Abstract
We study various properties of a perturbed signum-Gordon model, which has been obtained through the dimensional reduction of the called ‘first BPS submodel of the Skyrme model’. This study is motivated by the observation that the first BPS submodel of the Skyrme model may be partially responsible for the good qualities of the rational map ansatz approximation to the solutions of the Skyrme model. We investigate the existence, stability and various properties of oscillons and other time-dependent states in this perturbed signum-Gordon model.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
T.H.R. Skyrme, A non-linear field theory, Proc. Roy. Soc. Lond. 260 (1961) 127.
T.H.R. Skyrme, A unified field theory of mesons and baryons, Nucl. Phys. 31 (1962) 556.
T.H.R. Skyrme, Kinks and the Dirac equation, J. Math. Phys. 12 (1971) 1735 [INSPIRE].
C. Adam, J. Sanchez-Guillen and A. Wereszczynski, A Skyrme-type proposal for baryonic matter, Phys. Lett. B 691 (2010) 105 [arXiv:1001.4544] [INSPIRE].
C. Adam, J. Sanchez-Guillen and A. Wereszczynski, A BPS Skyrme model and baryons at large N c, Phys. Rev. D 82 (2010) 085015 [arXiv:1007.1567] [INSPIRE].
E. Bonenfant and L. Marleau, Nuclei as near BPS-Skyrmions, Phys. Rev. D 82 (2010) 054023 [arXiv:1007.1396] [INSPIRE].
E. Bonenfant, L. Harbour and L. Marleau, Near-BPS Skyrmions: non-shell configurations and Coulomb effects, Phys. Rev. D 85 (2012) 114045 [arXiv:1205.1414] [INSPIRE].
M.-O. Beaudoin and L. Marleau, Near-BPS Skyrmions: constant baryon density, Nucl. Phys. B 883 (2014) 328 [arXiv:1305.4944] [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].
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.B. Gudnason, Loosening up the Skyrme model, Phys. Rev. D 93 (2016) 065048 [arXiv:1601.05024] [INSPIRE].
S.B. Gudnason and M. Nitta, Modifying the pion mass in the loosely bound Skyrme model, Phys. Rev. D 94 (2016) 065018 [arXiv:1606.02981] [INSPIRE].
S.B. Gudnason, B. Zhang and N. Ma, Generalized Skyrme model with the loosely bound potential, Phys. Rev. D 94 (2016) 125004 [arXiv:1609.01591] [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].
G.S. Adkins and C.R. Nappi, The Skyrme model with pion masses, Nucl. Phys. B 233 (1984) 109 [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].
R.A. Battye and P.M. Sutcliffe, Symmetric Skyrmions, Phys. Rev. Lett. 79 (1997) 363 [hep-th/9702089] [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].
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].
C. Hajduk and B. Schwesinger, The breathing mode of nucleons and Δ isobars in the Skyrme model, Phys. Lett. B 140 (1984) 172 [INSPIRE].
U.B. Kaulfuss and U.-G. Meissner, The breathing mode of the modified Skyrmion, Phys. Lett. B 154 (1985) 193 [INSPIRE].
A. Hayashi and G. Holzwarth, Excited nucleon states in the Skyrme model, Phys. Lett. B 140 (1984) 175 [INSPIRE].
L.C. Biedenharn, Y. Dothan and M. Tarlini, Rotational-vibrational coupling in the Skyrmion model for baryons, Phys. Rev. D 31 (1985) 649 [INSPIRE].
I. Zahed, U.-G. Meissner and U.B. Kaulfuss, Low lying resonances in the Skyrme model using the semiclassical approximation, Nucl. Phys. A 426 (1984) 525 [INSPIRE].
J.D. Breit and C.R. Nappi, Phase shifts of the Skyrmion breathing mode, Phys. Rev. Lett. 53 (1984) 889 [INSPIRE].
W.T. Lin and B. Piette, Skyrmion vibration modes within the rational map ansatz, Phys. Rev. D 77 (2008) 125028 [arXiv:0804.4786] [INSPIRE].
M. Heusler, S. Droz and N. Straumann, Stability analysis of selfgravitating Skyrmions, Phys. Lett. B 271 (1991) 61 [INSPIRE].
C. Adam, C. Naya, J. Sanchez-Guillen and A. Wereszczynski, Rotational-vibrational coupling in the BPS Skyrme model of baryons, Phys. Lett. B 726 (2013) 892 [arXiv:1306.6337] [INSPIRE].
P. Bizon, T. Chmaj and A. Rostworowski, On asymptotic stability of the Skyrmion, Phys. Rev. D 75 (2007) 121702 [math-ph/0701037] [INSPIRE].
T. Ioannidou and A. Lukacs, Time-dependent Bogomolny-Prasad-Sommerfeld Skyrmions, J. Math. Phys. 57 (2016) 022901 [arXiv:1601.03048] [INSPIRE].
C. Adam, M. Haberichter, T. Romanczukiewicz and A. Wereszczynski, Radial vibrations of BPS Skyrmions, Phys. Rev. D 94 (2016) 096013 [arXiv:1607.04286] [INSPIRE].
C. Adam, M. Haberichter, T. Romanczukiewicz and A. Wereszczynski, Roper resonances and quasi-normal modes of Skyrmions, JHEP 03 (2018) 023 [arXiv:1710.00837] [INSPIRE].
D. Harland, J. Jaykka, Y. Shnir and M. Speight, Isospinning hopfions, J. Phys. A 46 (2013) 225402 [arXiv:1301.2923] [INSPIRE].
R. Rajaraman, H.M. Sommermann, J. Wambach and H.W. Wyld, Stability of the rotating Skyrmion, Phys. Rev. D 33 (1986) 287 [INSPIRE].
A. Halavanau and Y. Shnir, Isorotating baby Skyrmions, Phys. Rev. D 88 (2013) 085028 [arXiv:1309.4318] [INSPIRE].
R.A. Battye and M. Haberichter, Classically isospinning Hopf solitons, Phys. Rev. D 87 (2013) 105003 [arXiv:1301.6803] [INSPIRE].
R.A. Battye and M. Haberichter, Isospinning baby Skyrmion solutions, Phys. Rev. D 88 (2013) 125016 [arXiv:1309.3907] [INSPIRE].
D. Foster and N.S. Manton, Scattering of nucleons in the classical Skyrme model, Nucl. Phys. B 899 (2015) 513 [arXiv:1505.06843] [INSPIRE].
D. Foster and S. Krusch, Scattering of Skyrmions, Nucl. Phys. B 897 (2015) 697 [arXiv:1412.8719] [INSPIRE].
C. Adam, J. Sanchez-Guillen and A. Wereszczynski, BPS submodels of the Skyrme model, Phys. Lett. B 769 (2017) 362 [arXiv:1703.05818] [INSPIRE].
C. Adam, D. Foster, S. Krusch and A. Wereszczynski, BPS sectors of the Skyrme model and their non-BPS extensions, Phys. Rev. D 97 (2018) 036002 [arXiv:1709.06583] [INSPIRE].
H. Arodz and P. Klimas, Chain of impacting pendulums as non-analytically perturbed sine-Gordon system, Acta Phys. Polon. B 36 (2005) 787 [cond-mat/0501112].
H. Arodz, P. Klimas and T. Tyranowski, Field-theoretic models with V-shaped potentials, Acta Phys. Polon. B 36 (2005) 3861 [hep-th/0510204] [INSPIRE].
H. Arodz, P. Klimas and T. Tyranowski, Compact oscillons in the signum-Gordon model, Phys. Rev. D 77 (2008) 047701 [arXiv:0710.2244] [INSPIRE].
H. Arodz, P. Klimas and T. Tyranowski, Signum-Gordon wave equation and its self-similar solutions, Acta Phys. Polon. B 38 (2007) 3099 [hep-th/0701148] [INSPIRE].
P. Klimas, Perturbations of the signum-Gordon model, J. Phys. A 41 (2008) 095403 [arXiv:0711.2081] [INSPIRE].
B. Piette and W.J. Zakrzewski, Metastable stationary solutions of the radial d-dimensional sine-Gordon model, Nonlinearity 11 (1998) 1103.
D. Foster, The decay of Hopf solitons in the Skyrme model, J. Phys. A 50 (2017) 405401 [arXiv:1610.01571] [INSPIRE].
P. Dorey, K. Mersh, T. Romanczukiewicz and Y. Shnir, Kink-antikink collisions in the \( \phi \) 6 model, Phys. Rev. Lett. 107 (2011) 091602 [arXiv:1101.5951] [INSPIRE].
T. Romanczukiewicz and Ya. Shnir, Oscillon resonances and creation of kinks in particle collisions, Phys. Rev. Lett. 105 (2010) 081601 [arXiv:1002.4484] [INSPIRE].
T. Romanczukiewicz and Y. Shnir, Oscillons in the presence of external potential, JHEP 01 (2018) 101 [arXiv:1706.09234] [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: 1801.05454
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Klimas, P., Streibel, J.S., Wereszczynski, A. et al. Oscillons in a perturbed signum-Gordon model. J. High Energ. Phys. 2018, 102 (2018). https://doi.org/10.1007/JHEP04(2018)102
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2018)102