Radial vibrations of BPS skyrmions

Adam, C.; Haberichter, Mareike; Romańczukiewicz, T.; Wereszczyński, A.

doi:10.1103/physrevd.94.096013

Cited by 14 publications

(11 citation statements)

References 92 publications

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“…(2.10), a QNM may become a normal mode as m is increased. This has been shown to happen in the case of the B ¼ 1 Skyrmion [20,21]. We find repeated evidence that this also occurs for B > 1.…”

Section: Problem and Methodssupporting

confidence: 76%

Vibrational modes of Skyrmions

Gudnason

Halcrow

2018

Phys. Rev. D

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We study the vibrational modes of Skyrmions with baryon numbers one through eight in the standard Skyrme model. The vibrational modes are found in the harmonic approximation around the classical soliton solution and the real parts of the frequencies of the modes are extracted. We further classify the vibrational modes into representations of the symmetries possessed by the Skyrmion solutions. We find that there are approximately 7B low-lying modes for a Skyrmion with baryon number B, in addition to an infinite continuum of scattering modes. This result suggests that the instanton moduli space, which is 8Bdimensional, does not accurately describe the deformation space of Skyrmions as previously conjectured.

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Section: Problem and Methodssupporting

confidence: 76%

Vibrational modes of Skyrmions

Gudnason

Halcrow

2018

Phys. Rev. D

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“…Quasinormal modes are also often important in the classical evolution of dynamical systems, and indeed that is the context where they were first discussed [22]. The long-time dynamics are governed by the poles of the Green's function [23,24,25], with the position of the pole determining the nature of the mode. Poles corresponding to real frequencies are normal oscillational modes which in the linear approximation last infinitely long.…”

Section: Quasinormal Modesmentioning

confidence: 99%

“…. (25) Note that all of the poles are on the imaginary axis. These are not unstable modes because the stability of the kink solution is guaranteed by energy arguments and the topological charge.…”

Section: Comparison With Other Modelsmentioning

confidence: 99%

Resonant kink–antikink scattering through quasinormal modes

Dorey

Romańczukiewicz

2018

Physics Letters B

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We investigate the role that quasinormal modes can play in kink-antikink collisions, via an example based on a deformation of the φ 4 model. We find that narrow quasinormal modes can store energy during collision processes and later return it to the translational degrees of freedom. Quasinormal modes also decay, which leads to energy leakage, causing a closing of resonance windows and an increase of the critical velocity. We observe similar phenomena in an effective model, a small modification of the collectivecoordinate approach to the φ 4 model.

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“…For the oscillation (resonance) spectrum we assume η(t, r) = e ωt η(r) with ω = Ω+iΓ. Then, we arrive at the following functions for the corresponding Sturm-Liouville problem (for details of the procedure, see appendix A of [26]) where ξ 0 is the static solution. Finally, we can find an exact (algebraic) form of the effective potential for the Sturm-Liouville problem in the normal form.…”

Section: B Linear Perturbationmentioning

confidence: 99%

“…Moreover, we consider the family of potentials U (p) introduced above. We remark that the resonance structure in the pure BPS Skyrme model and its dependence on a particular form of the potential was carefully investigated in [26] (see also [31]). From a qualitative point of view, the asymptotics is completely dictated by the potential contribution.…”

Section: The Full Skyrme Model and The Role Of The Sextic Termmentioning

confidence: 99%

Roper resonances and quasi-normal modes of Skyrmions

Adam

Haberichter

Romańczukiewicz

et al. 2018

J. High Energ. Phys.

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Radial vibrations of charge one hedgehog Skyrmions in the full Skyrme model are analysed. We investigate how the properties of the lowest resonance modes (quasi normal modes) -their frequencies and widths -depend on the form of the potential (value of the pion mass as well as the addition of further potentials) and on the inclusion of the sextic term. Then we consider the inverse problem, where certain values for the frequencies and widths are imposed, and the field theoretic Skyrme model potential giving rise to them is reconstructed. This latter method allows to reproduce the physical Roper resonances, as well as further physical properties of nucleons, with high precision.PACS numbers: I. INTRODUCTIONThe Skyrme model [1] is an effective field theory (EFT) which bridges the underlying fundamental theory, Quantum Chromodynamics (QCD) -well understood in the perturbative, high energy regime -with the non-perturbative low energy region, beyond a scale where confinement and hadronisation leave only color-less states as observable particles. The natural field degrees of freedom in this regime are the lightest quasi-particles i.e., pions. The main attractiveness of the model originates from the fact that this field content is sufficient to describe, in principle, all other excitations -baryons and atomic nuclei -which emerge as non-perturbative states in such a mesonic fluid, or in the modern language, as topological solitons.This solitonic framework received further support from the large N c limit where it has been rigorously shown that QCD can be described by a weakly interacting theory of mesons [2]. Moreover, the pertinent topological index of the Skyrme model has been identified with the baryon charge. Finally, after the semiclassical quantization of zero modes of the classical solutions of the Skyrme model (Skyrmions) in a given topological sector (baryon charge) one got access to fermionic excitations of this classically purely bosonic theory. This opened the way for a realistic application of the Skyrme model for the description of baryons [3], [4] (proton, neutron, ∆ resonances), lighter nuclei and their excitation bands [5], [6] as well as higher nuclei, binding energies [7]-[9] and even infinite nuclear matter which defines properties of neutron stars [10], [11].In the baryon number one sector and with the SU(2) flavor group, there are two simple types of degrees of freedom of nucleons whose excitations can lead to new quasiparticles. First of all, an (iso)rotational excitation explains the ∆ resonance. Another possibility is to excite some vibrational degrees of freedom. This leads to new states which carry the same spin and isospin quantum numbers as the nucleons, i.e., the Roper resonances. The first three reasonably well established Ropers on top of the nucleons are: N (1440), N (1710), N (1880), which are highly short-living quasiparticles. Specifically, the first Roper N (1440) has a relatively wide Breit-Wigner width Γ = 300 MeV (and quite short mean life time τ = /Γ). While for the next two we hav...

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Radial vibrations of BPS skyrmions

Cited by 14 publications

References 92 publications

Vibrational modes of Skyrmions

Vibrational modes of Skyrmions

Resonant kink–antikink scattering through quasinormal modes

Roper resonances and quasi-normal modes of Skyrmions

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