Partial Conservation Of Axial-vector Current Research Articles

Charged current neutrino and antineutrino induced eta production off the nucleon

The charged current (anti)neutrino induced eta production from the nucleons is studied in a model based on the effective Lagrangians to evaluate the contribution from the nonresonant and resonant diagrams. The contribution from the nonresonant background terms has been obtained using a microscopic model based on the SU(3) chiral Lagrangians. The contribution from the resonant diagrams due to the low lying ${S}_{11}(1535)$, ${S}_{11}(1650)$, and ${P}_{11}(1710)$ resonances has been evaluated using an effective phenomenological Lagrangian with its parameters determined from the experimental values of their branching ratios and decay widths to the $N\ensuremath{\eta}$ channel. The model is first used to reproduce satisfactorily the experimental data from the MAINZ and JLab on the total cross sections for the photo- and electro- production of $\ensuremath{\eta}$ mesons, which fixes the model parameters in the vector current interaction. The partially conserved axial vector current (PCAC) hypothesis and generalized Goldberger-Treiman relation are used to fix the parameters of the axial vector current interaction. The model is then applied to study the weak production of eta mesons induced by the neutrinos and antineutrinos, and predicts the numerical values for the ${Q}^{2}$-distribution, $\ensuremath{\eta}$-momentum distribution, and the total cross section for the reactions ${\ensuremath{\nu}}_{\ensuremath{\mu}}+n\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}+p+\ensuremath{\eta}$ and ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}+p\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}+n+\ensuremath{\eta}$ in the energy region up to 2 GeV. It is found that the photo, electro, and (anti)neutrino induced production of eta mesons is dominated by the contribution from the ${S}_{11}(1535)$ resonance. The results discussed in this work are relevant for the present and future accelerator experiments like MicroBooNE, T2K, NOvA, MINERvA, T2-HyperK, and DUNE as well as for the atmospheric neutrino experiments.

Violation of partial conservation of the axial-vector current and two-body baryonicBandDsdecays

We study the two-body baryonic $B$ and ${D}_{s}$ decays based on the annihilation mechanism without the partial conservation of the axial-vector current (PCAC) at the GeV scale. We demonstrate that the contributions of ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}\overline{p}$, ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{0}\overline{p}$, and ${\overline{B}}_{s}^{0}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}\overline{\mathrm{\ensuremath{\Lambda}}}$ are mainly from the scalar and pseudoscalar currents with their branching ratios predicted to be around $(3.5,5.3,5.3)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}8}$, respectively, exactly the sizes of $\mathcal{B}(B\ensuremath{\rightarrow}\mathbf{B}{\overline{\mathbf{B}}}^{\ensuremath{'}})$ established by the data. We also apply the annihilation mechanism to all of the charmless two-body baryonic $B$ and ${D}_{s}$ decays. In particular, we can explain $\mathcal{B}({\overline{B}}_{(s)}^{0}\ensuremath{\rightarrow}p\overline{p})$ of order $1{0}^{\ensuremath{-}8}$ and $\mathcal{B}({D}_{s}^{+}\ensuremath{\rightarrow}p\overline{n})$ of order $1{0}^{\ensuremath{-}3}$, which are from the axial-vector currents. In addition, the branching ratios of ${\overline{B}}^{0}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}\overline{\mathrm{\ensuremath{\Lambda}}}$, ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}n\overline{p}$, and ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}{\overline{\mathrm{\ensuremath{\Sigma}}}}^{0}$ are predicted to be $(0.3,3.2,9.6)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}8}$, which can be measured by LHCb and viewed as tests for the violation of the partial conservation of the axial-vector current at the GeV scale.

A novel scheme for the wave function renormalization of the composite operators

We propose a novel renormalization scheme for the hadronic operators. The renormalization factor of the operator in this scheme is normalized by the correlation function at tree level in coordinate space. If we focus on the pseudo scalar operator, then its renormalization factor is related to the mass renormalization factor of the fermion through the partially conserved axial-vector current (PCAC) relation. Using the renormalization factor for the pseudo scalar operator in our scheme, we obtain the mass anomalous dimension of the SU(3) gauge theory coupled to N_f=12 massless fundamental fermions, which has an infrared fixed point (IRFP). The mass anomalous dimension at the IRFP is estimated as gamma_m^*= 0.044_{-0.024}^{+0.025} (stat.)_{-0.032}^{+0.057} (syst.).

Realistic implementation of massive Yang-Mills theory forρanda1mesons

We revisit the massive Yang-Mills approach to implement axial-/vector mesons into the chiral pion Lagrangian. Employing the non-linear realization of chiral symmetry, we compute vector and axial-vector spectral functions. This includes, for the first time, a resummation of the $\rho$ propagator in the $a_1$ selfenergy while maintaining a partially conserved axial-vector current (PCAC). A realistic $\rho$ propagator, combined with a recent idea of a chirally invariant continuum in the vector and axial-vector channels, turns out be critical to obtain a quantitative description of hadronic $\tau$-decay data which has not been achieved before in local-gauge approaches to the chiral lagrangian. The thus obtained model provides a realistic basis to rigorously address the long-standing question of chiral symmetry restoration in the context of dilepton data in heavy-ion collisions.

Current algebra derivation of temperature dependence of hadron couplings with currents

The vector and the axial-vector meson couplings with the vector and the axial-vector currents respectively at finite temperature have been obtained in Ref. \cite{Mallik} by calculating all the relevant one-loop Feynman graphs with vertices obtained from the effective chiral Lagrangian. On the other hand, the same couplings were also derived in Ref.\cite{Ioffe1} by applying the method of current algebra and the hypothesis of partial conservation of axial-vector current (PCAC). The latter method appears to miss certain terms; in the case of the vector meson coupling with the vector current, for example, a term containing the $\rho\omega\pi$ coupling is missed. A similar situation would also appear for the nucleon coupling with the nucleon current. In this note we resolve these differences.

QCD sum rules for the pseudoscalar decay constants: To constrain the strange quark mass

We study the higher order corrections of quark masses to the Gell-Mann--Oakes--Renner (GOR) relation by constructing QCD sum rules exclusively for pseudoscalar mesons from the axial-vector correlation function, $i\ensuremath{\int}{d}^{4}{\mathrm{xe}}^{\mathrm{ip}\ensuremath{\cdot}x}〈0|T[{A}_{\ensuremath{\mu}}{(x)A}_{\ensuremath{\nu}}(0)]|0〉.$ To project out the pseudoscalar meson contributions, we apply $\ensuremath{-}{p}^{\ensuremath{\mu}}{p}^{\ensuremath{\nu}}{/p}^{2}$ to this correlation function and construct sum rules for the decay constants of pseudoscalar mesons, ${f}_{\ensuremath{\pi}}{,f}_{k},$ and ${f}_{{\ensuremath{\eta}}_{8}}.$ The operator product expansion (OPE) is proportional to quark masses due to PCAC (partial conservation of axial-vector current). To leading order in quark mass, each sum rule reproduces the corresponding GOR relation. For kaon and ${\ensuremath{\eta}}_{8},$ the deviation from the GOR relation due to higher orders in quark mass is found to be substantial. But the deviation gives better agreement with phenomenology. Our sum rule provides a sensitive relation between ${f}_{K}$ and ${m}_{s},$ which stringently constrains the value for ${m}_{s}.$ To reproduce the experimental value for ${f}_{K},$ ${m}_{s}$ is found to be 186 MeV at 1 GeV scale. The ${f}_{{\ensuremath{\eta}}_{8}}$ sum rule also supports this finding.

Radiative muon capture on O, Al, Si, Ti, Zr, and Ag

The photon spectra from radiative muon capture (RMC) on O, Al, Si, Ti, Zr, and Ag have been measured for photon energies greater than 57 MeV using a cylindrical pair spectrometer at the TRIUMF cyclotron. Values of ${R}_{\ensuremath{\gamma}},$ the ratio of the radiative rate for photon energies above 57 MeV, to the nonradiative rate, are $1.67\ifmmode\pm\else\textpm\fi{}0.18,$ $1.40\ifmmode\pm\else\textpm\fi{}0.11,$ $2.09\ifmmode\pm\else\textpm\fi{}0.20,$ $1.30\ifmmode\pm\else\textpm\fi{}0.12,$ $1.31\ifmmode\pm\else\textpm\fi{}0.15$, and $1.12\ifmmode\pm\else\textpm\fi{}0.13$, respectively, in units of ${10}^{\ensuremath{-}5}$. The Al/Si rate difference confirms an earlier result. The Ti/Ca rate difference and the rate suppression in Zr and Ag are new results which confirm that the RMC rate is a much smoother function of neutron excess than of atomic number. This suggests that Pauli blocking is relatively more important for radiative capture than for nonradiative capture. The value of the ratio of the induced weak pseudoscalar to axial coupling constants, ${g}_{p}{/g}_{a},$ for O was found to be $4.9\ifmmode\pm\else\textpm\fi{}0.6,$ $6.3\ifmmode\pm\else\textpm\fi{}1.1$, or ${8.1}_{\ensuremath{-}2.1}^{+1.8}$, depending on the theory used to extract it. These values are in good or fair agreement with the partially conserved axial-vector current (PCAC) hypothesis. For the other nuclei studied, large model dependences or a lack of detailed RMC calculations made tests of the PCAC hypothesis difficult.

Chiral model of axial meson exchange currents in nuclei

The long-range part of the weak axial exchange currents (AXC) is considered in the framework of the chiral $\ensuremath{\sigma}$-$\ensuremath{\omega}$ model, which preserves basic symmetries of QCD and includes $\ensuremath{\sigma}$, $\ensuremath{\omega}$, and $\ensuremath{\pi}$ mesons. Linear and nonlinear realizations of the model are considered, and it is explicitly demonstrated that the way one splits relativistic many-body effects into AXC contributions and one-body relativistic corrections to the traditional nuclear axial current is model dependent. In the linear realization of the $\ensuremath{\sigma}$-$\ensuremath{\omega}$ model spatial two-body AXC are shown to be necessary to preserve the partial conservation of axial-vector current (PCAC) relation to order $O(1/M)$ in inverse nucleon mass. In the nonlinear realization of the model PCAC is satisfied for the one-body current identically. Indeed, it is shown that there are no AXC of order $O(1/M)$ in this realization, but one now has to include a new one-body relativistic correction of order $O(1/M)$ in the analysis to preserve PCAC for a single nucleon. A familiar result for axial exchange charge is reproduced in both models. The obtained correction terms are estimated in a simple unified analysis of electroweak processes with a few light nuclei.

Extended PCAC Relation and Nucleon Structure

We explore a consistent way to extend the old partially conserved axial vector current (PCAC) relation for a nucleon to a finite region. The paper includes an investigation of a chiral Ward–Takahashi identity, the explicit chiral symmetry breaking by a finite current quark mass, the extension of the PCAC relation and the physical consequences. Two explicit relations between the nucleon axial vector form factor , pseudo-scalar form factor and the pion-nucleon coupling constant are obtained. One of the relations is confirmed, within the experimental error, by observations in the region. The other one which relates and is studied by using known empirical facts and dispersion relation. Certain inconsistency, which is in favor of the introduction of a diquark condensation inside a nucleon, is revealed.

Equation of state with kaon condensates and neutron stars

Kaon condensation in dense neutron star matter is investigated on the basis of current algebra and PCAC (partially conserved axial-vector current). Second-order perturbation effects are incorporated naturally within framework, which are necessary to be consistent with KN scattering data, but we find it hardly affects K − condensation. The excitation energy of kaons in a nuclear medium is examined by combining the framework with a relativistic mean-field theory. Next we obtain the equation of state of the K −-condensed phase in neutron star matter, and clarify characteristic features of the system. There can occur a first-order phase transition from the normal phase to the K −-condensed one. Subsequently bulk structure of kaon-condensed neutron stars is studied. Softening of the equation of state due to kaon condensation has a large influence on the internal structure of the neutron star. As a dynamical property associated with the first-order phase transition, the energy release due to a collapse from a metastable configuration to a stable kaon-condensed one is estimated. Its implications for the gamma-ray bursts are briefly mentioned.

Diagrammatic approach to meson-meson scattering in the nonrelativistic quark potential model.

In this paper we use Born-order quark-exchange diagrams in a nonrelativistic potential model to describe low-energy scattering of $q\overline{q}$ mesons. A formalism for evaluating quark Born diagrams is developed, and as a first application we consider meson-meson scattering in channels in which $q\overline{q}$ annihilation is thought to be unimportant. In particular our results are relevant to $I=2 \ensuremath{\pi}\ensuremath{\pi}$ and $I=1 \mathrm{KK}$ elastic scattering. Simple rules for the Born diagrams are given, which allow the evaluation of scattering amplitudes in terms of external meson wave functions by inspection. These techniques are applied to systems having identical quarks, and ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}$, ${K}^{+}{K}^{+}$, and ${\ensuremath{\rho}}^{+}{\ensuremath{\rho}}^{+}$ elastic scattering phase shifts, cross sections, and equivalent potentials are derived as examples. The $S$-wave $I=2 \ensuremath{\pi}\ensuremath{\pi}$ phase shift for a Gaussian $q\overline{q}$ wave function with conventional quark model parameters ${\ensuremath{\alpha}}_{s}$, ${m}_{q}$, and ${\ensuremath{\beta}}_{\mathrm{SHO}}$ is found to be in good agreement with experiment and with Weinberg's PCAC (partial conservation of axial-vector current) result. At higher energies the predicted differential cross sections have the characteristic diffractive features of an exponential $t$ peak at small angles and vacuum quantum number exchange. The phase of the predicted amplitude however differs from the experimental diffractive amplitude, so these quark Born diagrams cannot be directly identified with the Pomeron of diffractive scattering phenomenology.

PCAC consistency. I. Kaon two- and three-body nonleptonic weak decays.

We show that the current-algebra--PCAC (partial conservation of axial-vector current) procedure applied consistently to each final-state pion predicts seven {ital K}{r arrow}2{pi} and {ital K}{r arrow}3{pi} decay amplitudes that very accurately reproduce the experimental results.

PCAC consistency. II. Charmed meson two- and three-body nonleptonic weak decays.

We extend the notion of PCAC (partial conservation of axial-vector current) consistency to calculate eight two-body weak decays {ital D}{r arrow}{ital {bar K}}{pi}, {ital {bar K}K}, {pi}{pi} and seven three-body weak decays {ital D}{r arrow}{ital {bar K}}{pi}{pi}, {ital {bar K}K}{pi},{pi}{pi}{pi}. Most of the fifteen predicted amplitudes are in reasonable agreement with the experimental results.

Why current algebra and PCAC are applicable for charmed-meson and -baryon weak decays.

By accounting for rapidly varying pole terms, the current-algebra-PCAC (partial conservation of axial-vector current) procedure properly measures large decay momentum corrections in charmed ${D}^{+}\ensuremath{\rightarrow}{\overline{K}}^{0}{\ensuremath{\pi}}^{+}$, ${D}^{+}\ensuremath{\rightarrow}{\overline{K}}^{0}{K}^{+}$, and ${\ensuremath{\Lambda}}_{c}^{+}\ensuremath{\rightarrow}p{\overline{K}}^{0}$ weak decays.

PION PHOTOPRODUCTION AT THRESHOLD AND LOW ENERGY THEOREMS REVISITED

This paper takes a second look at the methods used in deriving low energy theorems on pion photoproduction using the partially conserved axial vector current (PCAC) hypothesis. The discrepancy between a recent measurement of Eo+(γp→π0p) and theory is studied. Rescattering corrections to low energy theorems are made. A critique of some recent theory papers on this subject is presented.

Emission of soft pions in meson-nucleon interactions

The formalism of current algebra and partially conserved axial-vector current (PCAC) hypothesis is applied to study the Kp and πp interaction processes involving hyperons and one or two soft pions. The differential cross-sections for the processes are normalized to the differential cross-sections for the corresponding processes without the soft pions. Theoretical predictions for the ratio of cross-sections at various laboratory meson momenta are compared with the existing experimental data. Angular distributions are also given for different incoming meson momenta

Application of current algebra and partial conservation of axialvector current to kaon-proton interactions

A soft-pion study using current algebra and the partially conserved axial vector current (PCAC) hypothesis is made of the kaon-proton interaction processKp →Kp2π0. Considering both pions to be soft, the differential rate for the process is normalized to the differential rate of the corresponding process without the pions. Theoretical predictions for the ratio of cross-sections at various kaon momenta are compared with experimental results.

Nonleptonic decays of chiral solitons and a possible resolution of the S-wave/P-wave puzzle.

We calculate the nonleptonic weak decays of hyperons in the Skyrmion model of baryons. The weak-interaction chiral Lagrangian is that known from kaon decay, providing a zero-parameter description of the decay amplitudes. In the S waves the PCAC (partially conserved axial-vector current) relation is verified, but the magnitude emerges as a factor of 3 too small, probably indicating a slow convergence of the chiral expansion. In the P waves, new and important terms are found which are not included in standard analyses. These modify the PCAC treatment of hyperon decay and can provide the resolution of the long-standing S-wave/P-wave puzzle.

(V+A) components from the measured observables in muon capture.

We use the data on the average polarization and the longitudinal polarizaton of recoil in the process $^{12}\mathrm{C}$(${\ensuremath{\mu}}^{\mathrm{\ensuremath{-}}}$,${\ensuremath{\nu}}_{\ensuremath{\mu}}$${)}^{12}$B to extract independent values for leptonic (V+A) currents and induced pseudoscalar hadronic coupling. Present results give \ensuremath{\Vert}\ensuremath{\xi}\ensuremath{\Vert}<0.25 for the mixing parameter of the left-right-symmetric model, whereas ${f}_{P}$ is consistent with PCAC (partial conservation of axial-vector current). The interest of better precision in the longitudinal polarization, as well as the measurement of the asymmetry in the angular distribution, is discussed.

Renormalization of the axial-vector current in QCD.

Following the method of Ioffe and Smilga, the propagation of the baryon current in an external constant axial-vector field is considered. The close similarity of the operator-product expansion with and without an external field is shown to arise from the chiral invariance of gauge interactions in perturbation theory. Several sum rules corresponding to various invariants both for the nucleon and the hyperons are derived. The analysis of the sum rules is carried out by two independent methods, one called the ratio method and the other called the continuum method, paying special attention to the nondiagonal transitions induced by the external field between the ground state and excited states. Up to operators of dimension six, two new external-field-induced vacuum expectation values enter the calculations. Previous work determining these expectation values from PCAC (partial conservation of axial-vector current) are utilized. Our determination from the sum rules of the nucleon axial-vector renormalization constant GA, as well as the Cabibbo coupling constants in the SU3-symmetric limit (ms=0), is in reasonable accord with the experimental values. Uncertainties in the analysis are pointed out. The case of broken flavor SU3 symmetry is also considered. While in the ratio method, the results are stable for variation of the fiducial interval of the Borel mass parameter over which the left-hand side and the right-hand side of the sum rules are matched, in the continuum method the results are less stable. Another set of sum rules determines the value of the linear combination 7F-5D to be ≊0, or D/(F+D)≊(7/12). .AE