Roper resonances and quasi-normal modes of Skyrmions

Abstract

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...

The ϕ4 model with the BPS preserving defect

“…The frequencies of the antikink oscillation (which is the frequency of the first mode) together with two higher harmonics as well as two higher modes lie below the mass threshold ω = 2. Hence, the first propagating harmonics is the fourth one, which amounts to a rather high stability of the oscillating pair [27,35,36]. In addition, we see that this pair can be fully understood as an excited lump state.…”

“…We remark that the vanishing of ω 0 as α tends to − √ 2 leads to a very high stability of the oscillating topologically trivial lump (wobbling kink-antikink pair). The wobbling state can radiate but only by higher harmonics, which strongly suppresses its decay [29,35,36].…”

Resonant kink–antikink scattering through quasinormal modes

“…It is worth mentioning that having the linearised potential V(x) one can in principle reconstruct the field theory potential U(φ) [31,32]. However, except some rare cases, the procedure gives a very complicated potential which only can be found numerically, so we will not adopt this approach.…”

Oscillons in a perturbed signum-Gordon model

“…On the other hand, time-dependent configurations are needed in many physical applications of Skyrmions -especially in the (vibrational) quantization procedure. For example, small amplitude radial perturbations of static solitons contribute to some vibrational states, which have been interpreted as the Roper resonances [23][24][25][26][27][28][29][30][31][32][33][34][35]. Furthermore, (iso)-rotations influence shapes of Skyrmions and so can change their moments of inertia which in turn can modify the energies of quantum states [36][37][38][39][40].…”