Nucleon Magnetic Moments Research Articles

Chiral properties of the nucleon interpolating current and θ -dependent observables

We revisit the chiral properties of nucleon interpolating currents, and show that of the two leading order currents j1 and j2, only two linear combinations j1±j2 transform covariantly under the anomalous U(1)A symmetry. As a result, calculations of quantities which vanish by symmetry in the chiral limit may produce unphysical results if carried out with different linear combinations of the currents. This includes observables such as electric dipole moments, induced by the quantum chromodynamics (QCD) parameter θ, and the θ-dependence of the nucleon mass. For completeness, we also exhibit the leading order results for nucleon electric dipole moments (dn,p) induced by θ, and the nucleon magnetic moments (μn,p), when calculated using QCD sum rules for both the covariant choices of the nucleon interpolating current. The results in each channel, conveniently expressed as the ratios, dn,p/μn,p, are numerically consistent, and reflect the required physical dependence on θ. Published by the American Physical Society 2024

Magnetic moments of the octet, decuplet, low-lying charm, and low-lying bottom baryons in a nuclear medium

Abstract We study the magnetic moments of the octet, decuplet, low-lying charm, and low-lying bottom baryons with nonzero light quarks in symmetric nuclear matter using the quark–meson coupling (QMC) model, which satisfies the constraint for the allowed maximum change (swelling) of the in-medium nucleon size derived from the y-scaling data for 3He(e, e′) and 56Fe(e, e′). This is the first study to estimate the in-medium magnetic moments of the low-lying charm and bottom baryons with nonzero light quarks. The present QMC model also satisfies the expected allowed maximum enhancement of the nucleon magnetic moments in nuclear matter. Moreover, it has been proven that the calculated in-medium to free proton electromagnetic form factor (EMFF) ratios calculated within the QMC model reproduce well the proton EMFF super ratio extracted from $^4{\rm He}(\vec{e},e^{\prime }\vec{p})^3{\rm H}$ at Jefferson Laboratory. The medium modifications of the magnetic moments are estimated by evaluating the in-medium to free space baryon magnetic moment ratios to compensate the MIT bag deficiency to describe the free space octet baryon magnetic moments, where ratios are often measured directly in experiments even without knowing the absolute values, such as the free and bound proton electromagnetic form factors, as well as the European Muon Collaboration effect to extract the structure function F2 ratio of the bound to free nucleons by the corresponding cross section ratio. We also present the results calculated with the different current quark mass values for the strange and bottom quarks to see the possible impact. Furthermore, for practical use we give the explicit density-dependent parametrizations for the vector potentials of the baryons and light-(u, d) quarks, as well as for the effective masses of the baryons treated in this study, and of the mesons ω, ρ, K, K*, η, $\eta^{\prime}$, D, D*, B, and B*.

Nuclear charge densities in spherical and deformed nuclei: Toward precise calculations of charge radii

Background: Precise measurements of atomic transitions affected by electron-nucleus hyperfine interactions offer sensitivity to explore basic properties of the atomic nucleus and study fundamental symmetries, including the search for new physics beyond the standard model of particle physics. In particular, such measurements, augmented by atomic and nuclear calculations, will enable extraction of the higher-order radial moments of the charge-density distribution in spherical and deformed nuclei. The new data impose higher precision requirements on a theoretical description.Purpose: The nuclear charge density is composed of the proton point distribution folded with the nucleonic charge distributions. The latter induce subtle relativistic corrections due to the coupling of nucleon magnetic moments with the nuclear spin-orbit density. Additional corrections come from the effect of center-of-mass projection. We assess the precision of nuclear charge density calculations by studying the behavior of relativistic and center-of-mass motion corrections to the second and fourth charge radial moments. Special attention has been paid to the magnetic spin-orbit density associated with the local variations of the spin-orbit current.Methods: The calculations for semimagic and open-shell nuclei are performed in the framework of self-consistent mean-field theory using quantified energy density functionals and density-dependent pairing forces. We used the general expression for the spin-orbit form factor that is valid for spherical and deformed nuclei.Results: We studied the impact of various correction terms on the charge radii, fourth radial moments, diffraction radii, and surface thickness of spherical and deformed nuclei. The spin-orbit corrections to charge radial moments and surface thickness show strong shell fluctuations which can make an appreciable effect when aiming at high-precision predictions of isotopic shifts. The inclusion of relativistic and center-of-mass corrections impacts the quality of energy density functionals optimized to charge radii data.Conclusions: To establish reliable constraints on the existence of new forces from isotope shift measurements, precise calculations of nuclear charge densities of deformed nuclei are needed. The proper inclusion of the spin-orbit charge density and other correction terms is essential when aiming at extraction of subtle effects which become particularly visible in isotopic trends. It is also important when developing high-quality nuclear energy density functionals optimized using heterogeneous datasets involving absolute charge radii, differential charge radii, and charge form factor properties deduced from electron-scattering data.

Diquarks and nucleons under strong magnetic fields in the NJL model

We study the description of nucleons and diquarks in the presence of a uniform strong magnetic field within the framework of the two-flavor Nambu-Jona--Lasinio (NJL) model. Diquarks are constructed through the resummation of quark loop chains using the random phase approximation, while nucleons are treated as bound quark-diquark states described by a relativistic Fadeev equation, using the static approximation for quark exchange interactions. For charged particles, analytical calculations are performed using the Ritus eigenfunction method, which properly takes into account the breakdown of translation invariance that arises from the presence of Schwinger phases. Within this scheme, for definite model parametrizations we obtain numerical predictions for diquark and nucleon masses, which are compared with Chiral Perturbation Theory and Lattice QCD results. In addition, numerical estimations for nucleon magnetic moments are obtained.

Nucleon Electromagnetic Structure from Lattice QCD

We present an evaluation of nucleon to Δ electromagnetic form factors within Lattice QCD. The EMR and CMR ratios are calculated both in the quenched theory and using two degenerate flavors of dynamical Wilson fermions. We obtain values in qualitative agreement to experiment. In addition, we evaluate the isovector Sachs electromagnetic form factors of the nucleon both in the quenched and unquenched theory for momentum transfer squared in the range between 0.1 and 2 GeV2. The nucleon magnetic moment and r.m.s. radii are obtained using chiral effective theory to extrapolate to the physical pion mass.

Nucléon Electromagnetic Form Factors in a constituent-quark model

The electromagnetic form factors of the nucléon are calculated in an extended chiral constituent-quark model where the effective interaction is described by the exchange of pseudoscalar and vector mesons belonging to the pseudoscalar and pseudovector octet, respectively, and a scalar meson . Two-body current-density operators, constructed consistently with the extended model Hamiltonian in order to preserve gauge invariance and current conservation, are found to give a significant contribution to the nucléon magnetic form factors and improve the estimates of the nucleon magnetic moments.

Magnetic field dependence of Delta isobars properties in a Skyrme model

The properties of $\mathrm{\ensuremath{\Delta}}$ isobars in a uniform magnetic field are investigated. General relations between the magnetic moments of nucleons and $\mathrm{\ensuremath{\Delta}}$ isobars in a weak magnetic field are given. In a strong magnetic field, the masses and sizes of $\mathrm{\ensuremath{\Delta}}$ isobars depend on the magnetic field strength in different ways: the effective masses of ${\mathrm{\ensuremath{\Delta}}}^{++}$, ${\mathrm{\ensuremath{\Delta}}}^{+}$, and ${\mathrm{\ensuremath{\Delta}}}^{0}$ (the sizes of ${\mathrm{\ensuremath{\Delta}}}^{++}$ and ${\mathrm{\ensuremath{\Delta}}}^{+}$) first decrease (increase) and then increase (decrease), whereas the effective mass of ${\mathrm{\ensuremath{\Delta}}}^{\ensuremath{-}}$ (the sizes of ${\mathrm{\ensuremath{\Delta}}}^{0}$ and ${\mathrm{\ensuremath{\Delta}}}^{\ensuremath{-}}$) always increases (decrease). Our estimates show that, in the core part of the magnetar, the equation of state for $\mathrm{\ensuremath{\Delta}}$ isobars depends on the magnetic field, which affects the upper limit on the mass of the magnetar.

Dirac Shell Quark-core Model for the Study of Non-strange Baryonic Spectroscopy

A Dirac shell model is developed for the study of baryon spectroscopy, taking into account the most relevant results of the quark-diquark models. The lack of translational invariance of the shell model is avoided, in the present work, by introducing a scalar-isoscalar fictitious particle that represents the origin of quark shell interaction; in this way the states of the system are eigenstates of the total momentum of the baryon. Only one-particle excitations are considered. A two-quark core takes the place of the diquark, while the third quark is excited to reproduce the baryonic resonances. For the $N(939)$ and $\Delta(1232)$, that represent the ground states of the spectra, the three quarks are considered identical particles and the wave functions are completely antisymmetric. The model is used to calculate the spectra of the $N$ and $\Delta$ resonances and the nucleon magnetic moments. The results are compared to the present experimental data. Due to the presence of the core and to the one-particle excitations, the structure of the obtained spectra is analogous to that given by the quark-diquark models.

Role of Four Gravitational Constants in Nuclear Structure

This paper attempts to understand the role of the four gravitational constants in the nuclear structure whichhelps in understanding the nuclear elementary charge, the strong coupling constant, nuclear charge radii,nucleon magnetic moments, nuclear stability, nuclear binding energy and Neutron life time. The three assumed atomic gravitational constants help in understanding neutron-proton stability. Electromagnetic and nuclear gravitational constants play a role in understanding proton-electron mass ratio, Bohr radius and characteristic atomic radius. With reference to the weak gravitational constant, it is possible to predict the existence of a weakly interacting fermion of rest energy 585 GeV, called Higg’s fermion. Cosmological ‘dark matter’ research and observations can be carried out in this direction also.

Effect of external magnetic fields on nucleon mass in a hot and dense medium: Inverse magnetic catalysis in the Walecka model

Vacuum to nuclear matter phase transition has been studied in presence of constant external background magnetic field with the mean field approximation in Walecka model. The anomalous nucleon magnetic moment has been taken into account using the modified "weak" field expansion of the fermion propagator having non-trivial correction terms for charged as well as for neutral particles. The effect of nucleon magnetic moment is found to favour the magnetic catalysis effect at zero temperature and zero baryon density. However, extending the study to finite temperatures, it is observed that the anomalous nuclear magnetic moment plays a crucial role in characterizing the qualitative behaviour of vacuum to nuclear matter phase transition even in case of the weak external magnetic fields . The critical temperature corresponding to the vacuum to nuclear medium phase transition is observed to decrease with the external magnetic field which can be identified as the inverse magnetic catalysis in Walecka model whereas the opposite behaviour is obtained in case of vanishing magnetic moment indicating magnetic catalysis.

Sea quarks contribution to the nucleon magnetic moment and charge radius at the physical point

We report a comprehensive analysis of the light and strange disconnected-sea quarks contribution to the nucleon magnetic moment, charge radius, and the electric and magnetic form factors. The lattice QCD calculation includes ensembles across several lattice volumes and lattice spacings with one of the ensembles at the physical pion mass. We adopt a model-independent extrapolation of the nucleon magnetic moment and the charge radius. We have performed a simultaneous chiral, infinite volume, and continuum extrapolation in a global fit to calculate results in the continuum limit. We find that the combined light and strange disconnected-sea quarks contribution to the nucleon magnetic moment is ${\ensuremath{\mu}}_{M}(\mathrm{DI})=\ensuremath{-}0.022(11)(09)\text{ }\text{ }{\ensuremath{\mu}}_{N}$ and to the nucleon mean square charge radius is $⟨{r}^{2}{⟩}_{E}(\mathrm{DI})=\ensuremath{-}0.019(05)(05)\text{ }\text{ }{\mathrm{fm}}^{2}$ which is about $1/3$ of the difference between the $⟨{r}_{p}^{2}{⟩}_{E}$ of electron-proton scattering and that of a muonic atom and so cannot be ignored in obtaining the proton charge radius in the lattice QCD calculation. The most important outcome of this lattice QCD calculation is that while the combined light-sea and strange quarks contribution to the nucleon magnetic moment is small at about 1%, a negative 2.5(9)% contribution to the proton mean square charge radius and a relatively larger positive 16.3(6.1)% contribution to the neutron mean square charge radius come from the sea quarks in the nucleon. For the first time, by performing global fits, we also give predictions of the light and strange disconnected-sea quarks contributions to the nucleon electric and magnetic form factors at the physical point and in the continuum and infinite volume limits in the momentum transfer range of $0\ensuremath{\le}{Q}^{2}\ensuremath{\le}0.5\text{ }\text{ }{\mathrm{GeV}}^{2}$.

Strange Quark Magnetic Moment of the Nucleon at the Physical Point.

We report a lattice QCD calculation of the strange quark contribution to the nucleon's magnetic moment and charge radius. This analysis presents the first direct determination of strange electromagnetic form factors including at the physical pion mass. We perform a model-independent extraction of the strange magnetic moment and the strange charge radius from the electromagnetic form factors in the momentum transfer range of 0.051 GeV^{2}≲Q^{2}≲1.31 GeV^{2}. The finite lattice spacing and finite volume corrections are included in a global fit with 24 valence quark masses on four lattices with different lattice spacings, different volumes, and four sea quark masses including one at the physical pion mass. We obtain the strange magnetic moment G_{M}^{s}(0)=-0.064(14)(09)μ_{N}. The four-sigma precision in statistics is achieved partly due to low-mode averaging of the quark loop and low-mode substitution to improve the statistics of the nucleon propagator. We also obtain the strange charge radius ⟨r_{s}^{2}⟩_{E}=-0.0043(16)(14) fm^{2}.

Position space method for the nucleon magnetic moment in lattice QCD

The extraction of the magnetic form factor of the nucleon at zero momentum transfer is usually performed by adopting a parametrization for its momentum dependence and fitting the results obtained at finite momenta. We present a position space method that allows us to remove the momentum prefactor in the form factor decomposition and hence compute the magnetic form factor directly at zero momentum without the need to assume a functional form for its momentum dependence. The method is explored on one ensemble using $N_f=2+1+1$ Wilson twisted mass fermions with a light quark mass corresponding to $M_\pi\approx373\mathrm{GeV}$ and a lattice spacing of $a\approx0.082\mathrm{fm}$. We obtain results for the isovector magnetic moment and for the proton and neutron magnetic moments. The value we find for the isovector magnetic moment is larger as compared to fitting the form factor at the discrete values of the lattice momentum transfers using a dipole Ansatz, bringing it closer to the experimental value.

Relativistic quark-diquark model of baryons with a spin-isospin transition interaction: Non-strange baryon spectrum and nucleon magnetic moments

The relativistic interacting quark-diquark model of baryons, recently developed, is here extended to introduce a spin-isospin transition interaction into the mass operator. The refined version of the model is used to calculate the non strange baryon spectrum. The results are compared to the present experimental data.

Pure sea-quark contributions to the magnetic form factors ofΣbaryons

We propose the pure sea-quark contributions to the magnetic form factors of $\Sigma$ baryons, $G_{\Sigma^-}^u$ and $G_{\Sigma^+}^d$, as priority observables for the examination of sea-quark contributions to baryon structure, both in present lattice QCD simulations and possible future experimental measurement. $G_{\Sigma^-}^u$, the $u$-quark contribution to the magnetic form factor of $\Sigma^-$, and $G_{\Sigma^+}^d$, the $d$-quark contribution to the magnetic form factor of $\Sigma^+$, are similar to the strange quark contribution to the magnetic form factor of the nucleon, but promise to be larger by an order of magnitude. We explore the size of this quantity within chiral effective field theory, including both octet and decuplet intermediate states. The finite range regularization approach is applied to deal with ultraviolet divergences. Drawing on an established connection between quenched and full QCD, this approach makes it possible to predict the sea quark contribution to the magnetic form factor purely from the meson loop. In the familiar convention where the quark charge is set to unity $G_{\Sigma^-}^u = G_{\Sigma^+}^d$. We find a value of $-0.38^{+0.16}_{-0.17}\ \mu_N$, which is about seven times larger than the strange magnetic moment of the nucleon found in the same approach. Including quark charge factors, the $u$-quark contribution to the $\Sigma^-$ magnetic moment exceeds the strange quark contribution to the nucleon magnetic moment by a factor of 14.

Constraining nucleon strangeness

Determining the nonperturbative $s\bar{s}$ content of the nucleon has attracted considerable interest and been the subject of numerous experimental searches. These measurements used a variety of reactions and place important limits on the vector form factors observed in parity-violating (PV) elastic scattering and the parton distributions determined by deep inelastic scattering (DIS). In spite of this progress, attempts to relate information obtained from elastic and DIS experiments have been sparse. To ameliorate this situation, we develop an interpolating model using light-front wave functions capable of computing both DIS and elastic observables. This framework is used to show that existing knowledge of DIS places significant restrictions on our wave functions. The result is that the predicted effects of nucleon strangeness on elastic observables are much smaller than those tolerated by direct fits to PV elastic scattering data alone. Using our model, we find $-0.024 \le \mu_s \le 0.035$, and $-0.137 \le \rho^D_s \le 0.081$ for the strange contributions to the nucleon magnetic moment and charge radius. The model we develop also independently predicts the nucleon's strange spin content $\Delta s$ and scalar density $\langle N| \bar{s}s | N \rangle$, and for these we find agreement with previous determinations.

Chiral extrapolation of nucleon magnetic moments at next-to-leading-order

Nucleon magnetic moments display a rich nonanalytic dependence on the quark mass in both quenched and full QCD. They provide a forum for a detailed examination of the connection between quenched and full QCD made possible through the formalism of finite-range regularised chiral effective field theory. By defining meson-cloud and core contributions through the careful selection of a regularisation scale, one can correct the meson cloud of quenched QCD to make full QCD predictions. Whereas past success is based on unquenching the leading-order loop contributions, here we extend and test the formalism including next to leading-order (NLO) loop contributions. We discuss the subtleties associated with working at NLO and illustrate the role of higher-order corrections.

Chiral extrapolations for nucleon magnetic moments

Lattice QCD simulations have made significant progress in the calculation of nucleon electromagnetic form factors in the chiral regime in recent years. With simulation results achieving pion masses of order ~180 MeV, there is an apparent challenge as to how the physical regime is approached. By using contemporary methods in chiral effective field theory, both the quark-mass and finite-volume dependence of the isovector nucleon magnetic moment are carefully examined. The extrapolation to the physical point yields a result that is compatible with experiment, albeit with a combined statistical and systematic uncertainty of 10%. The extrapolation shows a strong finite-volume dependence; lattice sizes of L > 5 fm must be used to simulate results within 2% of the infinite-volume result for the magnetic moment at the physical pion mass.

Constraining Quark Angular Momentum through Semi-Inclusive Measurements

The determination of quark angular momentum requires the knowledge of the generalized parton distribution E in the forward limit. We assume a connection between this function and the Sivers transverse-momentum distribution, based on model calculations and theoretical considerations. Using this assumption, we show that it is possible to fit nucleon magnetic moments and semi-inclusive single-spin asymmetries at the same time. This imposes additional constraints on the Sivers function and opens a plausible way to quantifying quark angular momentum.

Gyromagnetic factors and atomic clock constraints on the variation of fundamental constants

We consider the effect of the coupled variations of fundamental constants on the nucleon magnetic moment. The nucleon g-factor enters into the interpretation of the measurements of variations in the fine-structure constant, alpha, in both the laboratory (through atomic clock measurements) and in astrophysical systems (e.g. through measurements of the 21 cm transitions). A null result can be translated into a limit on the variation of a set of fundamental constants, that is usually reduced to alpha. However, in specific models, particularly unification models, changes in alpha are always accompanied by corresponding changes in other fundamental quantities such as the QCD scale, Lambda_QCD. This work tracks the changes in the nucleon g-factors induced from changes in Lambda_QCD and the light quark masses. In principle, these coupled variations can improve the bounds on the variation of alpha by an order of magnitude from existing atomic clock and astrophysical measurements. Unfortunately, the calculation of the dependence of g-factors on fundamental parameters is notoriously model-dependent.