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)
- 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. https://doi.org/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. https://doi.org/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 = {Tue May 08 00:00:00 EDT 2018},
month = {Tue May 08 00:00:00 EDT 2018}
}
https://doi.org/10.1103/PhysRevC.97.055203
Web of Science
Works referenced in this record:
Electromagnetic form factors of the nucleon in effective field theory
journal, December 2012
- Bauer, T.; Bernauer, J. C.; Scherer, S.
- Physical Review C, Vol. 86, Issue 6
Electromagnetic moments of quasistable particle
journal, November 2010
- Ledwig, Tim; Pascalutsa, Vladimir; Vanderhaeghen, Marc
- Physical Review D, Vol. 82, Issue 9
The New Proton Radius Experiment at Jefferson Lab
conference, February 2017
- Gasparian, Ashot H.
- Proceedings of the 14th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU2016)
Nucleon electroweak form factors: Analysis of their spectral functions
journal, December 1996
- Bernard, V.; Kaiser, N.; Meißner, Ulf-G.
- Nuclear Physics A, Vol. 611, Issue 4
Electric and magnetic form factors of the proton
journal, July 2014
- Bernauer, J. C.; Distler, M. O.; Friedrich, J.
- Physical Review C, Vol. 90, Issue 1
Partial-Wave Dispersion Relations for the Process
journal, March 1960
- Frazer, William R.; Fulco, Jose R.
- Physical Review, Vol. 117, Issue 6
Model independent extraction of the proton magnetic radius from electron scattering
journal, October 2014
- Epstein, Zachary; Paz, Gil; Roy, Joydeep
- Physical Review D, Vol. 90, Issue 7
Field theory of nucleon to higher-spin baryon transitions
journal, September 1999
- Pascalutsa, Vladimir; Timmermans, Rob
- Physical Review C, Vol. 60, Issue 4
Progress in three-particle scattering from LQCD
journal, January 2017
- Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
- EPJ Web of Conferences, Vol. 137
Effect of a Pion-Pion Scattering Resonance on Nucleon Structure. II
journal, March 1960
- Frazer, William R.; Fulco, Jose R.
- Physical Review, Vol. 117, Issue 6
The structure of the nucleon: Elastic electromagnetic form factors
journal, July 2015
- Punjabi, V.; Perdrisat, C. F.; Jones, M. K.
- The European Physical Journal A, Vol. 51, Issue 7
The proton radius puzzle
journal, May 2015
- Carlson, Carl E.
- Progress in Particle and Nuclear Physics, Vol. 82
Quantum-mechanical picture of peripheral chiral dynamics
journal, August 2015
- Granados, C.; Weiss, C.
- Physical Review C, Vol. 92, Issue 2
Dispersion analysis of the nucleon form factors including meson continua
journal, March 2007
- Belushkin, M. A.; Hammer, H. -W.; Meißner, Ulf-G.
- Physical Review C, Vol. 75, Issue 3
Theory of the Low-Energy Pion-Pion Interaction
journal, July 1960
- Chew, Geoffrey F.; Mandelstam, Stanley
- Physical Review, Vol. 119, Issue 1
Measurement of the Proton’s Electric to Magnetic Form Factor Ratio from
journal, January 2007
- Crawford, C. B.; Sindile, A.; Akdogan, T.
- Physical Review Letters, Vol. 98, Issue 5
Nucleon electromagnetic form factors
journal, October 2007
- Perdrisat, C. F.; Punjabi, V.; Vanderhaeghen, M.
- Progress in Particle and Nuclear Physics, Vol. 59, Issue 2
Proton radius from electron-proton scattering and chiral perturbation theory
journal, March 2017
- Horbatsch, Marko; Hessels, Eric A.; Pineda, Antonio
- Physical Review C, Vol. 95, Issue 3
Reexamination of proton rms radii from low- power expansions
journal, January 2017
- Sick, Ingo; Trautmann, Dirk
- Physical Review C, Vol. 95, Issue 1
The size of the proton: Closing in on the radius puzzle
journal, November 2012
- Lorenz, I. T.; Hammer, H. -W.; Meißner, Ulf-G.
- The European Physical Journal A, Vol. 48, Issue 11
Analysis of electromagnetic nucleon form factors
journal, November 1976
- Höhler, G.; Pietarinen, E.; Sabba-Stefanescu, I.
- Nuclear Physics B, Vol. 114, Issue 3
Nucleons with chiral loops
journal, October 1988
- Gasser, J.; Sainio, M. E.; Švarc, A.
- Nuclear Physics B, Vol. 307, Issue 4
Novel evaluation of the two-pion contribution to the nucleon isovector form factors
journal, February 2006
- Belushkin, M. A.; Hammer, H. -W.; Meißner, Ulf-G.
- Physics Letters B, Vol. 633, Issue 4-5
Transverse Charge Densities
journal, November 2010
- Miller, Gerald A.
- Annual Review of Nuclear and Particle Science, Vol. 60, Issue 1
Lattice QCD and the Timelike Pion Form Factor
journal, August 2011
- Meyer, Harvey B.
- Physical Review Letters, Vol. 107, Issue 7
Quantization of an interacting spin- field and the isobar
journal, September 1998
- Pascalutsa, V.
- Physical Review D, Vol. 58, Issue 9
On-shell consistency of the Rarita-Schwinger field formulation
journal, August 2009
- Krebs, H.; Epelbaum, E.; Meißner, Ulf-G.
- Physical Review C, Vol. 80, Issue 2
Dispersive analysis of the scalar form factor of the nucleon
journal, June 2012
- Hoferichter, M.; Ditsche, C.; Kubis, B.
- Journal of High Energy Physics, Vol. 2012, Issue 6
Some General Relations between the Photoproduction and Scattering of Mesons
journal, July 1954
- Watson, Kenneth M.
- Physical Review, Vol. 95, Issue 1
The nucleon as a test case to calculate vector-isovector form factors at low energies
journal, January 2018
- Leupold, Stefan
- The European Physical Journal A, Vol. 54, Issue 1
Renormalization of relativistic baryon chiral perturbation theory and power counting
journal, September 2003
- Fuchs, T.; Gegelia, J.; Japaridze, G.
- Physical Review D, Vol. 68, Issue 5
Peripheral transverse densities of the baryon octet from chiral effective field theory and dispersion analysis
journal, August 2017
- Alarcón, J. M.; Hiller Blin, A. N.; Vicente Vacas, M. J.
- Nuclear Physics A, Vol. 964
Nucleon and form factors at low momentum transfer and small pion masses
journal, February 2012
- Ledwig, T.; Martin-Camalich, J.; Pascalutsa, V.
- Physical Review D, Vol. 85, Issue 3
Light-front representation of chiral dynamics in peripheral transverse densities
journal, July 2015
- Granados, C.; Weiss, C.
- Journal of High Energy Physics, Vol. 2015, Issue 7
Consistency of electron scattering data with a small proton radius
journal, June 2016
- Griffioen, Keith; Carlson, Carl; Maddox, Sarah
- Physical Review C, Vol. 93, Issue 6
Improved description of the -scattering phenomenology at low energies in covariant baryon chiral perturbation theory
journal, September 2013
- Alarcón, J. M.; Martin Camalich, J.; Oller, J. A.
- Annals of Physics, Vol. 336
First measurement of proton's charge form factor at very low Q2 with initial state radiation
journal, August 2017
- Mihovilovič, M.; Weber, A. B.; Achenbach, P.
- Physics Letters B, Vol. 771
Finite-Width Corrections to the Vector-Meson-Dominance Prediction for
journal, July 1968
- Gounaris, G. J.; Sakurai, J. J.
- Physical Review Letters, Vol. 21, Issue 4
Extraction of the proton radius from electron-proton scattering data
journal, July 2015
- Lee, Gabriel; Arrington, John R.; Hill, Richard J.
- Physical Review D, Vol. 92, Issue 1
Electromagnetic radii of nucleon and pion
journal, January 1975
- Höhler, G.; Pietarinen, E.
- Physics Letters B, Vol. 53, Issue 5
Correspondence of consistent and inconsistent spin-3/2 couplings via the equivalence theorem
journal, March 2001
- Pascalutsa, V.
- Physics Letters B, Vol. 503, Issue 1-2
Nucleon form factors in dispersively improved chiral effective field theory: Scalar form factor
journal, November 2017
- Alarcón, J. M.; Weiss, C.
- Physical Review C, Vol. 96, Issue 5
Baryon chiral perturbation theory in manifestly Lorentz invariant form
journal, July 1999
- Becher, T.; Leutwyler, H.
- The European Physical Journal C, Vol. 9, Issue 4
Low-energy analysis of the nucleon electromagnetic form factors
journal, January 2001
- Kubis, Bastian; Meißner, Ulf-G.
- Nuclear Physics A, Vol. 679, Issue 3-4
Polarization Transfer in the Reaction at and
journal, August 2010
- Paolone, M.; Malace, S. P.; Strauch, S.
- Physical Review Letters, Vol. 105, Issue 7
Chiral perturbation theory of muonic-hydrogen Lamb shift: polarizability contribution
journal, April 2014
- Alarcón, Jose Manuel; Lensky, Vadim; Pascalutsa, Vladimir
- The European Physical Journal C, Vol. 74, Issue 4
Proton and neutron electromagnetic form factors and uncertainties
journal, February 2018
- Ye, Zhihong; Arrington, John; Hill, Richard J.
- Physics Letters B, Vol. 777
Aspects of chiral pion-nucleon physics
journal, April 1997
- Bernard, V.; Kaiser, N.; Meißner, Ulf-G.
- Nuclear Physics A, Vol. 615, Issue 4
High-Precision Determination of the Electric and Magnetic Form Factors of the Proton
journal, December 2010
- Bernauer, J. C.; Achenbach, P.; Ayerbe Gayoso, C.
- Physical Review Letters, Vol. 105, Issue 24
Spectral functions of isoscalar-scalar and isovector-electromagnetic form factors of the nucleon at two-loop order
journal, August 2003
- Kaiser, N.
- Physical Review C, Vol. 68, Issue 2
Proton radius from electron scattering data
journal, May 2016
- Higinbotham, Douglas W.; Kabir, Al Amin; Lin, Vincent
- Physical Review C, Vol. 93, Issue 5
The size of the proton
journal, July 2010
- Pohl, Randolf; Antognini, Aldo; Nez, François
- Nature, Vol. 466, Issue 7303
Chiral dynamics and peripheral transverse densities
journal, January 2014
- Granados, C.; Weiss, C.
- Journal of High Energy Physics, Vol. 2014, Issue 1
The RMS charge radius of the proton and Zemach moments
journal, February 2011
- Distler, Michael O.; Bernauer, Jan C.; Walcher, Thomas
- Physics Letters B, Vol. 696, Issue 4
Nucleon electromagnetic form factors using lattice simulations at the physical point
journal, August 2017
- Alexandrou, C.; Constantinou, M.; Hadjiyiannakou, K.
- Physical Review D, Vol. 96, Issue 3
Light-front representation of chiral dynamics with Δ isobar and large-N c relations
journal, June 2016
- Granados, C.; Weiss, C.
- Journal of High Energy Physics, Vol. 2016, Issue 6
The strangeness content of the nucleon from effective field theory and phenomenology
journal, March 2014
- Alarcón, J. M.; Geng, L. S.; Martin Camalich, J.
- Physics Letters B, Vol. 730
Electromagnetic pion form factor in the timelike region
journal, January 1985
- Barkov, L. M.; Chilingarov, A. G.; Eidelman, S. I.
- Nuclear Physics B, Vol. 256
On the $\pi\pi$ π π continuum in the nucleon form factors and the proton radius puzzle
journal, November 2016
- Hoferichter, M.; Kubis, B.; Ruiz de Elvira, J.
- The European Physical Journal A, Vol. 52, Issue 11
The two-photon exchange contribution to muonic hydrogen from chiral perturbation theory
journal, October 2014
- Peset, Clara; Pineda, Antonio
- Nuclear Physics B, Vol. 887
The electromagnetic Sigma-to-Lambda hyperon transition form factors at low energies
journal, June 2017
- Granados, Carlos; Leupold, Stefan; Perotti, Elisabetta
- The European Physical Journal A, Vol. 53, Issue 6
Reconciling threshold and subthreshold expansions for pion–nucleon scattering
journal, July 2017
- Siemens, D.; Ruiz de Elvira, J.; Epelbaum, E.
- Physics Letters B, Vol. 770
Three-body unitarity with isobars revisited
journal, September 2017
- Mai, M.; Hu, B.; Döring, M.
- The European Physical Journal A, Vol. 53, Issue 9
Chiral representation of the scattering amplitude and the pion-nucleon sigma term
journal, March 2012
- Alarcón, J. M.; Camalich, J. Martin; Oller, J. A.
- Physical Review D, Vol. 85, Issue 5