Electroproduction Of Nucleon Resonances Research Articles

Resonance Electroproduction and the Origin of Mass

One of the greatest challenges within the Standard Model is to discover the source of visible mass. Indeed, this is the focus of a “Millennium Problem”, posed by the Clay Mathematics Institute. The answer is hidden within quantum chromodynamics (QCD); and it is probable that revealing the origin of mass will also explain the nature of confinement. In connection with these issues, this perspective will describe insights that have recently been drawn using contemporary methods for solving the continuum bound-state problem in relativistic quantum field theory and how they have been informed and enabled by modern experiments on nucleon-resonance electroproduction.

Nucleon-to-Roper electromagnetic transition form factors at large Q2

High-precision nucleon-resonance electroproduction data on a large kinematic domain of energy and momentum transfer have proven crucial in revealing novel features of strong interactions within the Standard Model and unfolding structural details of baryon excited states. Thus, in anticipation of new data reaching to unprecedented photon virtuality, we employ a quark-diquark approximation to the three valence-quark bound-state problem to compute $\gamma^\ast p \to R^+$ and $\gamma^\ast n \to R^0$ transition form factors on $Q^2/m_N^2 \in [0,12]$, where $m_N$ is the nucleon mass. Having simultaneously analysed both charged and neutral channels, we also provide a quark-flavour separation of the transition form factors. The results should be useful in planning new-generation experiments.

Electroproduction of theN*(1535)nucleon resonance in QCD

Following the 12 GeV upgrade, a dedicated experiment is planned with the Hall B CLAS12 detector at Jefferson Lab, with the aim to study electroproduction of nucleon resonances at high photon virtualities up to $Q^2 = 12$ GeV$^2$. In this work we present a QCD-based approach to the theoretical interpretation of these upcoming results in the framework of light-cone sum rules that combine perturbative calculations with dispersion relations and duality. The form factors are thus expressed in terms of $N^\ast(1535)$ light-front wave functions at small transverse separations, called distribution amplitudes. The distribution amplitudes can therefore be determined from the comparison with the experimental data on form factors and compared to the results of lattice QCD simulations. The results of the corresponding next-to-leading order calculation are presented and compared with the existing data. We find that the form factors are dominated by the twist-four distribution amplitudes that are related to the $P$-wave three-quark wave functions of the $N^\ast(1535)$, i.e. to contributions of orbital angular momentum.

Photoproduction and electroproduction of nucleon resonances in point form relativistic quantum mechanics

We employ point form relativistic quantum mechanics to calculate the photoproduction and electroproduction of nucleon resonances. Both the transverse and longitudinal transition amplitudes are computed based on the constituent quark model within the relativistic framework. The obtained results are compared with the calculations of the nonrelativistic approach and of the hypercentral potential model. Relativistic effects and discrepancies among the models are discussed.

Electroproduction of nucleon resonances

The unitary isobar model MAID has been extended and used for a partial wave analysis of pion photo- and electroproduction in the resonance region W < 2 GeV. Older data from the world data base and more recent experimental results from Mainz, Bates, Bonn and JLab for Q^2 up to 4.0 (GeV/c)^2 have been analyzed and the Q^2 dependence of the helicity amplitudes have been extracted for a series of four star resonances. We compare single-Q^2 analyses with a superglobal fit in a new parametrization of Maid2003 together with predictions of the hypercentral constituent quark model. As a result we find that the helicity amplitudes and transition form factors of constituent quark models should be compared with the analysis of bare resonances, where the pion cloud contributions have been subtracted.

Helicity and isospin asymmetries in the electroproduction of nucleon resonances.

We investigate the helicity asymmetries and isospin ratios of radiative transition amplitudes for nucleon resonances electroproduced off proton and neutron targets at momentum transfers of ${Q}^{2}\ensuremath{\le}3$ Ge${\mathrm{V}}^{2}$. Calculations were done in the framework of a relativized constituent quark model which includes many-body effects due to the quark interaction potential and a consistent relativistic approximation of the center-of-mass motion of the three-quark system. We find significant deviations from the predictions of the nonrelativistic quark models and the ${\mathrm{SU}(6)}_{W}$ algebraic approach based on the single-quark-transition hypothesis. Our calculated relativistic corrections lead to an overall better agreement with the experimental data. The question of whether some of the low-lying $P$-wave baryons are of hybrid nature is briefly discussed. Finally we analyze the electroexcitation of the missing (20,${1}^{+}$) $P$-wave resonances.

Helicity structure of nucleon resonance electroproduction and quark motion effect

Helicity structure of nucleon resonance electroproduction and quark motion effect

Electroproduction of Nucleon Resonances with Polarized Leptons

The electroproduction of nucleon resonances with polarized leptons and a polarized nucleon target is considered and compared with what is expected to be the behavior of deep inelastic polarized scattering. We find a set of nucleon resonances in the symmetric quark model such that their excitation gives the same results for the ratio of neutron to proton inelastic scattering and for the polarization asymmetry on protons and neutrons as does the naive quark-parton model. However, the symmetric quark model with harmonic forces predicts dramatic variations in the helicity structure of the excitation of the prominent nucleon resonances, which are not supported by the existing data. Additional tests of the symmetric quark model and a discussion of what is known of resonance excitation with what is expected in polarized deep inelastic scattering are presented.

Electromagnetic Excitations of the Nucleon in a Relativistic Quark Model

A variation of the relativistic quark model of Feynman, Ravndal, and Kislinger is considered that admits spatial wave functions normalizable in all components of the relative variables. With these wave functions, the matrix elements of the hadronic electromagnetic current between the nucleon and excited states are calculated for final states up to 1700 MeV in mass. Very good agreement between the predicted elastic nucleon electromagnetic form factors and experiment is obtained. Cross sections for the electroproduction of nucleon resonances through the third resonance are derived and compared with experiment. A discussion of the consistency and limitations of the model is presented.

Weak and Electroproduction of Nucleon Resonances in the Harmonic-Oscillator Quark Model

Using the model that the baryons are composed of quarks with harmonic interactions, we compute cross sections for high-energy neutrinos and electrons to excite the nucleon to the resonance states with masses below 1.9 GeV. The frame dependence of the nonrelativistic quark-model results is emphasized and discrepancies between some previous model calculations of electroproduction form factors and data are shown to be due to the frame chosen. For neutrino production, the model predicts that a significant excitation of the second and third resonance regions will be seen from neutrons, but with proton targets only the $\ensuremath{\Delta}(1236)$ excitation will be observed. An interesting result of the electroproduction calculation is the prediction that the ${P}_{11}(1470)$, while suppressed at small $t$ (and hence in photoproduction), will dominate over the ${S}_{11}(1550)$ and ${D}_{13}(1520)$ at large $t\ensuremath{\gtrsim}1.5{(\frac{\mathrm{GeV}}{c})}^{2}$.

Helicity structure of nucleon resonance electroproduction and the symmetric quark model

The symmetric quark model with harmonic forces is shown to lead to a rapid change with q 2 of the helicity structure for electroproduction of the second (D 13) and third (F 15) nucleon resonances. Preliminary results of coincidence measurements of pi-zero electroproduction in the resonance region are found to disagree with this prediction. Some further experimental tests and theoretical consequences of this failure are discussed.

Classical field model predictions for electroproduction of nucleon resonances

A more realistic calculation of electroproduction of nucleon resonances is performed within the framework of a previously developed model of oscillations of the meson field in the nucleon. The nucleon source and the ground-state meson field are determined from the elastic form factors, and the excitations of the meson field are described by continuum wave functions. The absolute cross sections thus obtained are in satisfactory agreement with the data on excitation of the higher resonances.

Scaling and the Behavior of Nucleon Resonances in Inelastic Electron-Nucleon Scattering

The behavior of elastic scattering and of the electroproduction of nucleon resonances is shown to be closely related to the behavior of deep-inelastic electron-nucleon scattering. This relation is discussed in the context of duality ideas taken from strong-interaction processes. These ideas suggest that a substantial part of the observed behavior of inelastic electron-nucleon scattering is due to a nondiffractive component of virtual photon-nucleon scattering. Through finite-energy sum rules, quantitative relations between the elastic and resonance electroproduction form factors and the deep-inelastic scattering are derived and the behavior of inelastic scattering near threshold is calculated.

Electroproduction of Nucleon Resonances in a Relativistic Quark Model

Electroproduction of Nucleon Resonances in a Relativistic Quark Model

Electroproduction of Nucleon Resonances and Implications for Coincidence Experiments

Electroproduction of Nucleon Resonances and Implications for Coincidence Experiments

Electroproduction of nucleon resonances in the region of high momentum transfer

We applyO3.1 analysis of electromagnetic-vertex functions to the electroproduction of resonances. This amounts to an investigation of theO3.1 Fourier transforms of matrix elements of the electromagnetic current between a single-nucleon state and a resonance. We discuss first the restrictions on the analytic structure of these Fourier transforms due to parity and current conservation. A pole in a Fourier transforms corresponds to a definite term in the asymptotic expansion of the form factors in the domain where the momentum transfer is spacelike and large. We exploit this fact for a detailed study of the production of Δ(1236). For the nucleon resonances of isospin 1/2 we make the “tower hypothesis” that one pole dominates simultaneously the form factors of all these resonances and the nucleon itself. This implies a constant value for the ratio of the production cross-sectionvs. the electronucleon elastic cross-section in the limit of large momentum transfers.

Relativistic Model for Electroproduction of Nucleon Resonances. II

Relativistic Model for Electroproduction of Nucleon Resonances. II

Relativistic Model for Electroproduction of Nucleon Resonances

We have made a simple model to obtain some estimates of the inelastic form factors for electron excitation of the nucleon resonances. The model is covariant and gauge invariant, and satisfies all the general requirements of the theory. It relies heavily on the lead of previous theoretical work on the form factor for the ${\frac{3}{2}}^{+}$, $\frac{3}{2}$ (1238-MeV) level. The basic idea is to take from experiment the knowledge of which nucleon states are resonant. We then look at single-pion electroproduction and project out the relevant multipoles from a covariant, gauge-invariant set of graphs which are thought to play an important role as an excitation mechanism. The multipoles are then multiplied by a final-state enhancement factor which provides a resonance mechanism. We give some theoretical justification for this procedure. If just the electron is detected, one measures the virtual-photon width for formation of the resonance, and our result contains the possibility that the resonance can decay into other channels than just $\ensuremath{\pi}+N$. We calculate only the inelastic form factors. The individual contributions of the resonance levels are normalized to photoabsorption, where such data exist. We keep $\ensuremath{\pi}$, $\ensuremath{\omega}$, and $N$ exchange as an excitation mechanism, and treat the over-all contribution of the $\ensuremath{\omega}$ exchange as a single parameter, with which we are able to fit all the existing inelastic-electron-scattering data. We actually find two equally acceptable fits with quite different properties. The $\ensuremath{\omega}$-nucleon coupling constant we get from this analysis is in reasonable agreement with other determinations of this quantity. Form factors for all the nucleon levels up through 2650 MeV are presented out to momentum transfers of interest in the SLAC experiments.

Electroproduction of nucleon resonances

We compute the differential cross section for the process e + p → e + pr where p R is a nucleon resonance characterized by parity π R , spin J, and mass M R . The two inelastic form factors describing this cross section are expressed in terms of three amplitudes characterizing the ( p, p R ) electromagnetic vertex. The kinematic and analytic structure of these three amplitudes as a function of q 2 are discussed. The case of the 33 resonance is discussed in some detail.

Electroproduction of nucleon resonances: J. D. Bjorken, Stanford Linear Accelerator Center, Stanford University, Stanford, California; and J. D. Walecka, A. P. Sloan Foundation Fellow, Department of Physics, Stanford University, Stanford, California

In high-energy heavy-ion collisions, partonic collectivity is evidenced by the constituent quark number scaling of elliptic flow anisotropy for identified hadrons. A breaking of this scaling and dominance of baryonic interactions is found for identified hadron collective flow measurements in sNN = 3 GeV Au+Au collisions. In this paper, we report measurements of the first- and second-order azimuthal anisotropic parameters, v1 and v2, of light nuclei (d, t, 3He, 4He) produced in sNN = 3 GeV Au+Au collisions at the STAR experiment. An atomic mass number scaling is found in the measured v1 slopes of light nuclei at mid-rapidity. For the measured v2 magnitude, a strong rapidity dependence is observed. Unlike v2 at higher collision energies, the v2 values at mid-rapidity for all light nuclei are negative and no scaling is observed with the atomic mass number. Calculations by the Jet AA Microscopic Transport Model (JAM), with baryonic mean-field plus nucleon coalescence, are in good agreement with our observations, implying baryonic interactions dominate the collective dynamics in 3 GeV Au+Au collisions at RHIC.