T. S. H. Lee

STUDIES OF NUCLEON RESONANCE STRUCTURE IN EXCLUSIVE MESON ELECTROPRODUCTION

Studies of the structure of excited baryons are key factors to the N* program at Jefferson Lab (JLab). Within the first year of data taking with the Hall B CLAS12 detector following the 12 GeV upgrade, a dedicated experiment will aim to extract the N* electrocouplings at high photon virtualities Q2. This experiment will allow exploration of the structure of N* resonances at the highest photon virtualities ever achieved, with a kinematic reach up to Q2 = 12 GeV2. This high-Q2 reach will make it possible to probe the excited nucleon structures at distance scales ranging from where effective degrees of freedom, such as constituent quarks, are dominant through the transition to where nearly massless bare-quark degrees of freedom are relevant. In this document, we present a detailed description of the physics that can be addressed through N* structure studies in exclusive meson electroproduction. The discussion includes recent advances in reaction theory for extracting N* electrocouplings from meson electropro...

ELECTROMAGNETIC MESON PRODUCTION IN THE NUCLEON RESONANCE REGION

Recent experimental and theoretical advances in investigating electromagnetic meson production reactions in the nucleon resonance region are reviewed. We give a description of current experimental facilities with electron and photon beams and present a unified derivation of most of the phenomenological approaches being used to extract the resonance parameters from the data. The analyses of π and η production data and the resulting transition form factors for the Δ(1232)P33, N(1535)S11, N(1440)P11, and N(1520)D13 resonances are discussed in detail. The status of our understanding of the reactions with production of two pions, kaons, and vector mesons is also reviewed.

Baryon resonance extraction from πN data using a unitary multichannel model

Abstract A unitary multi-channel approach, first developed by the Carnegie-Mellon Berkeley group, is applied to extract the pole positions, masses, and partial decay widths of nucleon resonances from the partial wave amplitudes for the transitions from πN to eight possible final baryon–meson states. Results of single energy analyses of the VPI group using the most current database are used in this analysis. A proper treatment of threshold effects and channel coupling within the unitarity constraint is shown to be crucial in extracting resonant parameters, especially for the resonance states, such as S11(1535), which have decay thresholds very close to the resonance pole position. The extracted masses and partial decay widths of baryon resonances up to about 2 GeV mass are listed and compared with the results from previous analyses. In many cases, the new results agree with previous analyses. However, some significant differences, in particular for the resonances that are weakly excited in πN reactions, are found.

Dynamical coupled-channel model of meson production reactions in the nucleon resonance region.

Abstract A dynamical coupled-channel model is presented for investigating the nucleon resonances ( N * ) in the meson production reactions induced by pions and photons. Our objective is to extract the N * parameters and to investigate the meson production reaction mechanisms for mapping out the quark–gluon substructure of N * from the data. The model is based on an energy-independent Hamiltonian which is derived from a set of Lagrangians by using a unitary transformation method. The constructed model Hamiltonian consists of (a) Γ V for describing the vertex interactions N * ↔ MB , π π N with MB = γ N , π N , η N , π Δ , ρ N , σ N , and ρ ↔ π π and σ ↔ π π , (b) v 22 for the non-resonant MB → M ′ B ′ and π π → π π interactions, (c) v MB , π π N for the non-resonant MB → π π N transitions, and (d) v π π N , π π N for the non-resonant π π N → π π N interactions. By applying the projection operator techniques, we derive a set of coupled-channel equations which satisfy the unitarity conditions within the channel space spanned by the considered two-particle MB states and the three-particle π π N state. The resulting amplitudes are written as a sum of non-resonant and resonant amplitudes such that the meson cloud effects on the N * decay can be explicitly calculated for interpreting the extracted N * parameters in terms of hadron structure calculations. We present and explain in detail a numerical method based on a spline-function expansion for solving the resulting coupled-channel equations which contain logarithmically divergentone-particle-exchange driving terms Z MB , M ′ B ′ ( E ) resulted from the π π N unitarity cut. This method is convenient, and perhaps more practical and accurate than the commonly employed methods of contour rotation/deformation, for calculating the two-pion production observables. For completeness in explaining our numerical procedures, we also present explicitly the formula for efficient calculations of a very large number of partial-wave matrix elements which are the input to the coupled-channel equations. Results for two pion photo-production are presented to illustrate the dynamical consequence of the one-particle-exchange driving term Z MB , M ′ B ′ ( E ) of the coupled-channel equations. We show that this mechanism, which contains the effects due to π π N unitarity cut, can generate rapidly varying structure in the reaction amplitudes associated with the unstable particle channels π Δ , ρ N , and σ N , in agreement with the analysis of Aaron and Amado [Phys. Rev. D13 (1976) 2581]. It also has large effects in determining the two-pion production cross sections. Our results indicate that cautions must be taken to interpret the N * parameters extracted from using models which do not include π π N cut effects. Strategies for performing a complete dynamical coupled-channel analysis of all of available data of meson photo-production and electro-production are discussed.

Disentangling the Dynamical Origin of P11 Nucleon Resonances

We show that two almost degenerate poles near the piDelta threshold and the next higher mass pole in the P11 partial wave of piN scattering evolve from a single bare state through its coupling with piN, etaN, and pipiN reaction channels. This finding provides new information on understanding the dynamical origins of the Roper N{*}(1440) and N{*}(1710) resonances listed by Particle Data Group. Our results for the resonance poles in other piN partial waves are also presented.

Neutral pion photoproduction on deuterium in baryon chiral perturbation theory to order q4

Abstract Threshold neutral pion photoproduction on the deuteron is studied in the framework of baryon chiral perturbation theory beyond next-to-leading order in the chiral expansion. To fourh orther in small momenta, the amplitude is finite and a sum of two- and three-body interactions with no undetermined parameters. With accurate theoretical and experimental input from the single nucleon sector for the proton amplitude, we investigate the sensitivity of the threshold cross section to the elementary γn → π 0 n amplitude. A precise measurement of the threshold cross section for γd → π 0 d is called for.

Determining pseudoscalar meson photoproduction amplitudes from complete experiments

A new generation of complete experiments is focused on a high precision extraction of pseudoscalar meson photoproduction amplitudes. Here, we review the development of the most general analytic form of the cross section, dependent upon the three polarization vectors of the beam, target and recoil baryon, including all single-, double- and triple-polarization terms involving 16 spin-dependent observables. We examine the different conventions that have been used by different authors, and we present expressions that allow the direct numerical calculation of any pseudoscalar meson photoproduction observables with arbitrary spin projections from the Chew–Goldberger–Low–Nambu amplitudes. We use this numerical tool to clarify apparent sign differences that exist in the literature, in particular with the definitions of six double-polarization observables. We also present analytic expressions that determine the recoil baryon polarization, together with examples of their potential use with quasi-4π detectors to deduce observables. As an illustration of the use of the consistent machinery presented in this review, we carry out a multipole analysis of the γp → K+Λ reaction and examine the impact of recently published polarization measurements. When combining data from different experiments, we utilize the Fierz identities to fit a consistent set of scales. In fitting multipoles, we use a combined Monte Carlo sampling of the amplitude space, with gradient minimization, and find a shallow χ2 valley pitted with a very large number of local minima. This results in broad bands of multipole solutions that are experimentally indistinguishable. While these bands have been noticeably narrowed by the inclusion of new polarization measurements, many of the multipoles remain very poorly determined, even in sign, despite the inclusion of data on eight different observables. We have compared multipoles from recent PWA codes with our model-independent solution bands and found that such comparisons provide useful consistency tests which clarify model interpretations. The potential accuracy of amplitudes that could be extracted from measurements of all 16 polarization observables has been studied with mock data using the statistical variations that are expected from ongoing experiments. We conclude that, while a mathematical solution to the problem of determining an amplitude free of ambiguities may require eight observables, as has been pointed out in the literature, experiments with realistically achievable uncertainties will require a significantly larger number.

Dynamical Model of Weak Pion Production Reactions

The dynamical model of pion electroproduction developed by Sato and Lee [Phys. Rev. C

The isoscalar S-wave

63,

\pi

055201 (2001)] has been extended to investigate the weak pion production reactions. With the conserved vector current hypothesis, the weak vector currents are constructed from electromagnetic currents by isospin rotations. Guided by the effective chiral Lagrangian method and using the unitary transformation method developed previously, the weak axial vector currents for