Abstract
Transverse densities describe the spatial distribution of electromagnetic current in the nucleon at fixed light-front time. At peripheral 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). 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 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. The methods developed here can be applied to other peripheral densities and to moments of the nucleon’s generalized parton distributions.
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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].
M. Burkardt, Impact parameter space interpretation for generalized parton distributions, Int. J. Mod. Phys. A 18 (2003) 173 [hep-ph/0207047] [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. Strikman and C. Weiss, Quantifying the nucleon’s pion cloud with transverse charge densities, Phys. Rev. C 82 (2010) 042201 [arXiv:1004.3535] [INSPIRE].
C. Granados and C. Weiss, Chiral dynamics and peripheral transverse densities, JHEP 01 (2014) 092 [arXiv:1308.1634] [INSPIRE].
C. Granados and C. Weiss, Light-front representation of chiral dynamics in peripheral transverse densities, JHEP 07 (2015) 170 [arXiv:1503.04839] [INSPIRE].
C. Granados and C. Weiss, Quantum-mechanical picture of peripheral chiral dynamics, Phys. Rev. C 92 (2015) 025206 [arXiv:1503.02055] [INSPIRE].
T.R. Hemmert, B.R. Holstein and J. Kambor, Heavy baryon chiral perturbation theory with light deltas, J. Phys. G 24 (1998) 1831 [hep-ph/9712496] [INSPIRE].
V. Pascalutsa, M. Vanderhaeghen and S.N. Yang, Electromagnetic excitation of the Δ(1232)-resonance, Phys. Rept. 437 (2007) 125 [hep-ph/0609004] [INSPIRE].
A. Calle Cordon and J.L. Goity, Baryon masses and axial couplings in the combined 1/N c and chiral expansions, Phys. Rev. D 87 (2013) 016019 [arXiv:1210.2364] [INSPIRE].
G. ’t Hooft, A planar diagram theory for strong interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
E. Witten, Baryons in the 1/n expansion, Nucl. Phys. B 160 (1979) 57 [INSPIRE].
R.F. Dashen, E.E. Jenkins and A.V. Manohar, The 1/N c expansion for baryons, Phys. Rev. D 49 (1994) 4713 [Erratum ibid. D 51 (1995) 2489] [hep-ph/9310379] [INSPIRE].
R.F. Dashen, E.E. Jenkins and A.V. Manohar, Spin flavor structure of large-N c baryons, Phys. Rev. D 51 (1995) 3697 [hep-ph/9411234] [INSPIRE].
T.D. Cohen and W. Broniowski, The role of the delta isobar in chiral perturbation theory and hedgehog soliton models, Phys. Lett. B 292 (1992) 5 [hep-ph/9208253] [INSPIRE].
T.D. Cohen, Chiral and large-N c limits of quantum chromodynamics and models of the baryon, Rev. Mod. Phys. 68 (1996) 599 [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].
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].
V. Pascalutsa and R. Timmermans, Field theory of nucleon to higher spin baryon transitions, Phys. Rev. C 60 (1999) 042201 [nucl-th/9905065] [INSPIRE].
V. Pascalutsa, Correspondence of consistent and inconsistent spin-3/2 couplings via the equivalence theorem, Phys. Lett. B 503 (2001) 85 [hep-ph/0008026] [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].
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].
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].
V.B. Berestetskii, E.M. Lifshitz and L.P. Pitayevskii, Quantum electrodynamics, 2nd edition, Course of theoretical physics volume IV, Butterworth-Heinemann (1982).
E.E. Jenkins, Large-N c baryons, Ann. Rev. Nucl. Part. Sci. 48 (1998) 81 [hep-ph/9803349] [INSPIRE].
G. Karl and J.E. Paton, Naive quark model for an arbitrary number of colors, Phys. Rev. D 30 (1984) 238 [INSPIRE].
A. Jackson, A.D. Jackson and V. Pasquier, The Skyrmion-Skyrmion interaction, Nucl. Phys. A 432 (1985) 567 [INSPIRE].
G.S. Adkins, C.R. Nappi and E. Witten, Static properties of nucleons in the Skyrme model, Nucl. Phys. B 228 (1983) 552 [INSPIRE].
I. Zahed and G.E. Brown, The Skyrme model, Phys. Rept. 142 (1986) 1 [INSPIRE].
J.M. Alarcon et al., in preparation.
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].
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].
V. Pascalutsa and M. Vanderhaeghen, Electromagnetic nucleon-to-Delta transition in chiral effective-field theory, Phys. Rev. Lett. 95 (2005) 232001 [hep-ph/0508060] [INSPIRE].
V. Pascalutsa and M. Vanderhaeghen, Large-N c relations for the electromagnetic N to Δ(1232) transition, Phys. Rev. D 76 (2007) 111501 [arXiv:0711.0147] [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].
T. Ledwig, V. Pascalutsa and M. Vanderhaeghen, Electromagnetic moments of quasi-stable particle, Phys. Rev. D 82 (2010) 091301 [arXiv:1004.5055] [INSPIRE].
T. Ledwig, J. Martin-Camalich, V. Pascalutsa and M. Vanderhaeghen, The nucleon and Δ(1232) form factors at low momentum-transfer and small pion masses, Phys. Rev. D 85 (2012) 034013 [arXiv:1108.2523] [INSPIRE].
C. Alexandrou et al., Quark transverse charge densities in the Δ(1232) from lattice QCD, Nucl. Phys. A 825 (2009) 115 [arXiv:0901.3457] [INSPIRE].
C. Alexandrou et al., Delta-baryon electromagnetic form factors in lattice QCD, Phys. Rev. D 79 (2009) 014507 [arXiv:0810.3976] [INSPIRE].
C. Aubin, K. Orginos, V. Pascalutsa and M. Vanderhaeghen, Magnetic moments of Delta and Omega-baryons with dynamical clover fermions, Phys. Rev. D 79 (2009) 051502 [arXiv:0811.2440] [INSPIRE].
Z. Dziembowski, H. Holtmann, A. Szczurek and J. Speth, Pionic corrections to nucleon electromagnetic properties in a light cone framework, Ann. Phys. 258 (1997) 1 [INSPIRE].
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Granados, C., Weiss, C. Light-front representation of chiral dynamics with Δ isobar and large-N c relations. J. High Energ. Phys. 2016, 75 (2016). https://doi.org/10.1007/JHEP06(2016)075
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DOI: https://doi.org/10.1007/JHEP06(2016)075