Nucleon States Research Articles

Factorization theorem relating Euclidean and light-cone parton distributions

In a large-momentum nucleon state, the matrix element of a gauge-invariant Euclidean Wilson line operator accessible from lattice QCD can be related to the standard light-cone parton distribution function through the large-momentum effective theory (LaMET) expansion. This relation is given by a factorization theorem with a non-trivial matching coefficient. Using the operator product expansion we prove the large-momentum factorization of the quasi-parton distribution function in LaMET, and show that the more recently discussed Ioffe-time distribution approach also obeys an equivalent factorization theorem. Explicit results for the coefficients are obtained and compared at one-loop. Our proof clearly demonstrates that the matching coefficients in the $\overline{\rm MS}$ scheme depend on the large partonic momentum rather than the nucleon momentum.

Center of Mass Motion of Short-Range Correlated Nucleon Pairs studied via the A(e,e^{'}pp) Reaction.

Short-range correlated (SRC) nucleon pairs are a vital part of the nucleus, accounting for almost all nucleons with momentum greater than the Fermi momentum (k_{F}). A fundamental characteristic of SRC pairs is having large relative momenta as compared to k_{F}, and smaller center of mass (c.m.) which indicates a small separation distance between the nucleons in the pair. Determining the c.m. momentum distribution of SRC pairs is essential for understanding their formation process. We report here on the extraction of the c.m. motion of proton-proton (pp) SRC pairs in carbon and, for the first time in heavier and ansymetric nuclei: aluminum, iron, and lead, from measurements of the A(e,e^{'}pp) reaction. We find that the pair c.m. motion for these nuclei can be described by a three-dimensional Gaussian with a narrow width ranging from 140 to 170 MeV/c, approximately consistent with the sum of two mean-field nucleon momenta. Comparison with calculations appears to show that the SRC pairs are formed from mean-field nucleons in specific quantum states.

K⁎ mesons with hidden charm arising from KX(3872) and KZc(3900) dynamics

Inspired by the recent discovery of the pentaquark states Pc(4450) and Pc(4380), which can be viewed as excited nucleon states with hidden charm, we study the three-body interaction of a kaon and a pair of DD¯⁎ in isospin 0 and 1. We show that the two body interactions stringently constrained by the existence of the Ds0⁎(2317), Ds1⁎(2460), X(3872), and Zc(3900), which are widely believed to contain large DK, D⁎K, and DD¯⁎ components, inevitably lead to the existence of a heavy K⁎ meson with hidden charm. Concrete coupled channel three-body calculations yield its mass and width as (4307±2)−i(9±2)MeV with I(JP)=1/2(1−). This state, if found experimentally, definitely cannot be accommodated in a qq¯ picture, and therefore presents a clear case of an exotic hadron.

Neutron magnetic polarizability with Landau mode operators

The application of a uniform background magnetic field makes standard quark operators utilising gauge-covariant Gaussian smearing inefficient at isolating the ground state nucleon at nontrivial field strengths. In the absence of QCD interactions, Landau modes govern the quark energy levels. There is evidence that residual Landau mode effects remain when the strong interaction is turned on. Here we introduce novel quark operators constructed from the two-dimensional $U(1)$ Laplacian eigenmodes that describe the Landau levels of a charged particle on a periodic finite lattice. These eigenmode-projected quark operators provide enhanced precision for calculating nucleon energy shifts in a magnetic field. Using asymmetric source and sink operators, we are able to encapsulate the predominant effects of both the QCD and QED interactions in the interpolating fields for the neutron. The neutron magnetic polarizability is calculated using these techniques on the $32^3 \times 64$ dynamical QCD lattices provided by the PACS-CS Collaboration. In conjunction with a chiral effective-field theory analysis, we obtain a neutron magnetic polarizability of $\beta^n = 2.05(25)(19) \times 10^{-4}$ fm$^3$, where the numbers in parentheses describe statistical and systematic uncertainties.

Evaluation of the Integrated Cross Sections of Reactions of Exclusive Pion and Kaon Electroproduction off Protons in the Resonance Region at Photon Virtualities from 5 to 12 GeV2

The integrated cross sections of the ep → eπ+n, ep → eπ0p, ep → eK+Λ, and ep → eK+Σ0 reactions are evaluated in the energy range of nucleon resonance excitation at photon virtualities Q2 from 5 to 12 GeV2. These exclusive channels will be explored at photon virtualities Q2 > 5 GeV2 for the first time in future experiments with the CLAS12 detector. The cross-section evaluation is based on the extrapolation of exclusive contributions to the inclusive structure functions F1 and F2 from a region of Q2 < 5 GeV2, in which the experimental data are available, to the region of higher Q2. This evaluation of cross sections is of particular importance in the development of the program of experiments with the CLAS12 detector for studying the structure of the ground and excited nucleon states, which may reveal the dynamics of strong interactions in the nonperturbative regime.

Holographic estimate of the meson cloud contribution to nucleon axial form factor

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 contribution to the nucleon axial form factor has a slower falloff with the square momentum transfer compared to typical estimates from quark models with meson cloud dressing.

Nucleon Resonance Structure from Exclusive Meson Electroproduction with CLAS

Studies of the nucleon resonance electroexcitation amplitudes in a wide range of photon virtualities offer unique information on many facets of strong QCD behind the generation of all prominent excited nucleon states. Advances in the evaluation of resonance electroexcitation amplitudes from the data measured with the CLAS detector and the future extension of these studies with the CLAS12 detector at Jefferson Lab are presented. For the first time, analyses of $\pi^0p$, $\pi^+n$, $\eta p$, and $\pi^+\pi^-p$ electroproduction off proton channels have provided electroexcitation amplitudes of most resonances in the mass range up to 1.8 GeV and at photon virtualities $Q^2 < 5$~GeV$^2$.Studies of the resonance electroexcitation amplitudes revealed the $N^*$ structure as a complex interplay between the inner core of three dressed quarks and the external meson-baryon cloud. The successful description of the $\Delta(1232)3/2^+$ and $N(1440)1/2^+$ electrocouplings achieved within the Dyson-Schwinger Equation approach under a traceable connection to the QCD Lagrangian and supported by the novel light front quark model demonstrated the relevance of dressed quarks with dynamically generated masses as an active structural component in baryons. Future experiments with the CLAS12 detector will offer insight into the structure of all prominent resonances at the highest photon virtualities, $Q^2 < 12$~GeV$^2$, ever achieved in exclusive reactions, thus addressing the most challenging problems of the Standard Model on the nature of hadron mass, quark-gluon confinement, and the emergence of nucleon resonance structures from QCD. A search for new states of hadronic matter, the so-called hybrid-baryons with glue as a structural component, will complete the long term efforts on the resonance spectrum exploration.

Collective and single-particle degrees of freedom in rotating nuclei

In 1937, Hermann Jahn and Edward Teller published their research describing a mechanism of symmetry breaking in nonlinear polyatomic molecules resulting in a lifting of orbital degeneracy of an electronic state (Proc. R. Soc. London, Ser. A 1937, 161, 220), yielding insight into molecular structure. The impact of symmetry breaking on the energy and structure of quantum states is not unique to molecules and may be applied to nuclei, involving degenerate nucleon states as opposed to electronic states. Reinhard and Otten showed that the nuclear Jahn–Teller effect provides a mechanism applicable to describe the commonly observed collective quadrupole surface motion (Nucl. Phys. A 1984, 420, 173). To take into account single-particle effects, it is important to properly model the valence nucleons, especially those occupying large angular momenta orbitals near the Fermi level. In this work, a model has been developed in which two valence nucleons of the same kind are coupled to an axially symmetric quadrupole deformed rotor of the D2 symmetry and interact through the nuclear delta force. To test this model, the band of the lowest-energy state at a given spin for 126Ce is reproduced. The resultant wavefunctions are then used to calculate the g factor, reduced electric quadrupole transition probability, and spectroscopic quadrupole moment all as a function of spin. This method lays the groundwork to explore higher order symmetries following the multipole expansion.

Finite continuum quasi distributions from lattice QCD

We present a new approach to extracting continuum quasi distributions from lattice QCD. Quasi distributions are defined by matrix elements of a Wilson-line operator extended in a spatial direction, evaluated between nucleon states at finite momentum. We propose smearing this extended operator with the gradient flow to render the corresponding matrix elements finite in the continuum limit. This procedure provides a nonperturbative method to remove the power-divergence associated with the Wilson line and the resulting matrix elements can be directly matched to light-front distributions via perturbation theory.

Structure of the Nucleon and its Excitations

The structure of the ground state nucleon and its finite-volume excitations are examined from three different perspectives. Using new techniques to extract the relativistic components of the nucleon wave function, the node structure of both the upper and lower components of the nucleon wave function are illustrated. A non-trivial role for gluonic components is manifest. In the second approach, the parity-expanded variational analysis (PEVA) technique is utilised to isolate states at finite momenta, enabling a novel examination of the electric and magnetic form factors of nucleon excitations. Here the magnetic form factors of low-lying odd-parity nucleons are particularly interesting. Finally, the structure of the nucleon spectrum is examined in a Hamiltonian effective field theory analysis incorporating recent lattice-QCD determinations of low-lying two-particle scattering-state energies in the finite volume. The Roper resonance of Nature is observed to originate from multi-particle coupled-channel interactions while the first radial excitation of the nucleon sits much higher at approximately 1.9 GeV.

Axial-vector form factors of the nucleon from lattice QCD

We present results for the form factors of the isovector axial vector current in the nucleon state using large scale simulations of lattice QCD. The calculations were done using eight ensembles of gauge configurations generated by the MILC collaboration using the HISQ action with 2+1+1 dynamical flavors. These ensembles span three lattice spacings $a \approx 0.06, 0.09$ and $0.12$ fm and light-quark masses corresponding to the pion masses $M_\pi \approx 135, 225$ and $310$ MeV. High-statistics estimates allow us to quantify systematic uncertainties in the extraction of $G_A(Q^2)$ and the induced pseudoscalar form factor $\tilde{G}_P(Q^2)$. We perform a simultaneous extrapolation in the lattice spacing, lattice volume and light-quark masses of the axial charge radius $r_A$ data to obtain physical estimates. Using the dipole ansatz to fit the $Q^2$ behavior we obtain $r_A|_{\rm dipole} = 0.49(3)$ fm, which corresponds to ${\cal M}_A = 1.39(9)$ GeV, and is consistent with ${\cal M}_A = 1.35(17)$ GeV obtained by the miniBooNE collaboration. The estimate obtained using the $z$-expansion is $r_A|_{z-{\rm expansion}} = 0.46(6)$ fm, and the combined result is $r_A|_{\rm combined} = 0.48(4)$ fm. Analysis of the induced pseudoscalar form factor $\tilde{G}_P(Q^2)$ yields low estimates for $g_P^\ast$ and $g_{\pi {\rm NN}}$ compared to their phenomenological values. To understand these, we analyze the partially conserved axial current (PCAC) relation by also calculating the pseudoscalar form factor. We find that these low values are due to large deviations in the PCAC relation between the three form factors and from the pion-pole dominance hypothesis.

Microscopic core-quasiparticle coupling model for spectroscopy of odd-mass nuclei

Predictions of the spectroscopic properties of low-lying states are critical for nuclear structure studies, but are problematic for nuclei with an odd nucleon due to the interplay of the unpaired single particle with nuclear collective degrees of freedom. In this work, a microscopic core-quasiparticle coupling (CQC) model based on the covariant density functional theory is developed that contains the collective excitations of even-mass cores and spherical single-particle states of the odd nucleon as calculated from a quadrupole collective Hamiltonian combined with a constrained triaxial relativistic Hartree-Bogoliubov model. Predictions of the new model for excitation energies, kinematic and dynamic moments of inertia, and transition rates are shown to be in good agreement with results of low-lying spectroscopy measurements of the axially deformed odd-proton nucleus $^{159}$Tb and the odd-neutron nucleus $^{157}$Gd. Future studies with additional nuclei are planned.

Temperature effects on nuclear pseudospin symmetry in the Dirac-Hartree-Bogoliubov formalism

We present finite temperature Dirac-Hartree-Bogoliubov (FTDHB) calculations for the tin isotope chain to study the dependence of pseudospin on the nuclear temperature. In the FTDHB calculation, the density dependence of the self-consistent relativistic mean fields, the pairing, and the vapor phase that takes into account the unbound nucleon states are considered self-consistently. The mean field potentials obtained in the FTDHB calculations are fit by Woods-Saxon (WS) potentials to examine how the WS parameters are related to the energy splitting of the pseudospin pairs as the temperature increases. We find that the nuclear potential surface diffuseness is the main driver for the pseudospin splittings and that it increases as the temperature grows. We conclude that pseudospin symmetry is better realized when the nuclear temperature increases. The results confirm the findings of previous works using RMF theory at $T=0$, namely that the correlation between the pseudospin splitting and the parameters of the Woods-Saxon potentials implies that pseudospin symmetry is a dynamical symmetry in nuclei. We show that the dynamical nature of the pseudospin symmetry remains when the temperature is considered in a realistic calculation of the tin isotopes, such as that of the Dirac-Hartree-Bogoliubov formalism.

Isospin breaking from diquark clustering

Although SU(2) isospin symmetry is generally assumed in the basic theory of the strong interaction, a number of significant violations have been observed in scattering and bound states of nucleons. Many of these violations can be attributed to the electromagnetic interaction but the question of how much of the violation is due to it remains open. A schematic model based on clustering of quarks in the interior of the confinement region of the two-nucleon system is introduced and evaluated. In this model the Coulomb interaction is the source of all isospin breaking. It draws on a picture of the quark density based on the diquark-quark model of hadron structure which has been investigated by a number of groups. The model produces three isospin breaking potentials connecting This illustrative model suggests that the breaking seen in the low-energy NN interaction may be understood in terms of the Coulomb force between members of diquark clusters. It allows the prediction of the charge symmetry breaking interaction and the $nn$ scattering length from the well measured $np$ singlet scattering length. Values of the $nn$ scattering length around $-18$ fm are favored. Since the model is based on the quark picture, it can be easily extended, in the SU(3) limit, to calculate isospin breaking in the strange sector in the corresponding channels. A natural consequence of isospin breaking from diquark clustering is that the breaking in the strange sector, as measured by the separation energy difference between $_{\Lambda}^4$H and $_{\Lambda}^4$He, is several times larger than that seen in the comparison of three-nucleon mirror nuclei as observed experimentally.

Direct Measurement of Nuclear Dependence of Charged Current Quasielasticlike Neutrino Interactions Using MINERvA.

Charged-current ν_{μ} interactions on carbon, iron, and lead with a final state hadronic system of one or more protons with zero mesons are used to investigate the influence of the nuclear environment on quasielasticlike interactions. The transferred four-momentum squared to the target nucleus, Q^{2}, is reconstructed based on the kinematics of the leading proton, and differential cross sections versus Q^{2} and the cross-section ratios of iron, lead, and carbon to scintillator are measured for the first time in a single experiment. The measurements show a dependence on the atomic number. While the quasielasticlike scattering on carbon is compatible with predictions, the trends exhibited by scattering on iron and lead favor a prediction with intranuclear rescattering of hadrons accounted for by a conventional particle cascade treatment. These measurements help discriminate between different models of both initial state nucleons and final state interactions used in the neutrino oscillation experiments.

Alpha-Like Clustering in $$^{20}$$ 20 Ne from a Quartetting Wave Function Approach

Quartetting ($\alpha$-like clustering) occurs in low density matter ($\le 0.03$ fm$^{-3}$) which exists, e.g., at the surface of nuclei. It is of interest for the $\alpha$ preformation to calculate the $\alpha$ decay of heavy nuclei such as $^{212}$Po, but also in light nuclei (e.g., $^{20}$Ne) which shows strong signatures of quartetting. We analyze the intrinsic structure of the $\alpha$-like cluster and the center of mass motion of the quartet, in particular the role of Pauli blocking. The Thomas-Fermi model for the (daughter) core nucleus is improved introducing quasiparticle nucleon states. Calculations performed for harmonic oscillator basis states show that the effective potential for the quartet center of mass motion remains nearly constant within the core nucleus. The relation to the THSR (Tohsaki-Horiuchi-Schuck-R\"opke) approach is discussed.

Dispersive approach to two-photon exchange in elastic electron-proton scattering

We examine the two-photon exchange corrections to elastic electron-proton scattering within a dispersive approach, including contributions from both Nucleon and Delta intermediate states. The dispersive analysis avoids off-shell uncertainties inherent in traditional approaches based on direct evaluation of loop diagrams, and guarantees the correct unitary behavior in the high energy limit. Using empirical information on the electromagnetic nucleon elastic and N-Delta transition form factors, we compute the two-photon exchange corrections both algebraically and numerically. Results are compared with recent measurements of e+p to e-p cross section ratios from the CLAS, VEPP-3 and OLYMPUS experiments, as well as with polarization transfer observables.

Transverse momentum dependent quark and gluon distributions of light nuclei

We investigate the unpolarized transverse momentum dependent (TMD) structure of light nuclei in the modified chiral quark exchange model (QEM), for the first time. To this end, we calculate the TMD quark and gluon distributions inside the bound state nucleons of the light nuclei based on the modified chiral quark model in which the TMD bare quark distributions of the bounded nucleons are needed. In order to compute these bare distributions, we first obtain the bare quark momentum densities using the QEM and then calculate the TMD bare distributions applying a theoretical method in which the light-cone variables are used. Finally, considering the nucleon structure of helium, tritium and deuteron nuclei, we obtain their TMD quark and gluon densities at low Q2 scale. It is shown that our results have appropriate properties that are expected for the TMD distribution functions.

Collinear parton distributions and the structure of the nucleon sea in a light-front meson-cloud model

The unpolarized, helicity and transversity parton distribution functions of the nucleon are studied within a convolution model where the bare nucleon is dressed by its virtual meson cloud. Using light-front time-ordered perturbation theory, the Fock states of the physical nucleon are expanded in a series involving a bare nucleon and two-particle, meson-baryon, states. The bare baryons and mesons are described with light-front wave functions (LFWFs) for the corresponding valence-parton components. Using a representation in terms of overlap of LFWFs, the role of the non-perturbative antiquark degrees of freedom and the valence quark contribution at the input scale of the model is discussed for the leading-twist collinear parton distributions. After introducing perturbative QCD effects through evolution to experimental scales, the results are compared with available data and phenomenological extractions. Predictions for the nucleon tensor charge are also presented, finding a very good agreement with recent phenomenological extractions.

Semirelativistic approximation to the γ*N→N(1520) and γ*N→N(1535) transition form factors

The representation of the wave functions of the nucleon resonances within a relativistic framework is a complex task. In a nonrelativistic framework the orthogonality between states can be imposed naturally. In a relativistic generalization, however, the derivation of the orthogonality condition between states can be problematic, particularly when the states have different masses. In this work we study the $N(1520)$ and $N(1535)$ states using a relativistic framework. We considered wave functions derived in previous works, but impose the orthogonality between the nucleon and resonance states using the properties of the nucleon, ignoring the difference of masses between the states (semirelativistic approximation). The $N(1520)$ and $N(1535)$ wave functions are then defined without any adjustable parameters and are used to make predictions for the valence quark contributions to the transition form factors. The predictions compare well with the data particularly for high momentum transfer, where the dominance of the quark degrees of freedom is expected.