skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Light-front representation of chiral dynamics with Δ isobar and large-N c relations

Abstract

Transverse densities describe the spatial distribution of electromagnetic current in the nucleon at fixed light-front time. At peripheral distances b = O(M π –1) the densities are governed by chiral dynamics and can be calculated model-independently using chiral effective field theory (EFT). Recent work has shown that the EFT results can be represented in first-quantized form, as overlap integrals of chiral light-front wave functions describing the transition of the nucleon to soft-pion-nucleon intermediate states, resulting in a quantum-mechanical picture of the peripheral transverse densities. We now extend this representation to include intermediate states with Δ isobars and implement relations based on the large-N c limit of QCD. We derive the wave function overlap formulas for the Δ contributions to the peripheral transverse densities by way of a three-dimensional reduction of relativistic chiral EFT expressions. Our procedure effectively maintains rotational invariance and avoids the ambiguities with higher-spin particles in the light-front time-ordered approach. We study the interplay of πN and πΔ intermediate states in the quantum-mechanical picture of the densities in a transversely polarized nucleon. We show that the correct N c-scaling of the charge and magnetization densities emerges as the result of the particular combination of currents generated by intermediatemore » states with degenerate N and Δ. The off-shell behavior of the chiral EFT is summarized in contact terms and can be studied easily. As a result, the methods developed here can be applied to other peripheral densities and to moments of the nucleon's generalized parton distributions.« less

Authors:
 [1];  [1]
  1. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1328670
Report Number(s):
JLAB-THY-16-2235; DOE/OR/23177-3781; arXiv:1603.08881
Journal ID: ISSN 1029-8479; PII: 4145
Grant/Contract Number:
AC05-06OR23177
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 6; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 1/N expansion; chiral Lagrangians; effective field theories

Citation Formats

Granados, C., and Weiss, C. Light-front representation of chiral dynamics with Δ isobar and large-Nc relations. United States: N. p., 2016. Web. doi:10.1007/JHEP06(2016)075.
Granados, C., & Weiss, C. Light-front representation of chiral dynamics with Δ isobar and large-Nc relations. United States. doi:10.1007/JHEP06(2016)075.
Granados, C., and Weiss, C. 2016. "Light-front representation of chiral dynamics with Δ isobar and large-Nc relations". United States. doi:10.1007/JHEP06(2016)075. https://www.osti.gov/servlets/purl/1328670.
@article{osti_1328670,
title = {Light-front representation of chiral dynamics with Δ isobar and large-Nc relations},
author = {Granados, C. and Weiss, C.},
abstractNote = {Transverse densities describe the spatial distribution of electromagnetic current in the nucleon at fixed light-front time. At peripheral distances b = O(Mπ–1) the densities are governed by chiral dynamics and can be calculated model-independently using chiral effective field theory (EFT). Recent work has shown that the EFT results can be represented in first-quantized form, as overlap integrals of chiral light-front wave functions describing the transition of the nucleon to soft-pion-nucleon intermediate states, resulting in a quantum-mechanical picture of the peripheral transverse densities. We now extend this representation to include intermediate states with Δ isobars and implement relations based on the large-Nc limit of QCD. We derive the wave function overlap formulas for the Δ contributions to the peripheral transverse densities by way of a three-dimensional reduction of relativistic chiral EFT expressions. Our procedure effectively maintains rotational invariance and avoids the ambiguities with higher-spin particles in the light-front time-ordered approach. We study the interplay of πN and πΔ intermediate states in the quantum-mechanical picture of the densities in a transversely polarized nucleon. We show that the correct Nc-scaling of the charge and magnetization densities emerges as the result of the particular combination of currents generated by intermediate states with degenerate N and Δ. The off-shell behavior of the chiral EFT is summarized in contact terms and can be studied easily. As a result, the methods developed here can be applied to other peripheral densities and to moments of the nucleon's generalized parton distributions.},
doi = {10.1007/JHEP06(2016)075},
journal = {Journal of High Energy Physics (Online)},
number = 6,
volume = 2016,
place = {United States},
year = 2016,
month = 6
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Save / Share:
  • The nucleon's electromagnetic form factors are expressed in terms of the transverse densities of charge and magnetization at fixed light-front time. At peripheral transverse distances b = O(M_pi^{-1}) the densities are governed by chiral dynamics and can be calculated model-independently using chiral effective field theory (EFT). We represent the leading-order chiral EFT results for the peripheral transverse densities as overlap integrals of chiral light-front wave functions, describing the transition of the initial nucleon to soft pion-nucleon intermediate states and back. The new representation (a) explains the parametric order of the peripheral transverse densities; (b) establishes an inequality between the spin-independentmore » and -dependent densities; (c) exposes the role of pion orbital angular momentum in chiral dynamics; (d) reveals a large left-right asymmetry of the current in a transversely polarized nucleon and suggests a simple interpretation. The light-front representation enables a first-quantized, quantum-mechanical view of chiral dynamics that is fully relativistic and exactly equivalent to the second-quantized, field-theoretical formulation. It relates the charge and magnetization densities measured in low-energy elastic scattering to the generalized parton distributions probed in peripheral high-energy scattering processes. The method can be applied to nucleon form factors of other operators, e.g. the energy-momentum tensor.« less
  • Motivated by recent remarks on the {Delta}{sup +} mass and comparisons between the quark model and relations based on large-N{sub c} with perturbative flavor breaking, two sets of {Delta} masses consistent with these constraints are constructed. These two sets, based either on an experimentally determined mass splitting or a quark model of isospin symmetry breaking, are shown to be inconsistent. The model dependence of this inconsistency is examined, and suggestions for improved experiments are made. An explicit quark model calculation and mass relations based on the large-N{sub c} limit with perturbative flavor breaking are compared. The expected level of accuracymore » of such relations is realized in the quark model, except for mass relations derived by combining others which correspond to different SU(6) representations. It is shown that the {Delta}{sup 0} and {Delta}{sup ++} pole masses and {Delta}{sup 0}{minus}{Delta}{sup +}=({Delta}{sup {minus}}{minus}{Delta}{sup ++})/3{approx_equal}1.5thinspMeV are more consistent with model expectations than the analogous Breit-Wigner masses and their splittings. {copyright} {ital 1998} {ital The American Physical Society}« less
  • Starting from the Hamiltonian equation of motion in QCD we find a single variable light-front equation for QCD which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. This light-front wave equation is equivalent to the equations of motion which describe the propagation of spin-J modes on anti-de Sitter (AdS) space.
  • We analyze the current matrix elements in the general collinear (Breit) frames and find the relation between the ordinary (or canonical) helicity amplitudes and the light-front helicity amplitudes. Using the conservation of angular momentum, we derive a general angular condition which should be satisfied by the light-front helicity amplitudes for any spin system. In addition, we obtain the light-front parity and time-reversal relations for the light-front helicity amplitudes. Applying these relations to the spin-1 form factor analysis, we note that the general angular condition relating the five helicity amplitudes is reduced to the usual angular condition relating the four helicitymore » amplitudes due to the light-front time-reversal condition. We make some comments on the consequences of the angular condition for the analysis of the high-Q{sup 2} deuteron electromagnetic form factors, and we further apply the general angular condition to the electromagnetic transition between spin-1 /2 and spin-3/2 systems and find a relation useful for the analysis of the N-Delta transition form factors. We also discuss the scaling law and the subleading power corrections in the Breit and light-front frames.« less