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Title: Nucleon form factors in dispersively improved chiral effective field theory. II. Electromagnetic form factors

Abstract

We study the nucleon electromagnetic form factors (EM FFs) using a recently developed method combining Chiral Effective Field Theory ($$\chi$$EFT) and dispersion analysis. The spectral functions on the two-pion cut at $$t > 4 M_\pi^2$$ are constructed using the elastic unitarity relation and an $N/D$ representation. $$\chi$$EFT is used to calculate the real unctions $$J_\pm^1 (t) = f_\pm^1(t)/F_\pi(t)$$ (ratios of the complex $$\pi\pi \rightarrow N \bar N$$ partial-wave amplitudes and the timelike pion FF), which are free of $$\pi\pi$$ rescattering. Rescattering effects are included through the empirical timelike pion FF $$|F_\pi(t)|^2$$. The method allows us to compute the isovector EM spectral functions up to $$t \sim 1$$ GeV$^2$ with controlled accuracy (LO, NLO, and partial N2LO). With the spectral functions we calculate the isovector nucleon EM FFs and their derivatives at $t = 0$ (EM radii, moments) using subtracted dispersion relations. We predict the values of higher FF derivatives with minimal uncertainties and explain their collective behavior. Finally, we estimate the individual proton and neutron FFs by adding an empirical parametrization of the isoscalar sector. Excellent agreement with the present low-$Q^2$ FF data is achieved up to $$\sim$$0.5 GeV$^2$ for $$G_E$$, and up to $$\sim$$0.2 GeV$^2$ for $$G_M$$. Our results can be used to guide the analysis of low-$Q^2$ elastic scattering data and the extraction of the proton charge radius.

Authors:
;
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1436377
Alternate Identifier(s):
OSTI ID: 1438371
Report Number(s):
JLAB-THY-17-2568; DOE/OR/-23177-4230; arXiv:1710.06430
Journal ID: ISSN 2469-9985; PRVCAN; 055203
Grant/Contract Number:  
AC05-06OR23177; FPA2016-77313-P
Resource Type:
Published Article
Journal Name:
Physical Review C
Additional Journal Information:
Journal Name: Physical Review C Journal Volume: 97 Journal Issue: 5; Journal ID: ISSN 2469-9985
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Alarcón, J. M., and Weiss, C. Nucleon form factors in dispersively improved chiral effective field theory. II. Electromagnetic form factors. United States: N. p., 2018. Web. doi:10.1103/PhysRevC.97.055203.
Alarcón, J. M., & Weiss, C. Nucleon form factors in dispersively improved chiral effective field theory. II. Electromagnetic form factors. United States. doi:10.1103/PhysRevC.97.055203.
Alarcón, J. M., and Weiss, C. Tue . "Nucleon form factors in dispersively improved chiral effective field theory. II. Electromagnetic form factors". United States. doi:10.1103/PhysRevC.97.055203.
@article{osti_1436377,
title = {Nucleon form factors in dispersively improved chiral effective field theory. II. Electromagnetic form factors},
author = {Alarcón, J. M. and Weiss, C.},
abstractNote = {We study the nucleon electromagnetic form factors (EM FFs) using a recently developed method combining Chiral Effective Field Theory ($\chi$EFT) and dispersion analysis. The spectral functions on the two-pion cut at $t > 4 M_\pi^2$ are constructed using the elastic unitarity relation and an $N/D$ representation. $\chi$EFT is used to calculate the real unctions $J_\pm^1 (t) = f_\pm^1(t)/F_\pi(t)$ (ratios of the complex $\pi\pi \rightarrow N \bar N$ partial-wave amplitudes and the timelike pion FF), which are free of $\pi\pi$ rescattering. Rescattering effects are included through the empirical timelike pion FF $|F_\pi(t)|^2$. The method allows us to compute the isovector EM spectral functions up to $t \sim 1$ GeV$^2$ with controlled accuracy (LO, NLO, and partial N2LO). With the spectral functions we calculate the isovector nucleon EM FFs and their derivatives at $t = 0$ (EM radii, moments) using subtracted dispersion relations. We predict the values of higher FF derivatives with minimal uncertainties and explain their collective behavior. Finally, we estimate the individual proton and neutron FFs by adding an empirical parametrization of the isoscalar sector. Excellent agreement with the present low-$Q^2$ FF data is achieved up to $\sim$0.5 GeV$^2$ for $G_E$, and up to $\sim$0.2 GeV$^2$ for $G_M$. Our results can be used to guide the analysis of low-$Q^2$ elastic scattering data and the extraction of the proton charge radius.},
doi = {10.1103/PhysRevC.97.055203},
journal = {Physical Review C},
number = 5,
volume = 97,
place = {United States},
year = {2018},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
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DOI: 10.1103/PhysRevC.97.055203

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