Lightfront representation of chiral dynamics with Δ isobar and largeN _{c} relations
Abstract
Transverse densities describe the spatial distribution of electromagnetic current in the nucleon at fixed lightfront time. At peripheral distances b = O(M _{π} ^{–1}) the densities are governed by chiral dynamics and can be calculated modelindependently using chiral effective field theory (EFT). Recent work has shown that the EFT results can be represented in firstquantized form, as overlap integrals of chiral lightfront wave functions describing the transition of the nucleon to softpionnucleon intermediate states, resulting in a quantummechanical picture of the peripheral transverse densities. We now extend this representation to include intermediate states with Δ isobars and implement relations based on the largeN _{c} limit of QCD. We derive the wave function overlap formulas for the Δ contributions to the peripheral transverse densities by way of a threedimensional reduction of relativistic chiral EFT expressions. Our procedure effectively maintains rotational invariance and avoids the ambiguities with higherspin particles in the lightfront timeordered approach. We study the interplay of πN and πΔ intermediate states in the quantummechanical 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 »
 Authors:
 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) (SC26)
 OSTI Identifier:
 1328670
 Report Number(s):
 JLABTHY162235; DOE/OR/231773781; arXiv:1603.08881
Journal ID: ISSN 10298479; PII: 4145
 Grant/Contract Number:
 AC0506OR23177
 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 10298479
 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. Lightfront representation of chiral dynamics with Δ isobar and largeNc relations. United States: N. p., 2016.
Web. doi:10.1007/JHEP06(2016)075.
Granados, C., & Weiss, C. Lightfront representation of chiral dynamics with Δ isobar and largeNc relations. United States. doi:10.1007/JHEP06(2016)075.
Granados, C., and Weiss, C. 2016.
"Lightfront representation of chiral dynamics with Δ isobar and largeNc relations". United States.
doi:10.1007/JHEP06(2016)075. https://www.osti.gov/servlets/purl/1328670.
@article{osti_1328670,
title = {Lightfront representation of chiral dynamics with Δ isobar and largeNc relations},
author = {Granados, C. and Weiss, C.},
abstractNote = {Transverse densities describe the spatial distribution of electromagnetic current in the nucleon at fixed lightfront time. At peripheral distances b = O(Mπ–1) the densities are governed by chiral dynamics and can be calculated modelindependently using chiral effective field theory (EFT). Recent work has shown that the EFT results can be represented in firstquantized form, as overlap integrals of chiral lightfront wave functions describing the transition of the nucleon to softpionnucleon intermediate states, resulting in a quantummechanical picture of the peripheral transverse densities. We now extend this representation to include intermediate states with Δ isobars and implement relations based on the largeNc limit of QCD. We derive the wave function overlap formulas for the Δ contributions to the peripheral transverse densities by way of a threedimensional reduction of relativistic chiral EFT expressions. Our procedure effectively maintains rotational invariance and avoids the ambiguities with higherspin particles in the lightfront timeordered approach. We study the interplay of πN and πΔ intermediate states in the quantummechanical picture of the densities in a transversely polarized nucleon. We show that the correct Ncscaling 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 offshell 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
}

The nucleon's electromagnetic form factors are expressed in terms of the transverse densities of charge and magnetization at fixed lightfront time. At peripheral transverse distances b = O(M_pi^{1}) the densities are governed by chiral dynamics and can be calculated modelindependently using chiral effective field theory (EFT). We represent the leadingorder chiral EFT results for the peripheral transverse densities as overlap integrals of chiral lightfront wave functions, describing the transition of the initial nucleon to soft pionnucleon intermediate states and back. The new representation (a) explains the parametric order of the peripheral transverse densities; (b) establishes an inequality between the spinindependentmore »Cited by 2

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