-pion and infinite-momentum techniques, a very small amplitude $A({p}_{+}^{+})=\ensuremath{-}\ensuremath{\alpha}3.02\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ is found. A simple description of SU(3)-symmetry breaking, reproducing the observed nonleptonic decay amplitudes again, predicts $A({p}_{+}^{+})=\ensuremath{-}\ensuremath{\alpha}3.04\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$. Useful insights may be gained from $\ensuremath{\Delta}I=1$ parity-violating experiments, such as $\ensuremath{\gamma}$ asymmetry in the $n+p\ensuremath{\rightarrow}d+\ensuremath{\gamma}$ reaction.

Nonleptonic charmed-meson decays

In this paper we compute and interrelate various nonleptonic charmed-meson decay matrix elements. With the assumption that the decay Hamiltonian is in the ..delta..I = 1 form, numerous decay rates are interrelated. The predictions are compared to the experiment whenever sufficient data is available. In other cases we compare our results to those of the statistical model of Quigg and Rosner. To estimate the value of the D ..-->.. K-bar..pi pi.. decay amplitudes we make use of PCAC (partial conservation of axial-vector current) and we attribute the enhancement of these amplitudes relative to D ..-->.. K-bar..pi.. amplitudes to the final-state interactions. We suggest an approximate treatment of the problem and show that even though the parameter dependence is unavoidable it is possible to obtain the desired enhancement. Some numerical and graphical results are presented.

Light-plane commutators and corrections to partial conservation of axial-vector current

Corrections to the partially conserved axial-vector current hypothesis are evaluated by taking into account the contributions of the radially excited pseudoscalar mesons, whose existence is predicted in the quark model. The coupling of these mesons to the axial-vector current is first order in chiral-symmetry breaking. Several sum rules, related to matrix elements of light-plane commutators of charges and divergences of currents, are analyzed. Predictions are made for some decay modes of the radially excited pseudoscalar and vector mesons.

Adler zero and the dual multiperipheral model

We show that the ..pi pi.. ..-->.. ..pi pi.. Adler PCAC (partial conservation of axial-vector current) condition requires a Reggeon intercept ..cap alpha.. (0) approx. = 0.5 within a broad class of multiperipheral models at the planar and cylinder levels. In the planar approximation this is closely related to the cancellation of the Reggeon-Reggeon cut.