Nucleon Axial-vector Form Factors Research Articles

Nucleon axial-vector form factor and radius from future neutrino experiments

Nucleon axial-vector form factor and radius from future neutrino experiments

Nucleon axial form factor at large momentum transfers

Using a Poincaré-covariant quark+diquark Faddeev equation and related symmetry-preserving weak interaction current, we deliver parameter-free predictions for the nucleon axialvector form factor, G_A(Q^2), on the domain 0le x=Q^2/m_N^2le 10, where m_N is the nucleon mass. We also provide a detailed analysis of the flavour separation of the proton G_A into contributions from valence u and d quarks; and with form factors available on such a large Q^2 domain, predictions for the flavour-separated axial-charge light-front transverse spatial density profiles. Our calculated axial charge ratio g_A^d/g_A^u=-0.32(2) is consistent with available experimental data and markedly larger in magnitude than the value typical of nonrelativistic quark models. The value of this ratio is sensitive to the strength of axialvector diquark correlations in the Poincaré-covariant nucleon wave function. Working with a realistic axialvector diquark content, the d and u quark transverse density profiles are similar. Some of these predictions could potentially be tested with new data on threshold pion electroproduction from the proton at large Q^2.

Nucleon axial-vector and pseudoscalar form factors and PCAC relations

We use a continuum quark+diquark approach to the nucleon bound-state problem in relativistic quantum field theory to deliver parameter-free predictions for the nucleon axial and induced pseudoscalar form factors, $G_A$ and $G_P$, and unify them with the pseudoscalar form factor $G_5$ or, equivalently, the pion-nucleon form factor $G_{\pi NN}$. We explain how partial conservation of the axial-vector current and the associated Goldberger-Treiman relation are satisfied once all necessary couplings of the external current to the building blocks of the nucleon are constructed consistently; in particular, we fully resolve the seagull couplings to the diquark-quark vertices associated with the axial-vector and pseudoscalar currents. Among the results we describe, the following are worth highlighting. A dipole form factor defined by an axial charge $g_A=G_A(0)=1.25(3)$ and a mass-scale $M_A = 1.23(3) m_N$, where $m_N$ is the nucleon mass, can accurately describe the pointwise behaviour of $G_A$. Concerning $G_P$, we obtain the pseudoscalar charge $g_p^\ast = 8.80(23)$, and find that the pion pole dominance approach delivers a reliable estimate of the directly computed result. Our computed value of the pion-nucleon coupling constant, $g_{\pi NN}/m_N =14.02(33)/{\rm GeV}$ is consistent with recent precision determinations.

On the axial-vector form factor of the nucleon and chiral symmetry

We consider the chiral Lagrangian with nucleon, isobar, and pion degrees of freedom. The baryon masses and the axial-vector form factor of the nucleon are derived at the one-loop level. We explore the impact of using on-shell baryon masses in the loop expressions. As compared to results from conventional chiral perturbation theory we find significant differences. An application to QCD lattice data is presented. We perform a global fit to the available lattice data sets for the baryon masses and the nucleon axial-vector form factor, and determine the low-energy constants relevant at hbox {N}^3LO for the baryon masses and at hbox {N}^2LO for the form factor. Partial finite-volume effects are considered. We point out that the use of on-shell masses in the loops results in non-analytic behavior of the baryon masses and the form factor as function of the pion mass, which becomes prominent for larger lattice volumes than presently used.

Measurement of the quasielastic axial vector mass in neutrino interactions on oxygen

The weak nucleon axial-vector form factor for quasi-elastic interactions is determined using neutrino interaction data from the K2K Scintillating Fiber detector in the neutrino beam at KEK. More than 12,000 events are analyzed, of which half are charged-current quasi-elastic interactions nu-mu n to mu- p occurring primarily in oxygen nuclei. We use a relativistic Fermi gas model for oxygen and assume the form factor is approximately a dipole with one parameter, the axial vector mass M_A, and fit to the shape of the distribution of the square of the momentum transfer from the nucleon to the nucleus. Our best fit result for M_A = 1.20 \pm 0.12 GeV. Furthermore, this analysis includes updated vector form factors from recent electron scattering experiments and a discussion of the effects of the nucleon momentum on the shape of the fitted distributions.

Axial vector form factor of nucleons in a light-cone diquark model

The nucleon axial vector form factor is investigated in a light-cone quark spectator diquark model, in which Melosh rotations are applied to both the quark and vector diquark. It is found that this model gives a very good description of available experimental data and the results have very little dependence on the parameters of the model. The relation between the nucleon axial constant and the anomalous magnetic moment of nucleons is also discussed.

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.

Nucleon axial-vector form factor in perturbative QCD.

Nucleon axial-vector form factor in perturbative QCD.

The nucleon axial vector form factor in an improved constituent quark model

The nucleon axial vector form factor calculated in an improved constituent quark model is found to be in better agreement with the data if the effect of boost is taken into account. A comparison with the results in other quark models is made. The electromagnetic form factors of the proton calculated in this model are found to be in reasonable agreement with the data.

Quasielastic neutrino scattering: A measurement of the weak nucleon axial-vector form factor

The quasielastic reaction ${\ensuremath{\nu}}_{\ensuremath{\mu}}n\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}p$ was studied in an experiment using the BNL 7-foot deuterium bubble chamber exposed to the wide-band neutrino beam with an average energy of 1.6 GeV. A total of 1138 quasielastic events in the momentum-transfer range ${Q}^{2}=0.06\ensuremath{-}3.00$ (${\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$ were selected by kinematic fitting and particle identification and were used to extract the axial-vector form factor ${F}_{A}({Q}^{2})$ from the ${Q}^{2}$ distribution. In the framework of the conventional $V\ensuremath{-}A$ theory, we find that the dipole parametrization is favored over the monopole. The value of the axial-vector mass ${M}_{A}$ in the dipole parametrization is 1.07\ifmmode\pm\else\textpm\fi{}0.06 GeV, which is in good agreement with both recent neutrino and electroproduction experiments. In addition, the standard assumptions of conserved vector current and no second-class currents are checked.

Electroproduction of low hadronic masses

A model satisfying analytic, unitary, and soft-meson requirements is found to account for all electroproduction data in the $\ensuremath{\Delta}(3,3)$ region even at very high photon momentum transfers. The $\ensuremath{\Delta}$, pion, and nucleon axial-vector form factors are discussed within the framework of this simple yet accurate model.

Determination of the nucleon axial vector form-factor from πΔ electroproduction near threshold

From measurements of the reaction ep→e π − Δ ++ near threshold the nucleon axial-vector form factor is determined, using the PCAC calculations by Adler and Weisberger. The results are consistent with form factor determinations from single pion electroproduction. A dipole fit yields m A = (1.18 ± 0.07) GeV.

Threshold π+ electroproduction at high-momentum transfer: A determination of the nucleon axial vector form factor

Threshold π + electroproduction has been measured at momentum transfers ‖ k 2‖ of 0.45, 0.58 and 0.88 (GeV/ c) 2, extending the range of earlier measurements. Using PCAC and current algebra-based models we have deduced the axial vector form factor of the nucleon G A( k 2), and find that the dipole parametrisation is favoured over the monopole. The value of M A in the dipole parametrisation is, in a weak PCAC model, 0.96 ± 0.03 GeV, in excellent agreement with neutrino measurements. The threshold cross section is also in excellent agreement with the predictions of a fixed- t dispersion relation model.

Virtual radiative pion capture: Current algebra description, information on nucleon axial form factors and chiral symmetry breaking

We analyse the reaction π−p → l+l−n at low energies, in the «quasi-threshold» configuration, using equal-time current commutators. We derive a simple expression of the amplitude, in terms of nucleon axial vector form factors, and a consistency relation for the nonstrange quark massmp, indicating a small valuemp ≈ 15 MeV.

Meson exchange currents in deuteron electrodisintegration and the nucleon axial vector form factor

Double differential cross sections for deuteron electrodisintegration near threshold from back-scattered electrons were calculated for electron four-momentum transfer squares in the range 0 ⩽ Δ 2 ⩽ 15 fm −2 and for final n- p relative energies in the range 0 ⩽ E rel ⩽ 15 MeV using the Reid hard-core parametrization of the n- p potential and considering the free nucleon or impulse process and various one-pion exchange processes. Particular attention was paid to the study of the form factors of the mesonic processes and to the dependence of the cross section on various n- p potentials. In particular, the cross section was found to be dominated by the impulse process for Δ 2 ⩽ 8 fm −2 and by the catastrophic meson exchange process for Δ 2 ⩾ 8 fm −2. Since in dispersion theories, the catastrophic process is proportional to the isovector Dirac nucleon form factor F 1 V ( Δ 2) while in PCAC-current algebra theories it is proportional to the nucleon axial vector form factor F A ( Δ 2), a determination of the catastrophic form factor was under-taken. It was found that the experimental data was reasonably fitted by F A(Δ 2) = (1 + Δ 2 m A 2 ) −2 with m A = 0.81 GeV. This value of m A is within the range of values determined termined from neutrino scattering experiments. Further, the cross section was found to be relatively insensitive to the n- p potential employed providing it exhibits repulsive core behavior for r ≲ 0.5 fm. Finally, possible parametrizations of the off-shell contributions to the pion form factor and contributions to the cross section from scattering to the 3 S 1- 3 D 1 and l > 0 final states were examined.

Deuteron electrodisintegration and the nucleon axial vector form factor

Calculated deuteron electrodisintegration cross-sections by back-scattered electrons give the major contribution at momentum transfer squares above 6 fm −2 as arising from the catastrophic process, which in PCAC-current algebra theories is proportional to the axial vector form factor. Experimental data is reasonably fitted by F A (Δ 2) = ( 1+Δ 2 m 2 A ) −2 with m A = 0.81 GeV.

Threshold electroproduction experiments and the axial vector form factor

Data from three coincidence experiments which measure the cross section for π + electroproduction around threshold are compared. Application of the PCAC motivated pseudovector Born approximation model yields corresponding values of the nucleon axial vector form factor for spacelike momentum transfer up to 0.6 GeV 2. Attention is paid to possible theoretical uncertainties and to the influence of the first pion-nucleon resonance. (Recent single arm SLAC results are also included.)

Pion electroproduction and photoproduction including PCAC

The PCAC constraints on pion electroproduction and photoproduction are considered in order to construct models applicable to these processes at low and high energies. In particular the roles of the nucleon axial vector form factor and the pion electromagnetic form factor are investigated.

Uncorrelated Effect for the Nucleon Axial Vector Form Factor

Uncorrelated Effect for the Nucleon Axial Vector Form Factor

Generalized Vector Dominance Theory and Vertex Functions

A simple model formula for the hadronic form factors as a ratio of two $\ensuremath{\Gamma}$ functions is examined from the point of view of its consistency with the beta-function model and with the chiral properties of the vector and axial-vector currents. It is shown that similar models may hold simultaneously for the simplest vector and axial-vector form factors while maintaining consistency with the Veneziano model of the four-point function, and with the requirements of a conserved vector current, partially conserved axial-vector current, and the Gell-Mann algebra of currents. An infinite class of such solutions is found: Defining form factors by $〈{\ensuremath{\pi}}^{+}({p}_{2})|{{V}_{\ensuremath{\mu}}}^{0}(0)|{\ensuremath{\pi}}^{+}({p}_{1})〉={F}_{V}(t){({p}_{1}+{p}_{2})}_{\ensuremath{\mu}}$ and $〈\ensuremath{\sigma}({p}_{2})|{{A}_{\ensuremath{\mu}}}^{0}(0)|{\ensuremath{\pi}}^{0}({p}_{1})〉={{F}_{A}}^{+}(t){({p}_{1}+{p}_{2})}_{\ensuremath{\mu}}+{{F}_{A}}^{\ensuremath{-}}(t){({p}_{1}+{p}_{2})}_{\ensuremath{\mu}}$, where $t={({p}_{1}+{p}_{2})}^{2}$, we find the solutions ${F}_{V}(t)\ensuremath{\propto}\frac{\ensuremath{\Gamma}(1\ensuremath{-}{\ensuremath{\alpha}}_{V}(t))}{\ensuremath{\Gamma}({r}_{V}+1\ensuremath{-}{\ensuremath{\alpha}}_{V}(t))}$ and ${{F}_{A}}^{+}(t)\ensuremath{\propto}\frac{\ensuremath{\Gamma}(1\ensuremath{-}{\ensuremath{\alpha}}_{A}(t))}{\ensuremath{\Gamma}({r}_{A}+1\ensuremath{-}{\ensuremath{\alpha}}_{A}(t))}$, where ${\ensuremath{\alpha}}_{V}(t)$ is the $\ensuremath{\rho}$ Regge trajectory and ${\ensuremath{\alpha}}_{A}(t)$ is the $\ensuremath{\pi}\ensuremath{-}{A}_{1}$ Regge trajectory. The power behaviors of ${F}_{A}(t)$ and ${F}_{V}(t)$ for $|t|\ensuremath{\rightarrow}\ensuremath{\infty}$ are not determined absolutely, but the relative power is found to be ${r}_{V}\ensuremath{-}{r}_{A}=\frac{1}{2}$, as a consequence of a quantization rule for the trajectory intercepts. Scalar and pseudoscalar form factors are treated also, with similar results; in the approximation used here, however, it is required that the pseudoscalar form factor $P(t)$ in $〈\ensuremath{\sigma}({p}_{2})|{\ensuremath{\partial}}_{\ensuremath{\mu}}{{A}_{\ensuremath{\mu}}}^{0}(0)|{\ensuremath{\pi}}^{0}({p}_{1})〉={{M}_{\ensuremath{\pi}}}^{2}P(t)$ be dominated by the ground-state pion alone, that is, $P(t)\ensuremath{\propto}\frac{\ensuremath{\Gamma}(\ensuremath{-}{\ensuremath{\alpha}}_{A}(t))}{\ensuremath{\Gamma}(1\ensuremath{-}{\ensuremath{\alpha}}_{A}(t))}$, in order to ensure absence of non-gauge-invariant terms in the matrix element $〈{\ensuremath{\pi}}^{+}({p}_{2})|{{V}_{\ensuremath{\mu}}}^{0}(0)|{\ensuremath{\pi}}^{+}({p}_{1})〉$. In order to consider matrix elements of the vector- and axial-vector-current operators between other hadron states, we write generalized field-current identities, using the forms of ${F}_{V}(t)$ and ${{F}_{A}}^{+}(t)$, and make a universality hypothesis that the vector mesons $\ensuremath{\rho}$ and ${A}_{1}$ and their higher recurrences couple universally to the independent helicity amplitudes of the Breit frame. As an example, a treatment of the nucleon electromagnetic and axial-vector form factors is given, leading to simple model formulas for the Sachs form factors ${G}_{E}(t)$ and ${G}_{M}(t)$, and the axial-vector form factor ${G}_{A}(t)$, which for spacelike values of $t$ agree well with the experimental results.