Low-energy analysis of the nucleon electromagnetic form factors

Journal of High Energy Physics, 2014

In the partonic (or light-front) description of relativistic systems the electromagnetic form factors are expressed in terms of frame-independent charge and magnetization densities in transverse space. This formulation allows one to identify the chiral components of nucleon structure as the peripheral densities at transverse distances b = O(M −1 π ) and compute them in a parametrically controlled manner. A dispersion relation connects the large-distance behavior of the transverse charge and magnetization densities to the spectral functions of the Dirac and Pauli form factors near the two-pion threshold at timelike t = 4M 2 π , which can be computed in relativistic chiral effective field theory. Using the leading-order approximation we (a) derive the asymptotic behavior (Yukawa tail) of the isovector transverse densities in the "chiral" region b = O(M −1 π ) and the "molecular" region b = O(M 2 N /M 3 π ); (b) perform the heavy-baryon expansion of the transverse densities; (c) explain the relative magnitude of the peripheral charge and magnetization densities in a simple mechanical picture; (d) include ∆ isobar intermediate states and study the peripheral transverse densities in the large-N c limit of QCD; (e) quantify the region of transverse distances where the chiral components of the densities are numerically dominant; (f) calculate the chiral divergences of the b 2 -weighted moments of the isovector transverse densities (charge and anomalous magnetic radii) in the limit M π → 0 and determine their spatial support. Our approach provides a concise formulation of the spatial structure of the nucleon's chiral component and offers new insights into basic properties of the chiral expansion. It relates the information extracted from low-t elastic form factors to the generalized parton distributions probed in peripheral high-energy scattering processes.

Physical Review C

The nucleon's peripheral transverse charge and magnetization densities are computed in chiral effective field theory. The densities are represented in first-quantized form, as overlap integrals of chiral light-front wave functions describing the transition of the nucleon to soft pion-nucleon intermediate states. The orbital motion of the pion causes a large left-right asymmetry in a transversely polarized nucleon. The effect attests to the relativistic nature of chiral dynamics [pion momenta k = O(Mπ)] and could be observed in form factor measurements at low momentum transfer.

Journal of High Energy Physics

The nucleon's electromagnetic form factors are expressed in terms of the transverse densities of charge and magnetization at fixed light-front time. At peripheral transverse distances b = O(M −1 π ) the densities are governed by chiral dynamics and can be calculated model-independently using chiral effective field theory (EFT). We represent the leading-order chiral EFT results for the peripheral transverse densities as overlap integrals of chiral light-front wave functions, describing the transition of the initial nucleon to soft pion-nucleon intermediate states and back. The new representation (a) explains the parametric order of the peripheral transverse densities; (b) establishes an inequality between the spin-independent and -dependent densities; (c) exposes the role of pion orbital angular momentum in chiral dynamics; (d) reveals a large left-right asymmetry of the current in a transversely polarized nucleon and suggests a simple interpretation. The light-front representation enables a first-quantized, quantum-mechanical view of chiral dynamics that is fully relativistic and exactly equivalent to the second-quantized, field-theoretical formulation. It relates the charge and magnetization densities measured in low-energy elastic scattering to the generalized parton distributions probed in peripheral high-energy scattering processes. The method can be applied to nucleon form factors of other operators, e.g. the energy-momentum tensor.

Physical Review D, 2004

We study nuclear µ − − e − conversion in the general framework of an effective Lagrangian approach without referring to any specific realization of the physics beyond the standard model (SM) responsible for lepton flavor violation (L f /). We examine the impact of a specific hadronization prescription on the analysis of new physics in nuclear µ − −e − conversion and stress the importance of vector meson exchange between lepton and nucleon currents. A new issue of this mechanism is the presence of the strange quark vector current contribution induced by the φ meson. This allows us to extract new limits on the L f / lepton-quark effective couplings from the existing experimental data.

Physical Review D, 2013

We revisit the status of Lepton Flavor Violating (LFV) µeqq contact interactions from the view point of µ − − e −-conversion in nuclei. We consider their contribution to this LFV process via the two mechanisms on the hadronic level: direct nucleon and meson exchange ones. In the former case the quarks are embedded directly into the nucleons while in the latter in mesons which then interact with nucleons in a nucleus. We revise and in some cases reevaluate the hadronic parameters relevant for both mechanisms and calculate the contribution of the above mentioned contact interactions in coherent µ − − e −-conversion in various nuclei. Then we update our previous upper bounds and derive new ones for the scales of the µeqq contact interactions from the experimental limits on the capture rates of µ − − e −-conversion. We compare these limits with the ones derived in the literature from other LFV processes and comment on the prospects of LHC searches related to the contact µeqq interactions.

Physical Review D, 2008

We calculate chiral corrections to the semileptonic vector and axial quark coupling constants using a manifestly Lorentz covariant chiral quark approach up to order O(p 4) in the two-and tree-flavor picture. These couplings are then used in the evaluation of the corresponding couplings which govern the semileptonic transitions between octet baryon states. In the calculation of baryon matrix elements we use a general ansatz for the spatial form of the quark wave function, without referring to a specific realization of hadronization and confinement of quarks in baryons. Matching the physical amplitudes calculated within our approach to the model-independent predictions of baryon chiral perturbation theory (ChPT) allows to deduce a connection between our parameters and those of baryon ChPT.

Few-Body Systems, 2007

The relativistic amplitudes of pion photo-and electroproduction are calculated by dispersion relations at constant t. Several sum rules and low-energy theorems for the threshold amplitudes are investigated within this technique. The continuation of the amplitudes to sub-threshold kinematics is shown to provide a unique framework to derive the low-energy constants of chiral perturbation theory by global properties of the excitation spectrum.

Physical Review D, 2007

The meson-cloud model of the nucleon consisting of a system of three valence quarks surrounded by a meson cloud is applied to study the electroweak structure of the proton and neutron. Light-cone wavefunctions are derived for the dressed nucleon as pictured to be part of the time a bare nucleon and part of the time a baryon-meson system. Configurations are considered where the baryon can be a nucleon or a ∆ and the meson can be a pion as well as a vector meson such as the ρ or the ω. An overall good description of the electroweak form factors is obtained. The contribution of the meson cloud is small and only significant at low Q 2. Mixedsymmetry S ′-wave components in the wavefunction are most important to reproduce the neutron electric form factor. Charge and magnetization densities are deduced as a function of both the radial distance from the nucleon center and the transverse distance with respect to the direction of the three-momentum transfer. In the latter case a central negative charge is found for the neutron. The up and down quark distributions associated with the Fourier transform of the axial form factor have opposite sign, with the consequence that the probability to find an up (down) quark with positive helicity is maximal when it is (anti)aligned with the proton helicity.

Physical Review C

Properties of hot and dense matter are calculated in the framework of quantum hadro-dynamics by including contributions from two-loop (TL) diagrams arising from the exchange of iso-scalar and iso-vector mesons between nucleons. Our extension of mean-field theory (MFT) employs the same five density-independent coupling strengths which are calibrated using the empirical properties at the equilibrium density of iso-spin symmetric matter. Results of calculations from the MFT and TL approximations are compared for conditions of density, temperature, and proton fraction encountered in the study of core-collapse supernovae, young and old neutron stars, and mergers of compact binary stars. The TL results for the equation of state (EOS) of cold pure neutron matter at sub-and near-nuclear densities agree well with those of modern quantum Monte Carlo and effective field-theoretical approaches. Although the high-density EOS in the TL approximation for cold and beta-equilibrated neutron-star matter is substantially softer than its MFT counterpart, it is able to support a 2M neutron star required by recent precise determinations. In addition, radii of 1.4M stars are smaller by ∼ 1 km than obtained in MFT and lie in the range indicated by analysis of astronomical data. In contrast to MFT, the TL results also give a better account of the single-particle or optical potentials extracted from analyses of medium-energy proton-nucleus and heavy-ion experiments. In degenerate conditions, the thermal variables are well reproduced by results of Landau's Fermi-Liquid theory in which density-dependent effective masses feature prominently. The ratio of the thermal components of pressure and energy density expressed as Γ th = 1 + (P th / th), often used in astrophysical simulations, exhibits a stronger dependence on density than on proton fraction and temperature in both MFT and TL calculations. The prominent peak of Γ th at supra-nuclear density found in MFT is, however, suppressed in TL calculations. This outcome is analogous to results of non-relativistic models when exchange contributions from finite-range interactions are included in addition to those of contact interactions.

Physical Review C, 2013

The objectives of the present work are twofold. The first is to address and resolve some of the differences present in independent, chiral-effective-field-theory (χEFT) derivations up to one loop, recently appeared in the literature, of the nuclear charge and current operators. The second objective is to provide a complete set of χEFT predictions for the structure functions and tensor polarization of the deuteron, for the charge and magnetic form factors of 3 He and 3 H, and for the charge and magnetic radii of these few-nucleon systems. The calculations use wave functions derived from high-order chiral two-and three-nucleon potentials and Monte Carlo methods to evaluate the relevant matrix elements. Predictions based on conventional potentials in combination with χEFT charge and current operators are also presented. There is excellent agreement between theory and experiment for all these observables for momentum transfers up to q 2.0-2.5 fm -1 ; for a subset of them, this agreement extends to momentum transfers as high as q ≃ 5-6 fm -1 . A complete analysis of the results is provided.

Physical Review C, 2011

We have analyzed pion-nucleon scattering using the manifestly relativistic covariant framework of Infrared Regularization up to O(q 3) in the chiral expansion, where q is a generic small momentum. We describe the low-energy phase shifts with a similar quality as previously achieved with Heavy Baryon Chiral Perturbation Theory, √ s 1.14 GeV. New values are provided for the O(q 2) and O(q 3) low-energy constants, which are compared with previous determinations. This is also the case for the scattering lengths and volumes. Finally, we have unitarized the previous amplitudes and as a result the energy range where data are reproduced increases significantly.

Journal of Physics G: Nuclear and Particle Physics, 2001

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.

Physical Review D, 2003

The spin structure of the nucleon is analyzed in the framework of a Lorentz-invariant formulation of baryon chiral perturbation theory. The structure functions of doubly virtual Compton scattering are calculated to one-loop accuracy (fourth order in the chiral expansion). We discuss the generalization of the Gerasimov-Drell-Hearn sum rule, the Burkhardt-Cottingham sum rule and moments of these. We give predictions for the forward and the longitudinal-transverse spin polarizabilities of the proton and the neutron at zero and finite photon virtuality. A detailed comparison to results obtained in heavy baryon chiral perturbation theory is also given.

Physical Review D, 2005

The strong and electromagnetic decays of the ground-state tensor mesons are studied in an effective field approach. A fit to the well-known experimental data is performed. The decay ratios of the tensor glueball are evaluated and possible candidates are discussed.

The European Physical Journal A, 2005

We analyze the Fubini-Furlan-Rosetti sum rule in the framework of covariant baryon chiral perturbation theory to leading one-loop accuracy and including next-to-leading order polynomial contributions. We discuss the relation between the subtraction constants in the invariant amplitudes and certain low-energy constants employed in earlier chiral perturbation theory studies of threshold neutral pion photoproduction off nucleons. In particular, we consider the corrections to the sum rule due to the finite pion mass and show that below the threshold they agree well with determinations based on fixed-t dispersion relations. We also discuss the energy dependence of the electric dipole amplitude E0+.

Physical review, 2020

We present results for the isovector (pn) electromagnetic form factors of the nucleon using 11 ensembles of gauge configurations generated by the MILC Collaboration using the highly improved staggered quark action with 2 þ 1 þ 1 dynamical flavors. These ensembles span four lattice spacings a ≈ 0.06, 0.09, 0.12 and 0.15 fm and three values of the light-quark masses corresponding to the pion masses M π ≈ 135, 225 and 315 MeV. High-statistics estimates using the truncated-solver method allow us to quantify various systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, lattice volume and light-quark masses. We analyze the Q 2 dependence of the form factors calculated over the range 0.05 ≲ Q 2 ≲ 1.4 GeV 2 using both the model-independent z expansion and the dipole Ansatz. Our final estimates, using the z-expansion fit, for the isovector root-mean-square radius of nucleon are r E ¼ 0.769ð27Þð30Þ fm, r M ¼ 0.671ð48Þð76Þ fm and μ p-n ¼ 3.939ð86Þð138Þ Bohr magneton. The first error is the combined uncertainty from the leading-order analysis, and the second is an estimate of the additional uncertainty due to using the leading-order chiral-continuum-finite-volume fits. The estimates from the dipole Ansatz, r E ¼ 0.765ð11Þð8Þ fm, r M ¼ 0.704ð21Þð29Þ fm and μ p-n ¼ 3.975ð84Þð125Þ Bohr magneton, are consistent with those from the z expansion but with smaller errors. Our analysis highlights three points. First, all our data for form factors from the 11 ensembles and existing lattice data on, or close to, physical mass ensembles from other collaborations collapse more clearly onto a single curve when plotted versus Q 2 =M 2 N as compared to Q 2 with the scale set by quantities other than M N . The difference between these two ways of analyzing the data is indicative of discretization errors, some of which presumably cancel when the data are plotted versus Q 2 =M 2 N . Second, the size of the remaining deviation of this common curve from the Kelly curve is small and can be accounted for by statistical and possible systematic uncertainties. Third, to improve lattice estimates for hr 2 E i, hr 2 M i and μ, high-statistics data for Q 2 < 0.1 GeV 2 are needed.

Physical review, 2022

We present a high statistics study of the isovector nucleon charges and form factors using seven ensembles of 2 þ 1-flavor Wilson-clover fermions. The axial vector and pseudoscalar form factors obtained on each of these ensembles satisfy the partially conserved axial current relation between them once the lowest energy Nπ excited state is included in the spectral decomposition of the correlation functions used for extracting the ground state matrix elements. Similarly, we find evidence that the Nππ excited state contributes to the correlation functions with the insertion of the vector current, consistent with the vector meson dominance model. The resulting form factors are consistent with the Kelly parametrization of the experimental electric and magnetic data. Our final estimates for the isovector charges are g u-d A ¼ 1.32ð6Þð5Þ sys , g u-d S ¼ 1.06ð9Þð6Þ sys , and g u-d T ¼ 0.97ð3Þð2Þ sys , where the first error is the overall analysis uncertainty and the second is an additional combined systematic uncertainty. The form factors yield: (i) the axial charge radius squared, hr 2 A i u-d ¼ 0.428ð53Þð30Þ sys fm 2 ; (ii) the induced pseudoscalar charge, g à P ¼ 7.9ð7Þð9Þ sys ; (iii) the pion-nucleon coupling, g πNN ¼ 12.4ð1.2Þ; (iv) the electric charge radius squared, hr 2 E i u-d ¼ 0.85ð12Þð19Þ sys fm 2 ; (v) the magnetic charge radius squared, hr 2 M i u-d ¼ 0.71ð19Þð23Þ sys fm 2 ; and (vi) the magnetic moment, μ u-d ¼ 4.15ð22Þð10Þ sys . All our results are consistent with phenomenological/experimental values but with larger errors. Last, we present a Padé parametrization of the axial, electric, and magnetic form factors over the range 0.04 < Q 2 < 1 GeV 2 for phenomenological studies.