The quasi-elastic scattering of muon neutrino and electrons on a carbon target are analyzed using the relativistic distorted-wave impulse approximation (RDWIA). We also evaluate the contribution of the two-particle and two-hole meson exchange current ($2p-2h$ MEC) to electroweak response functions. The nuclear model dependence of the (anti)neutrino cross sections is studied within the RDWIA+MEC approach and RDWIA model with the large nucleon axial mass. It is shown that the results for the squared momentum transfer distribution $dσ/dQ^2$ and for invariant mass of the final hadronic system distribution $dσ/dW$ obtained within these models are substantially different.
We study the modification of the nucleon axial form factor in nuclear matter. The internal quark substructure of the nucleon is self-consistently described by the quark meson coupling model. We find that the axial form factor of the bound nucleon is quenched considerably from that of the free nucleon. The axial vector coupling constant is reduced by roughly 10% at normal nuclear matter density and the axial form factor varies within 8% for moderate momentum transfer.
Current issues associated with nucleon axial matrix elements are studied, including the Goldberger-Treiman discrepancy, the induced pseudoscalar, and SU(3) chiral perturbation theory.
We discuss the axial form factors of the nucleon within the context of the nonrelativistic chiral quark model. Partial conservation of the axial current (PCAC) imposed at the quark operator level enforces an axial coupling for the constituent quarks which is smaller than unity. This leads to an axial coupling constant of the nucleon $g_A$ in good agreement with experiment. PCAC also requires the inclusion of axial exchange currents. Their effects on the axial form factors are analyzed. We find only small exchange current contributions to $g_A$, which is dominated by the one-body axial current.…
The weak decay as well as the strong nucleon coupling constants of the isoscalar axial vector meson $f_1 (1285)$ are estimated within the octet quark model. It is shown that the empirical value for the coupling of $\overline{s}s$ quarkonium to nucleons can be understood by attributing the $f_1(1285)$-nucleon coupling to the $a_0πN$ triangle diagram.
We calculate the nucleon form factors G_A and G_P of the isovector axial-vector current and the pion-nucleon form factor G_piN in manifestly Lorentz-invariant baryon chiral perturbation theory up to and including order O(p^4). In addition to the standard treatment including the nucleon and pions, we also consider the axial-vector meson a_1 as an explicit degree of freedom. This is achieved by using the reformulated infrared renormalization scheme. We find that the inclusion of the axial-vector meson effectively results in one additional low-energy coupling constant that we determine by a fit t…
In a chiral quark model where chiral symmetry is introduced via a non-linear sigma model, we evaluate the axial couplings g_A(0), g_A^8(0) and g_A^0(0 )related to the spin structure of the nucleon. Our calculation includes one-body and two-body axial current and pion absorption operators, which satisfy the Partial Conservation of Axial Current (PCAC) condition. While g_A(0) is dominated by the one-body axial current we find significant corrections due to two-body axial exchange currents in g_A^8(0) and g_A^0(0). Interestingly, the axial current associated with gluon exchange reduces g_A^8(0) f…
The axial exchange current operator that arises from the coupling of the axial field to the pion and effective scalar field in nuclei is constructed. The spatial dependence of this exchange current operator may be determined directly from the nucleon-nucleon interaction. This "$πσ$"-axial exchange current contributes about 5\% to the quenching of the nucleon axial current coupling constant $g_A^{GT}$ in heavy nuclei.
We calculate the muon capture rate on the deuteron to next-to-next-to-leading order in the pionless effective field theory. The result can be used to constrain the two-nucleon isovector axial coupling L_{1,A} to +/- 2 fm^3 if the muon capture rate is measured to 2% level. From this, one can determine the neutrino-deuteron break up reactions and the pp-fusion cross section in the sun to a same level of accuracy.
New QCD sum rules for the nucleon axial-vector current coupling constants are derived. One set is derived from a generalized correlator of spin-1/2 interpolating fields, and the other with a mixed correlator of spin-1/2 and spin-3/2 fields. Using a recently-developed Monte-Carlo based uncertainty analysis and techniques for determining the optimal interpolating fields, the predicative ability of QCD sum rules for axial-vector current coupling constants are determined. We find the previous studies of this matrix element are based on an invalid sum rule. A combined analysis of this sum rule toge…
Axial-vector Current and General Unpolarized Electroweak Single-nucleon Responses
Center for Theoretical Physics, Department of Physics and Laboratory for Nuclear Science, Massachusetts Institute of Technology（麻省理工学院理论物理中心、物理系及核科学实验室）；The Ohio State University（俄亥俄州立大学）
Within the framework of the improved quantum molecular dynamics model, the medium modifications on the free nucleon-nucleon elastic cross sections are investigated. By using various in-medium nucleon-nucleon elastic cross sections in the model, the nucleon-induced reactions on various targets are simulated, and the excitation functions of reaction cross sections in the energy range from 25 MeV to 1 GeV are calculated. By comparing the calculations with the experimental data, an isospin, density, and momentum-dependence medium correction factor on free nucleon-nucleon elastic cross sections is …
In order to extract information on the strength of quark-quark correlations in the axial vector (a.v.) diquark channel ($J^P=1^+, T=1$), we analyze the quark light cone momentum distributions in the nucleon, in particular their flavor dependencies, and the static properties of the nucleon. To construct the nucleon as a relativistic 3-quark bound state, we use a simple 'static' approximation to the full Faddeev equation in the Nambu-Jona-Lasinio model, including correlations in the scalar ($J^P=0^+, T=0$) and a.v. diquark channels. It is shown that the a.v. diquark correlations should be rather…
Nucleon momentum distribution (NMD), particularly its high-momentum components, is essential for understanding the nucleon--nucleon ($ NN $) correlations in nuclei. Herein, we develop the studies of NMD of $^{56}\text{Fe}$ from the axially deformed relativistic mean-field (RMF) model. Moreover, we introduce the effects of $ NN $ correlation into the RMF model from phenomenological models based on deuteron and nuclear matter. For the region $ k<k_{\text{F}} $, the effects of deformation on the NMD of the RMF model are investigated using the total and single-particle NMDs. For the region $ k>k_{…
Starting from the axial heavy meson exchange currents, constructed earlier in conjunction with the Bethe--Salpeter equation, we first present the axial $ρ$--, $ω$-- and $a_1$ meson exchange Feynman amplitudes that satisfy the partial conservation of the axial current. Employing these amplitudes, we derive the corresponding weak axial heavy meson exchange currents in the leading order in the 1/M expansion ($M$ is the nucleon mass), suitable for the nuclear physics calculations beyond the threshold energies and with wave functions obtained by solving the Schrödinger equation with one--boson exch…
Bethe-Salpeter equation is applied to nucleon-nucleon elastic scattering at the intermediate energy. The differential cross section and the polarization are calculated in terms of the phase shift analysis method using the two-body potential derived from the Bethe-Salpeter equation. The lowest-order Born approximation for the K-matrix is corrected by including the inverse square part of the potential.
The axial form factor of the nucleon is studied in a two-component model consisting of a three-quark intrinsic structure surrounded by a meson cloud. The experimental data in the space-like region are well reproduced with a minimal number of parameters. The results are similar to those obtained from a dipole fit up to 1 GeV$^2$, but they surprisingly show a zero between 2 and 3 GeV$^2$. Such behavior, predicted by the present model completely disagrees with the dipole parametrization. The theoretical expression for the form factor is then analytically extrapolated to the time-like region, givi…
The relativized hypercentral Constituent Quark Model is used for the calculation of the elastic electromagnetic form factors of the nucleon. The results are compared with the recent measurements at Jlab.
Phenomenological Lagrangians that exhibit (broken) chiral symmetry as well as isospin violation suggest short-range charge symmetry breaking (CSB) nucleon-nucleon potentials with a $\mbox{\boldmath $σ$}_1 \!\cdot\!\mbox{\boldmath $σ$}_2$ structure. This structure could be realized by the mixing of axial-vector ($1^+$) mesons in a single-meson exchange picture. The Coleman-Glashow scheme for $ΔI_{z}=1$ charge symmetry breaking applied to meson and baryon $SU(2)$ mass splittings suggests a universal scale. This scale can be extended to $ΔI=1$ nonstrange CSB transitions $\langle a_1^\circ|H_{em}|…
The sensitivity of nucleon-nucleus elastic scattering observables to the off-shell structure of nucleon-nucleon t-matrices, derived from realistic NN potentials, is investigated within the context of a full-folding model based on the impulse approximation. Our study uses recently developed NN potential models, which describe a subset of the NN data base with a $χ^2$ per datum $\sim$1, which means that the NN t-matrices are essentially on-shell equivalent. We calculate proton-nucleus elastic scattering observables for $^{16}$O, $^{40}$Ca, and $^{208}$Pb between 100 and 200 MeV laboratory energy…
A partial-wave analysis of NN elastic scattering data has been completed. This analysis covers an expanded energy range, from threshold to a laboratory kinetic energy of 2.5 GeV, in order to include recent elastic pp scattering data from the EDDA collaboration. The results of both single-energy and energy-dependent analyses are described.
The deuteron axial current is sensitive both to the form of the implementation of relativistic dynamics as well as to the details of the deuteron D state at moderate momentum transfer, making it a natural partner to the magnetic form factor for exploring details of nucleon-nucleon dynamics and associated electroweak properties.
A partial-wave analysis (PWA) of NN elastic scattering data has been completed. This analysis covers an expanded energy range, from threshold to a laboratory kinetic energy of 3 GeV, in order to include recent elastic pp polarized scattering measurements performed at SATURNE II. Results of the energy-dependent fit are compared with single-energy solutions and Saclay amplitudes obtained via the direct-reconstruction approach. We also comment on the status of Eps1 in the low-energy region.
We investigate the importance of the three-nucleon (3N) force contact terms in elastic nucleon-deuteron (Nd) scattering by applying the N$^4$LO$^+$ chiral semi-local momentum space (SMS) regularized nucleon-nucleon (NN) chiral potential supplemented by N$^2$LO and all subleading N$^4$LO three-nucleon force (3NF) contact terms. Strength parameters of the contact terms were obtained by least squares fitting of theoretical predictions to cross section and analyzing powers data at three energies of the impinging nucleon. Although the N$^3$LO contributions to the 3N force were completely neglected,…
Neutron-deuteron elastic scattering cross sections are calculated at different energies using modern nucleon-nucleon interactions and the Tucson-Melbourne three-nucleon force adjusted to the triton binding energy. Predictions based on NN forces only underestimate nucleon-deuteron data in the minima at higher energies starting around 60 MeV. Adding the three-nucleon forces fills up those minima and reduces the discrepancies significantly.
General expressions for all parity-conserving polarization observables of elastic electron-nucleon scattering in the one-photon exchange approximation are derived for a general frame of reference, i.e.\ not assumming scattering off a nucleon at rest and not specializing to a specific system of coordinates. Essentially, the given expressions are also valid for the inverse process, i.e.\ nucleon scattering off electrons.
The reaction of the elastic electron-deuteron scattering at high momentum transfer is investigated within the Bethe-Salpeter approach. The relativistic covariant Graz II separable kernel of nucleon-nucleon interactions is used to analyze the deuteron structure functions, form factors and tensor of polarization components. The modern data for the electromagmetic nucleons structure from the double polarization experiments as well as some other models of the nucleon form factors are considered.
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.
A previous model on inclusive charged-current quasi-elastic nuclear reactions is extended to include neutral- and charged-current nucleon emission reactions. The problem of outgoing nucleon propagation is treated by means of a Monte Carlo simulation.
We present microscopic calculations of low energy scattering observables in all possible four nucleon systems : n-3H, p-3He and p-3H. Results were obtained by solving Faddeev-Yakubovski equations in configuration space, appropriately modified to include Coulomb and three-nucleon forces.
With twisted boundary conditions on the quark fields, we study nucleon matrix elements of the axial current utilizing twisted heavy baryon chiral perturbation theory. One can explore the momentum transfer dependence of the axial form factors more easily than by using ordinary lattice quantized momenta alone. As examples, we derive expressions for the nucleon axial radius and pseudoscalar form factor.
We analyze the nucleon axial-vector coupling to two loops in chiral perturbation theory. We show that chiral extrapolations based on this representation require lattice data with pion masses below 300 MeV.
It is shown that the strong volume-dependence of the axial charge of the nucleon seen in lattice QCD calculations can be understood quantitatively in terms of the pion-induced interactions between neighbouring nucleons. The associated wave function renormalization leads to an increased suppression of the axial charge as the strength of the interaction increases, either because of a decrease in lattice size or in pion mass.
We review the current status of experimental and theoretical understanding of the axial nucleon structure at low and moderate energies. Topics considered include (quasi)elastic (anti)neutrino-nucleon scattering, charged pion electroproduction off nucleons and ordinary as well as radiative muon capture on the proton.
We consider corrections to nucleon correlation functions arising from times that are far from the asymptotic limit. For such times, the single nucleon state is contaminated by the pion-nucleon and pion-delta continuum. We use heavy baryon chiral perturbation theory to derive the spectral representation of the nucleon two-point function. Finite time corrections to the axial current correlation function are also derived. Pion-nucleon excited state contributions drive the axial correlator upward, while contributions from the interference of pion-delta and pion-nucleon states drive the axial corre…
The contribution of axial anomaly to charge symmetry breaking in pion-nucleon coupling constants is calculated within instanton model for QCD vacuum. It has been demonstrated that the contribution is large and allows to explain Nolen-Schiffer anomaly.
The charged-current double differential neutrino cross section, measured by the MiniBooNE Collaboration, has been analyzed using a microscopical model that accounts for, among other nuclear effects, long range nuclear (RPA) correlations and multinucleon scattering. We find that MiniBooNE data are fully compatible with the world average of the nucleon axial mass in contrast with several previous analyses which have suggested an anomalously large value. We also discuss the reliability of the algorithm used to estimate the neutrino energy.
Recently, we have worked out the axial two-nucleon current operator to leading one-loop order in chiral effective field theory using the method of unitary transformation. Our final expressions, however, differ from the ones derived by the JLab-Pisa group using time-ordered perturbation theory (Phys. Rev. C 93, no. 1, 015501 (2016) Erratum: [Phys. Rev. C 93, no. 4, 049902 (2016)] Erratum: [Phys. Rev. C 95, no. 5, 059901 (2017)]). In this paper we consider the box diagram contribution to the axial current and demonstrate that the results obtained using the two methods are unitary equivalent at t…
We compute the axial and pseudoscalar form factors of the nucleon in the Dyson-Schwinger approach. To this end, we solve a covariant three-body Faddeev equation for the nucleon wave function and determine the matrix elements of the axialvector and pseudoscalar isotriplet currents. Our only input is a well-established and phenomenologically successful ansatz for the nonperturbative quark-gluon interaction. As a consequence of the axial Ward-Takahashi identity that is respected at the quark level, the Goldberger-Treiman relation is reproduced for all current-quark masses. We discuss the timelike…
We investigate the axial-vector nucleon-to-delta transition form factors in the framework of relativistic baryon chiral perturbation theory at the one-loop order using the complex-mass renormalization scheme. We determine the available six free parameters by fitting to an empirical parametrization of the form factors obtained from the BNL neutrino bubble chamber experiments. A unique feature of our calculation is the prediction of a non-vanishing form factor $C_3^A(Q^2)$. Moreover, our results show a surprising sensitivity to the coupling constant $\texttt{g}_1$ of the leading-order Lagrangian…
We analyze magnetic and axial two-nucleon contact terms in a combined large-$N_c$ and pionless effective field theory expansion. These terms play important roles in correctly describing, e.g., the low-energy cross section of radiative neutron capture and the deuteron magnetic moment. We show that the large-$N_c$ expansion hints towards a hierarchy between the two leading-order magnetic terms that matches that found in phenomenological fits. We also comment on the issue of naturalness in different Lagrangian bases.
In this contribution, baryon axial-vector couplings are studied in the framework of the combined 1/Nc and chiral expansions. This framework is implemented on the basis of the emergent spin-flavor symmetry in baryons at large Nc and HBChPT, and linking both expansions (ξ-expansion), where 1/Nc is taken to be a quantity O(p). The study is carried out including one-loop contributions, which corresponds to O(ξ^3) for baryon masses and O(ξ^2) for the axial couplings. An analysis of the Lattice QCD results for the axial couplings of both N and Δis presented.
The axial form factor G_A of the nucleon is investigated for the Goldstone-boson-exchange constituent quark model using the point-form approach to relativistic quantum mechanics. The results, being covariant, show large contributions from relativistic boost effects. The predictions are obtained directly from the quark-model wave functions, without any further input such as vertex or constituent-quark form factors, and fall remarkably close to the available experimental data.
We present results on the nucleon scalar, axial and tensor charges, as well as, on the first moments of the unpolarized, polarized and transversity parton distributions using $N_f=2$ and $N_f=2+1+1$ twisted mass fermions. These include an ensemble that yields the physical value of the ratio of the nucleon to the pion mass. Results on the axial charges of hyperons and charmed baryons are also presented for a range of pion masses including the physical one.
Motivated by the emerging possibilities to study threshold pion electroproduction at large momentum transfers at Jefferson Laboratory following the 12 GeV upgrade, we provide a short theory summary and an estimate of the nucleon axial form factor for large virtualities in the $Q^2 = 1-10~\text{GeV}^2$ range using next-to-leading order light-cone sum rules.
The isospin breaking in the nucleon isovector axial charge, $g_A^3$, are calculated within the external field QCD sum-rule approach. The isospin violations arising from the difference in up and down current quark masses and in up and down quark condensates are included; electromagnetic effects are not considered. We find $δg^3_A/g^3_A \approx (0.5-1.0)\times 10^{-2}$, where $δg^3_A = (g^3_A)_p + (g^3_A)_n$ and $ g^3_A = [(g^3_A)_p - (g^3_A)_n]/2$. Using the Goldberger-Treiman relation, we also obtain an estimate of the isospin breaking in the pion-nucleon coupling constant, $(g_{ppπ_0}-g_{nnπ_…
We report lattice QCD results on the axial charges of ground and excited nucleon states of both parities. This is the first study of these quantities with approximately chiral (CI) fermions. Two energy levels in the range of the negative parity resonances N*(1535) and N*(1650) are observed and we determine the axial charge for both. We obtain a small axial charge for one of them, which is consistent with the chiral symmetry restoration in this state as well as with the small axial charge of the N*(1535) predicted within the quark model. This result agrees with the findings of Takahashi et al. …
We use light-front Holography to estimate the valence quark and the meson cloud contributions to the nucleon axial form factor. The free couplings of the holographic model are determined by the empirical data and by the information extracted from lattice QCD. The holographic model provides a good description of the empirical data when we consider a meson cloud mixture of about 30\% in the physical nucleon state. The estimate of the valence quark contribution to the nucleon axial form factor compares well with the lattice QCD data for small pion masses. Our estimate of the meson cloud contribut…
The nucleon self-energy and its relation to the nucleon axial charge gA are discussed at large Nc. The energy is compared for the hedgehog, conventional, and recently proposed dichotomous nucleon wavefunctions which give different values for gA. We consider their energies at both perturbative and non-perturbative levels. In perturbative estimates, we take into account the pion exchanges among quarks up to the third orders of axial charge vertices, including the many-body forces such as the Wess-Zumino terms. It turns out that the perturbative pion exchanges among valence quarks give the same l…
We present results on the nucleon axial form factors within lattice QCD using two flavors of degenerate twisted mass fermions. Volume effects are examined using simulations at two volumes of spatial length $L=2.1$ fm and $L=2.8$ fm. Cut-off effects are investigated using three different values of the lattice spacings, namely $a=0.089$ fm, $a=0.070$ fm and $a=0.056$ fm. The nucleon axial charge is obtained in the continuum limit and chirally extrapolated to the physical pion mass enabling comparison with experiment.
We show a relationship between elastic electron scattering observables and the elastic neutrino cross section that provides a straightforward determination of the latter from experimental data of the former and relates their uncertainties. An illustration of this procedure is presented using a Hartree-Fock mean field for the nuclear structure of a set of even-even nuclear targets, using the spectra of the neutrinos produced in pion decay at rest. We also analyze the prospects to measure the incoherent axial contribution to the neutrino elastic scattering in odd targets.
Quasielastic neutrino-nucleon scattering is a basic signal process for neutrino oscillation studies. At accelerator energies, the corresponding cross section is subject to significant uncertainty due to the poorly constrained axial-vector form factor of the nucleon. A model-independent description of the axial-vector form factor is presented. Data from the MiniBooNE experiment for quasielastic neutrino scattering on carbon are analyzed under the assumption of a definite nuclear model. The value of the axial mass parameter, m_A=0.85^{+0.22}_{-0.07} +/- 0.09 GeV, is found to differ significantly…
Two new sets of QCD sum rules for the nucleon axial coupling constants are derived using the external-field technique and generalized interpolating fields. An in-depth study of the predicative ability of these sum rules is carried out using a Monte-Carlo based uncertainty analysis. The results show that the standard implementation of the QCD sum rule method has only marginal predicative power for the nucleon axial coupling constants, as the relative errors are large. The errors range from approximately 50 to 100% compared to the nucleon mass obtained from the same method, which has only 10% to…
We report on our calculation of the nucleon axial and tensor charges in 2+1-flavor QCD with dynamical overlap quarks. Gauge ensembles are generated at a single lattice spacing 0.12 fm and at a strange quark mass close to its physical value. We employ the all-mode-averaging technique to calculate the relevant nucleon correlation functions, and the disconnected quark loop is efficiently calculated by using the all-to-all quark propagator. We present our preliminary results for the isoscalar and isovector charges obtained at pion masses $m_π$ = 450 and 540 MeV.
A joint fit to neutrino-nucleon scattering and pion electroproduction data is performed to evaluate the nucleon axial form factor in the two-component model consisting of a three-quark intrinsic structure surrounded by a meson cloud. Further constrains on the model are obtained by re-evaluating the electromagnetic form factor using electron scattering data. The results of the axial form factor show sizable differences with respect to the widely used dipole model. The impact of such changes on the Charged-Current Quasi-Elastic neutrino-nucleus cross-section is evaluated in the SuSAv2 nuclear mo…
We examine the effects of SU(3) breaking in the matrix elements of the flavour-diagonal axial currents between octet baryon states and find that SU(3) breaking may be substantial for some matrix elements. We estimate the strange axial matrix element in the proton to be between -0.35 and 0 and the matrix element of the flavour-singlet current in the proton to be between -0.1 and +0.3 from the E-143 measurement g_1(x) . The up-quark content of the $Ξ^-$ is discussed and its implications for nonleptonic weak processes discussed. We also estimate the matrix element of the axial current coupling to…
The Bayesian approach for feed-forward neural networks has been applied to the extraction of the nucleon axial form factor from the neutrino-deuteron scattering data measured by the Argonne National Laboratory (ANL) bubble chamber experiment. This framework allows to perform a model-independent determination of the axial form factor from data.. When the low $0.05 < Q^2 < 0.10$ GeV$^2$ data is included in the analysis, the resulting axial radius disagrees with available determinations. Furthermore, a large sensitivity to the corrections from the deuteron structure is obtained. In turn, when the…
