Abstract
An omega-meson extension of the Skyrme model — without the Skyrme term but including the pion mass — first considered by Adkins and Nappi is studied in detail for baryon numbers 1 to 8. The static problem is reformulated as a constrained energy minimisation problem within a natural geometric framework and studied analytically on compact domains, and numerically on Euclidean space. Using a constrained second-order Newton flow algorithm, classical energy minimisers are constructed for various values of the omegapion coupling. At high coupling, these Skyrmion solutions are qualitatively similar to the Skyrmions of the standard Skyrme model with massless pions. At sufficiently low coupling, they show similarities with those in the lightly bound Skyrme model: the Skyrmions of low baryon number dissociate into lightly bound clusters of distinct 1-Skyrmions, and the classical binding energies for baryon numbers 2 through 8 have realistic values.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
T.H.R. Skyrme, A unified field theory of mesons and baryons, Nucl. Phys. 31 (1962) 556 [INSPIRE].
G. ’t Hooft, Symmetry breaking through Bell-Jackiw anomalies, Phys. Rev. Lett. 37 (1976) 8 [INSPIRE].
G.H. Derrick, Comments on nonlinear wave equations as models for elementary particles, J. Math. Phys. 5 (1964) 1252 [INSPIRE].
G.S. Adkins and C.R. Nappi, Stabilization of chiral solitons via vector mesons, Phys. Lett. B 137 (1984) 251 [INSPIRE].
U.G. Meissner and I. Zahed, Skyrmions in the presence of vector mesons, Phys. Rev. Lett. 56 (1986) 1035 [INSPIRE].
M. Bando, T. Kugo and K. Yamawaki, Nonlinear realization and hidden local symmetries, Phys. Rept. 164 (1988) 217 [INSPIRE].
M. Harada and K. Yamawaki, Hidden local symmetry at loop: a new perspective of composite gauge boson and chiral phase transition, Phys. Rept. 381 (2003) 1 [hep-ph/0302103] [INSPIRE].
P. Sutcliffe, Skyrmions, instantons and holography, JHEP 08 (2010) 019 [arXiv:1003.0023] [INSPIRE].
P. Sutcliffe, Skyrmions in a truncated BPS theory, JHEP 04 (2011) 045 [arXiv:1101.2402] [INSPIRE].
C. Naya and P. Sutcliffe, Skyrmions in models with pions and rho mesons, JHEP 05 (2018) 174 [arXiv:1803.06098] [INSPIRE].
C. Naya and P. Sutcliffe, Skyrmions and clustering in light nuclei, Phys. Rev. Lett. 121 (2018) 232002 [arXiv:1811.02064] [INSPIRE].
Y.-L. Ma et al., Hidden local symmetry and infinite tower of vector mesons for baryons, Phys. Rev. D 86 (2012) 074025 [arXiv:1206.5460] [INSPIRE].
Y.-L. Ma, G.-S. Yang, Y. Oh and M. Harada, Skyrmions with vector mesons in the hidden local symmetry approach, Phys. Rev. D 87 (2013) 034023 [arXiv:1209.3554] [INSPIRE].
Y.-L. Ma, M. Harada, H.K. Lee, Y. Oh, B.-Y. Park and M. Rho, Dense baryonic matter in the hidden local symmetry approach: Half-skyrmions and nucleon mass, Phys. Rev. D 88 (2013) 014016 [Erratum ibid. 88 (2013) 079904] [arXiv:1304.5638] [INSPIRE].
Y.-L. Ma, M. Harada, H.K. Lee, Y. Oh, B.-Y. Park and M. Rho, Dense baryonic matter in conformally-compensated hidden local symmetry: Vector manifestation and chiral symmetry restoration, Phys. Rev. D 90 (2014) 034015 [arXiv:1308.6476] [INSPIRE].
Y.-L. Ma and M. Rho, Scale-chiral symmetry, ω meson and dense baryonic matter, Phys. Rev. D 97 (2018) 094017 [arXiv:1612.04079] [INSPIRE].
P. Sutcliffe, Multi-Skyrmions with vector mesons, Phys. Rev. D 79 (2009) 085014 [arXiv:0810.5444] [INSPIRE].
J.M. Speight, A simple mass-splitting mechanism in the Skyrme model, Phys. Lett. B 781 (2018) 455 [arXiv:1803.11216] [INSPIRE].
D. Foster and P. Sutcliffe, Baby Skyrmions stabilized by vector mesons, Phys. Rev. D 79 (2009) 125026 [arXiv:0901.3622] [INSPIRE].
H. Urakawa, Calculus of variations and harmonic maps, American Mathematical Society, U.S.A. (1993).
J.M. Speight and M. Svensson, On the strong coupling limit of the Faddeev-Hopf model, Commun. Math. Phys. 272 (2007) 751 [math/0605516] [INSPIRE].
T.J. Willmore, Riemannian geometry, Oxford University Press, Oxford U.K. (1987).
N.S. Manton, Geometry of Skyrmions, Commun. Math. Phys. 111 (1987) 469 [INSPIRE].
R.T. Smith, The second variation formula for harmonic mappings, Proc. Amer. Math. Soc. 47 (1975) 229.
D. Harland, Topological energy bounds for the Skyrme and Faddeev models with massive pions, Phys. Lett. B 728 (2014) 518 [arXiv:1311.2403] [INSPIRE].
C. Adam and A. Wereszczynski, Topological energy bounds in generalized Skyrme models, Phys. Rev. D 89 (2014) 065010 [arXiv:1311.2939] [INSPIRE].
N.R. Walet, Quantizing the B = 2 and B = 3 skyrmion systems, Nucl. Phys. A 606 (1996) 429 [hep-ph/9603273] [INSPIRE].
C.J. Houghton, N.S. Manton and P.M. Sutcliffe, Rational maps, monopoles and Skyrmions, Nucl. Phys. B 510 (1998) 507 [hep-th/9705151] [INSPIRE].
C.J. Halcrow, Vibrational quantisation of the B = 7 Skyrmion, Nucl. Phys. B 904 (2016) 106 [arXiv:1511.00682] [INSPIRE].
C.J. Halcrow, C. King and N.S. Manton, A dynamical α-cluster model of 16 O, Phys. Rev. C 95 (2017) 031303 [arXiv:1608.05048] [INSPIRE].
J.I. Rawlinson, An alpha particle model for Carbon-12, Nucl. Phys. A 975 (2018) 122 [arXiv:1712.05658] [INSPIRE].
S.B. Gudnason and C. Halcrow, B = 5 Skyrmion as a two-cluster system, Phys. Rev. D 97 (2018) 125004 [arXiv:1802.04011] [INSPIRE].
C.J. Halcrow, C. King and N.S. Manton, Oxygen-16 spectrum from tetrahedral vibrations and their rotational excitations, Int. J. Mod. Phys. E 28 (2019) 1950026 [arXiv:1902.09424] [INSPIRE].
J.I. Rawlinson, Coriolis terms in Skyrmion Quantization, Nucl. Phys. B 949 (2019) 114800 [arXiv:1908.03414] [INSPIRE].
Particle Data Group collaboration, Review of particle physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
R.A. Battye, S. Krusch and P.M. Sutcliffe, Spinning skyrmions and the skyrme parameters, Phys. Lett. B 626 (2005) 120 [hep-th/0507279] [INSPIRE].
C. Adam, J. Sanchez-Guillen and A. Wereszczynski, On the spin excitation energy of the nucleon in the Skyrme model, Int. J. Mod. Phys. E 25 (2016) 1650097 [arXiv:1608.00979] [INSPIRE].
S.B. Gudnason, Exploring the generalized loosely bound Skyrme model, Phys. Rev. D 98 (2018) 096018 [arXiv:1805.10898] [INSPIRE].
S. Bjarke Gudnason and C. Halcrow, Vibrational modes of Skyrmions, Phys. Rev. D 98 (2018) 125010 [arXiv:1811.00562] [INSPIRE].
M. Gillard, D. Harland and M. Speight, Skyrmions with low binding energies, Nucl. Phys. B 895 (2015) 272 [arXiv:1501.05455] [INSPIRE].
M. Gillard, D. Harland, E. Kirk, B. Maybee and M. Speight, A point particle model of lightly bound skyrmions, Nucl. Phys. B 917 (2017) 286 [arXiv:1612.05481] [INSPIRE].
S. Baldino, S. Bolognesi, S.B. Gudnason and D. Koksal, Solitonic approach to holographic nuclear physics, Phys. Rev. D 96 (2017) 034008 [arXiv:1703.08695] [INSPIRE].
B.J. Schroers, Dynamics of moving and spinning Skyrmions, Z. Phys. C 61 (1994) 479 [hep-ph/9308236] [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].
T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [INSPIRE].
L. Bartolini, S. Bolognesi and A. Proto, From the Sakai-Sugimoto model to the generalized Skyrme model, Phys. Rev. D 97 (2018) 014024 [arXiv:1711.03873] [INSPIRE].
A. Jackson, A.D. Jackson, A.S. Goldhaber, G.E. Brown and L.C. Castillejo, A modified skyrmion, Phys. Lett. B 154 (1985) 101 [INSPIRE].
S. Zenkin, V. Kopeliovich and B. Stern, Interaction of solitons in the Skyrme model (in Russian), Sov. J. Nucl. Phys. 45 (1987) 106.
V.B. Kopeliovich, A.M. Shunderuk and G.K. Matushko, Mass splittings of nuclear isotopes in chiral soliton approach, Phys. Atom. Nucl. 69 (2006) 120 [nucl-th/0404020] [INSPIRE].
G.-J. Ding and M.-L. Yan, Nucleon-antinucleon Interaction from the Modified Skyrme Model, Phys. Rev. C 75 (2007) 034004 [nucl-th/0702037] [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
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2004.12862
Electronic supplementary material
ESM 1
(TAR 729 kb)
Rights and permissions
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.
About this article
Cite this article
Gudnason, S.B., Speight, J.M. Realistic classical binding energies in the ω-Skyrme model. J. High Energ. Phys. 2020, 184 (2020). https://doi.org/10.1007/JHEP07(2020)184
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2020)184