Nucleon Magnetic Moments Research Articles

Examination of the strangeness contribution to the nucleon magnetic moment

We examine the nucleon strangeness magnetic moment ${\ensuremath{\mu}}_{s}$ with a lowest order meson cloud model. We observe that (1) strangeness in the nucleon is a natural requirement of the empirical relation ${\ensuremath{\mu}}_{p}∕{\ensuremath{\mu}}_{n}=\ensuremath{-}3∕2$, which favors an SU(3) octet meson cloud instead of merely the SU(2) pions. (2) In a consistent perturbative calculation, the quark vertex contribution to ${\ensuremath{\mu}}_{s}$ is divergently positive, the meson cloud contribution to ${\ensuremath{\mu}}_{s}$ is divergently negative, and the sum is convergent and negative. (3) In the rest frame of the nucleon, ${\ensuremath{\mu}}_{s}$ cannot be separated into a quark part and an antiquark part, neither can ${\ensuremath{\mu}}_{s}$ be calculated via the spin and orbital angular momentum of the strange quarks and antiquarks. (4) While the overall sign of ${\ensuremath{\mu}}_{s}$ is under debate, the spin part of ${\ensuremath{\mu}}_{s}$ (which is related to the strange quark tensor charge) is better known to be negative.

Spin-orbital structure of the nucleon magnetic moment

How the nucleon magnetic moment originates from the quark spin and orbital motions is an important issue of the nucleon structure. The Gordon decomposition separates the quark vector current and magnetic moment into a spin and an orbital parts. We show that the spin part is related to the quark tensor charge, thus can be determined experimentally and computed reliably by lattice QCD. Knowledge of the spin-orbital structure of the nucleon magnetic moment would also shed light on the nucleon spin problem. As an example, we show that the spin part of the nucleon strangeness magnetic moment ${\ensuremath{\mu}}_{s}$ is negative. If the experimental result of a positive ${\ensuremath{\mu}}_{s}$ is confirmed, then the orbital motion of strange quarks must be important in the nucleon.

Pion mass dependence of nucleon magnetic moments

The relevance of the pion mass, provenient from a term which explicitely breaks chiral symmetry in the Lagrangian, for nucleon magnetic moment in the frame work of the Skyrme model in two different versions: the usual one model and a modified one which includes a coupling to a light scalar meson field, the sigma s(<img id="_x0000_i1026" src="../../img/revistas/bjp/v34n1a/a08img11.gif" align=absmiddle> 500 - 600 MeV). Results are compared to other calculations. Our main motivation comes from usual extrapolations for values of low energy QCD observables obtained in lattices with large values of pion/quark masses toward realistic value of m p which do not allow it. We do a comparison with results from the Cloudy Bag Model and a chiral hadronic model from chiral perturbation theory. There are several resulting extrapolations from the region of large pion mass to the realistic value depending on the considered model for low energy QCD.

Chiral extrapolations of nucleon properties from lattice QCD

We report on recent work about the study of quark mass dependence of nucleon magnetic moments and axial-vector coupling constant. We examine the feasibility of chiral effective field theory methods for the extrapolation of lattice QCD data obtained at relative large pion masses down to the physical values.

The fuzzy bag and baryonic properties with center of mass and recoil corrections

The fuzzy bag is a hadronic model which has features both of the bag model (energy-momentum conservation, QCD vacuum energy) and of relativistic potential models (confinement achieved through a potential). It is also a chiral model, with the unique property that the pion field is suppressed in the interior of the bag by means of a scalar potential, and yet chiral symmetry is preserved. This scalar potential allows one to control how far the pion field can penetrate in the interior of the bag. We calculate the masses of the fundamental baryon octet taking into account the center of mass, one-gluon exchange and one-pion exchange corrections. We also calculate the nucleon axial charge, charge radii and magnetic moments including center of mass and recoil corrections. The agreement with experiment is excellent, and the results indicate that the pion field is suppressed only very close to the center of the bag.

NUCLEON SPIN AND MAGNETIC MOMENT STRUCTURE

This talk reports the phenomenological model and the nonperturbative QCD studies of the nucleon spin and magnetic moment structure.

Nucleon form factors from a covariant quark core: Limits in their description

In treating the relativistic 3-quark problem, a dressed-quark propagator parameterization is used which is compatible with recent lattice data and pion observables. Furthermore 2-quark correlations are modeled as a series of quark loops in the scalar and axialvector channel. The resulting reduced Faddeev equations are solved for nucleon and delta. Nucleon electromagnetic form factors are calculated in a fully covariant and gauge-invariant scheme. Whereas the proton electric form factor G E and the nucleon magnetic moments are described correctly, the neutron electric form factor and the ratio G E/G M for the proton appear to be quenched. The influence of vector mesons on the form factors is investigated which amounts to a 25% modification of the electromagnetic proton radii within this framework.

Quark mass dependence of nucleon properties and extrapolations from lattice QCD

We summarize developments concerning the quark mass dependence of nucleon magnetic moments and the axial-vector coupling constant g A . The aim is to explore the feasibility of chiral effective field theory methods for the extrapolation of lattice QCD results, from the relatively large quark masses that can be handled in such computations down to the physically relevant range.

Continuum moment equations on the lattice

An analysis is given as to why one can not directly evaluate continuum moment equations, i.e., equations involving powers of the position variable times charge, current, or energy/momentum operators, on the lattice. I examine two cases: a three point function evaluation of the nucleon magnetic moment and a four point function (charge overlap) evaluation of the pseudoscalar charge radius.

Lattice study of the magnetic moment and the spin structure of the nucleon

Using an approach free from momentum extrapolation, we calculate the nucleon magnetic moment and the fraction of the nucleon spin carried by the quark angular momentum in the quenched lattice QCD approximation. Quarks with three values of lattice masses, 210, 124 and 80 MeV, are formulated on the lattice using the standard Wilson approach. At every mass, 100 gluon configurations on 16^3 x 32 lattice with \beta=6.0 are used for statistical averaging. The results are compared with the previous calculations with momentum extrapolation. The contribution of the disconnected diagrams is studied at the largest quark mass using noise theory technique.

Baryon magnetic moments in the effective quark Lagrangian approach

An effective quark Lagrangian is derived from first principles through bilocal gluon field correlators. It is used to write down equations for baryons, containing both perturbative and nonperturbative fields. As a result one obtains magnetic moments of octet and decuplet baryons without introduction of constituent quark masses and using only string tension as an input. Magnetic moments come out on average in reasonable agreement with experiment, except for nucleons and $\Sigma^-$. The predictions for the proton and neutron are shown to be in close agreement with the empirical values once we choose the string tension such to yield the proper nucleon mass. Pionic corrections to the nucleon magnetic moments have been estimated. In particular, the total result of the two-body current contributions are found to be small. Inclusion of the anomalous magnetic moment contributions from pion and kaon loops leads to an improvement of the predictions.

Electromagnetic structure of the nucleon in the perturbative chiral quark model

We apply the perturbative chiral quark model (PCQM) at one loop to analyze the electromagnetic structure of nucleons. This model is based on an effective Lagrangian, where baryons are described by relativistic valence quarks and a perturbative cloud of Goldstone bosons. Including the electromagnetic interaction we first develop the formalism up to one loop in the Goldstone boson fluctuation relying on renormalization by use of counterterms. Local gauge invariance is satisfied both on the Lagrangian level and also for the relevant baryon matrix elements in the Breit frame. We apply the formalism to obtain analytical expressions for the nucleon charge and magnetic form factors, which are expressed in terms of fundamental parameters of low-energy pion-nucleon physics (weak pion decay constant, axial nucleon coupling, strong pion-nucleon form factor) and of only one model parameter (radius of the nucleonic three-quark core). A detailed numerical analysis of the nucleon magnetic moments, charge and magnetic radii, and also the momentum dependence of form factors is presented.

Lattice QCD calculations of hadron structure: Constituent quarks and chiral symmetry

New data from parity-violating experiments on the deuteron now allow isolation of the strange-quark contribution to the nucleon magnetic moment, G_M^s(0), without the uncertainty surrounding the anapole moment of the nucleon. Still, best estimates place G_M^s(0) > 0. It is illustrated how this experimental result challenges the very cornerstone of the constituent quark model. The chiral physics giving rise to G_M^s(0) \sim 0 is illustrated.

Lattice QCD analysis of the strangeness magnetic moment of the nucleon

The outcome of the SAMPLE Experiment suggests that the strange-quark contribution to the nucleon magnetic moment, G_M^s(0), may be greater than zero. This result is very difficult to reconcile with expectations based on the successful baryon magnetic-moment phenomenology of the constituent quark model. We show that careful consideration of chiral symmetry reveals some rather unexpected properties of QCD. In particular, it is found that the valence u-quark contribution to the magnetic moment of the neutron can differ by more than 50% from its contribution to the Xi^0 magnetic moment. This hitherto unforeseen result leads to the value G_M^s(0) = -0.16 +/- 0.18 with a systematic error, arising from the relatively large strange quark mass used in existing lattice calculations, that would tend to shift G_M^s(0) towards small positive values.

Nucleon magnetic moments in an extended chiral constituent quark model

We present results for the nucleon magnetic moments in the context of an extended chiral constituent quark model based on the mechanism of the Goldstone boson exchange, as suggested by the spontaneous breaking of chiral symmetry in QCD. The electromagnetic charge-current operator is consistently deduced from the model Hamiltonian, which includes all force components for the pseudoscalar, vector and scalar meson exchanges. Thus, the continuity equation is satisfied for each piece of the interaction, avoiding the introduction of any further parameter. A good agreement with experimental values is found. The role of isoscalar two-body operators, not constrained by the continuity equation, is also investigated.

Cold Ideal Equation of State for Strongly Magnetized Neutron Star Matter: Effects on Muon Production and Pion Condensation

Neutron stars with very strong surface magnetic fields have been suggested as the site for the origin of observed soft gamma repeaters (SGRs). In this paper we investigate the influence of such strong magnetic fields on the properties and internal structure of these strongly magnetized neutron stars (magnetars). We study properties of a degenerate equilibrium ideal neutron-proton-electron (npe) gas with and without the effects of the anomalous nucleon magnetic moment in a strong magnetic field. The presence of a sufficiently strong magnetic field changes the ratio of protons to neutrons as well as the neutron drip density. We also study the appearance of muons as well as pion condensation in strong magnetic fields. We discuss the possibility that boson condensation in the interior of magnetars might be a source of SGRs.

Incorporating chiral symmetry in extrapolations of octet baryon magnetic moments

We explore methods of extrapolating lattice calculations of hadronic observables to the physical regime, while respecting the constraints of chiral symmetry and heavy quark effective theory. In particular, we extrapolate lattice results for magnetic moments of the spin-1/2 baryon octet to the physical pion mass and compare with experimental measurements. The success previously reported for extrapolations of the nucleon magnetic moments carries over to the Σ baryons. A study of the residual discrepancies in the Ξ baryon moments suggests that it is important to have new simulation data with a more realistic strange quark mass.

Nucleon spin with and without hyperon data: a new tool for analysis

We present a simple explanation of the underlying physics in the use of hyperon decay data to obtain information about proton spin structure. We also present an alternative input using nucleon magnetic moment data and show that the results from the two approaches are nearly identical. The role of symmetry breaking is clarified while pointing out that simple models explaining the violation of the Gottfried sum rule via pion emission tend to lose the good SU(3) predictions from Cabibbo theory for hyperon decays.

Nucleon magnetic moments beyond the perturbative chiral regime

The quark mass dependence of nucleon magnetic moments is explored over a wide range. Quark masses currently accessible to lattice QCD, which lie beyond the regime of chiral perturbation theory $(\ensuremath{\chi}\mathrm{PT})$, are accessed via the cloudy bag model (CBM). The latter reproduces the leading nonanalytic behavior of $\ensuremath{\chi}\mathrm{PT}$, while modeling the internal structure of the hadron under investigation. We find that the predictions of the CBM are succinctly described by the simple formula ${\ensuremath{\mu}}_{N}{(m}_{\ensuremath{\pi}})={\ensuremath{\mu}}_{N}^{(0)}/(1+\ensuremath{\alpha}{m}_{\ensuremath{\pi}}+\ensuremath{\beta}{m}_{\ensuremath{\pi}}^{2})$, which reproduces the lattice data, as well as the leading nonanalytic behavior of $\ensuremath{\chi}\mathrm{PT}$. As this form also incorporates the anticipated Dirac moment behavior in the limit ${m}_{\ensuremath{\pi}}\ensuremath{\rightarrow}\ensuremath{\infty}$, it constitutes a powerful method for extrapolating lattice results to the physical mass regime.

N + p → d + γ in effective field theory

The radiative capture process n + p → d + γ provides clear evidence for meson exchange currents in nuclear physics. We compute this process at low energies using a recently developed power counting for the effective field theory that describes nucleon-nucleon interactions. The leading order contribution to this process comes from the photon coupling to the nucleon magnetic moments. At subleading order there are other contributions. Among these are graphs where the photon couples directly to pions, i.e. meson exchange currents. These diagrams are divergent and require the presence of a local four-nucleon-one-photon counterterm. The coefficient of this operator is determined by the measured cross section, σ expt = 334.2±0.5 mb, for incident neutrons with speed | v| = 2200 m/s.