Abstract
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 − 1 π ) 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-independent 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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D.E. Soper, The Parton Model and the Bethe-Salpeter Wave Function, Phys. Rev. D 15 (1977) 1141 [INSPIRE].
M. Burkardt, Impact parameter dependent parton distributions and off forward parton distributions for ζ → 0, Phys. Rev. D 62 (2000) 071503 [Erratum ibid. D 66 (2002) 119903] [hep-ph/0005108] [INSPIRE].
G.A. Miller, Charge Density of the Neutron, Phys. Rev. Lett. 99 (2007) 112001 [arXiv:0705.2409] [INSPIRE].
G.A. Miller, Transverse Charge Densities, Ann. Rev. Nucl. Part. Sci. 60 (2010) 1 [arXiv:1002.0355] [INSPIRE].
M. Burkardt, Impact parameter space interpretation for generalized parton distributions, Int. J. Mod. Phys. A 18 (2003) 173 [hep-ph/0207047] [INSPIRE].
C.E. Carlson and M. Vanderhaeghen, Empirical transverse charge densities in the nucleon and the nucleon-to-Delta transition, Phys. Rev. Lett. 100 (2008) 032004 [arXiv:0710.0835] [INSPIRE].
S. Venkat, J. Arrington, G.A. Miller and X. Zhan, Realistic Transverse Images of the Proton Charge and Magnetic Densities, Phys. Rev. C 83 (2011) 015203 [arXiv:1010.3629] [INSPIRE].
C. Granados and C. Weiss, Chiral dynamics and peripheral transverse densities, JHEP 01 (2014) 092 [arXiv:1308.1634] [INSPIRE].
P.A.M. Dirac, Forms of Relativistic Dynamics, Rev. Mod. Phys. 21 (1949) 392 [INSPIRE].
H. Leutwyler and J. Stern, Relativistic Dynamics on a Null Plane, Annals Phys. 112 (1978) 94 [INSPIRE].
S.J. Brodsky, H.-C. Pauli and S.S. Pinsky, Quantum chromodynamics and other field theories on the light cone, Phys. Rept. 301 (1998) 299 [hep-ph/9705477] [INSPIRE].
C. Granados and C. Weiss, Quantum-mechanical picture of peripheral chiral dynamics, arXiv:1503.02055 [INSPIRE].
M.G. Schmidt, A simple connection between covariant Feynman formalism and time ordered perturbation theory in the infinite momentum frame, Phys. Rev. D 9 (1974) 408 [INSPIRE].
A. Fernandez-Pacheco, J.A. Grifols and I.A. Schmidt, A Relativistic Description of the Electromagnetic Form-factor of the Deuteron, Nucl. Phys. B 151 (1979) 518 [INSPIRE].
M. Sawicki, Soft charge form-factor of the pion, Phys. Rev. D 46 (1992) 474 [INSPIRE].
W. Jaus, Covariant analysis of the light front quark model, Phys. Rev. D 60 (1999) 054026 [INSPIRE].
C.-R. Ji, W. Melnitchouk and A.W. Thomas, Equivalence of pion loops in equal-time and light-front dynamics, Phys. Rev. D 80 (2009) 054018 [arXiv:0906.3497] [INSPIRE].
M. Burkardt, K.S. Hendricks, C.-R. Ji, W. Melnitchouk and A.W. Thomas, Pion momentum distributions in the nucleon in chiral effective theory, Phys. Rev. D 87 (2013) 056009 [arXiv:1211.5853] [INSPIRE].
C.-R. Ji, W. Melnitchouk and A.W. Thomas, Anatomy of relativistic pion loop corrections to the electromagnetic nucleon coupling, Phys. Rev. D 88 (2013) 076005 [arXiv:1306.6073] [INSPIRE].
M. Strikman and C. Weiss, Quantifying the nucleon’s pion cloud with transverse charge densities, Phys. Rev. C 82 (2010) 042201 [arXiv:1004.3535] [INSPIRE].
M. Strikman and C. Weiss, Chiral dynamics and the growth of the nucleon’s gluonic transverse size at small x, Phys. Rev. D 69 (2004) 054012 [hep-ph/0308191] [INSPIRE].
M. Strikman and C. Weiss, Chiral dynamics and partonic structure at large transverse distances, Phys. Rev. D 80 (2009) 114029 [arXiv:0906.3267] [INSPIRE].
T. Becher and H. Leutwyler, Baryon chiral perturbation theory in manifestly Lorentz invariant form, Eur. Phys. J. C 9 (1999) 643 [hep-ph/9901384] [INSPIRE].
J. Gasser, M.E. Sainio and A. Svarc, Nucleons with Chiral Loops, Nucl. Phys. B 307 (1988) 779 [INSPIRE].
V. Bernard, N. Kaiser, J. Kambor and U.G. Meissner, Chiral structure of the nucleon, Nucl. Phys. B 388 (1992) 315 [INSPIRE].
B. Kubis and U.-G. Meissner, Low-energy analysis of the nucleon electromagnetic form-factors, Nucl. Phys. A 679 (2001) 698 [hep-ph/0007056] [INSPIRE].
N. Kaiser, Spectral functions of isoscalar scalar and isovector electromagnetic form-factors of the nucleon at two loop order, Phys. Rev. C 68 (2003) 025202 [nucl-th/0302072] [INSPIRE].
L.L. Frankfurt and M.I. Strikman, High-Energy Phenomena, Short Range Nuclear Structure and QCD, Phys. Rept. 76 (1981) 215 [INSPIRE].
S.L. Adler, Sum rules for the axial vector coupling constant renormalization in beta decay, Phys. Rev. 140 (1965) B736 [Erratum ibid. 149 (1966) 1294] [Erratum ibid. 175 (1968) 2224] [INSPIRE].
W.I. Weisberger, Unsubtracted Dispersion Relations and the Renormalization of the Weak Axial Vector Coupling Constants, Phys. Rev. 143 (1966) 1302 [INSPIRE].
G.A. Miller, M. Strikman and C. Weiss, Realizing vector meson dominance with transverse charge densities, Phys. Rev. C 84 (2011) 045205 [arXiv:1105.6364] [INSPIRE].
M.A. Belushkin, H.W. Hammer and U.G. Meissner, Dispersion analysis of the nucleon form-factors including meson continua, Phys. Rev. C 75 (2007) 035202 [hep-ph/0608337] [INSPIRE].
I.T. Lorenz, H.W. Hammer and U.-G. Meissner, The size of the proton — closing in on the radius puzzle, Eur. Phys. J. A 48 (2012) 151 [arXiv:1205.6628] [INSPIRE].
G. Hohler et al., Analysis of Electromagnetic Nucleon Form-Factors, Nucl. Phys. B 114 (1976) 505 [INSPIRE].
X.-D. Ji, Deeply virtual Compton scattering, Phys. Rev. D 55 (1997) 7114 [hep-ph/9609381] [INSPIRE].
N. Kivel and M.V. Polyakov, Breakdown of chiral expansion for parton distributions, Phys. Lett. B 664 (2008) 64 [arXiv:0707.2208] [INSPIRE].
N. Kivel, M.V. Polyakov and A. Vladimirov, Large-N Summation of Chiral Logs for Generalized Parton Distributions, Phys. Rev. D 79 (2009) 014028 [arXiv:0809.2064] [INSPIRE].
I.A. Perevalova, M.V. Polyakov, A.N. Vall and A.A. Vladimirov, Chiral Inflation of the Pion Radius, arXiv:1105.4990 [INSPIRE].
E. Leader and C. Lorcé, The angular momentum controversy: What’s it all about and does it matter?, Phys. Rept. 541 (2014) 163 [arXiv:1309.4235] [INSPIRE].
X.-D. Ji, Gauge-Invariant Decomposition of Nucleon Spin, Phys. Rev. Lett. 78 (1997) 610 [hep-ph/9603249] [INSPIRE].
X. Ji, X. Xiong and F. Yuan, Proton Spin Structure from Measurable Parton Distributions, Phys. Rev. Lett. 109 (2012) 152005 [arXiv:1202.2843] [INSPIRE].
X. Ji, X. Xiong and F. Yuan, Probing Parton Orbital Angular Momentum in Longitudinally Polarized Nucleon, Phys. Rev. D 88 (2013) 014041 [arXiv:1207.5221] [INSPIRE].
X. Ji, X. Xiong and F. Yuan, Transverse Polarization of the Nucleon in Parton Picture, Phys. Lett. B 717 (2012) 214 [arXiv:1209.3246] [INSPIRE].
E. Leader, New relation between transverse angular momentum and generalized parton distributions, Phys. Rev. D 85 (2012) 051501 [arXiv:1109.1230] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1503.04839
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Granados, C., Weiss, C. Light-front representation of chiral dynamics in peripheral transverse densities. J. High Energ. Phys. 2015, 170 (2015). https://doi.org/10.1007/JHEP07(2015)170
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2015)170