Fermion scattering on topological solitons in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">C</mml:mi><mml:mi mathvariant="double-struck">P</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>model

Loginov, A.

doi:10.1103/physrevd.107.065011

Phys. Rev. D

2023

DOI: 10.1103/physrevd.107.065011

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Fermion scattering on topological solitons in theCPN−1model

A. Loginov

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Cited by 3 publications

References 30 publications

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Spectral flow of fermions in the ℂP2 (anti-)instanton, and the sphaleron with vanishing topological charge

Amari,

Sawado,

Yamamoto

2024

J. High Energ. Phys.

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The spectral flow is ubiquitous in the physics of soliton-fermion interacting systems. We study the spectral flows related to a continuous deformation of background soliton solutions, which enable us to develop insight into the emergence of fermionic zero modes and the localization mechanism of fermion densities. We investigate a ℂP2 nonlinear sigma model in which there are the (anti-) instantons and also the sphalerons with vanishing topological charge. The standard Yukawa coupling of the fermion successfully generates infinite towers of the spectra and the spectral flow is observed when increasing the size of such solitons. At that moment, the localization of the fermions on the solitons emerges. The avoided crossings are also observed in several stages of the exchange of the flows, they are indicating a manifestation of the fermion exchange of the localizing nature.

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Spectral flow of fermions in the ℂP2 (anti-)instanton, and the sphaleron with vanishing topological charge

Amari,

Sawado,

Yamamoto

2024

J. High Energ. Phys.

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Asymptotic states for kink–meson scattering

Evslin

2023

Eur. Phys. J. C

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The definition of a quantum state corresponding to a wave packet far from a global soliton is considered. We define an asymptotic quantum state corresponding to a localized wave packet of elementary quanta far from a kink. We demand that the state satisfies two properties. First, it must evolve in time via a rigid translation of the wave packet, up to the usual wave packet spreading and corrections which are exponentially suppressed in the distance to the kink. Second, the state must be invariant under a simultaneous translation of the kink and the wave packet. We explicitly construct the leading quantum corrections to an asymptotic state consisting of a meson approaching a kink. We expect this construction to readily generalize to elementary quanta in the presence of any global soliton.

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Fermion-soliton scattering in a modified $$\mathbb{C}\mathbb{P}^{1}$$ model

Loginov

2024

Eur. Phys. J. C

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The scattering of fermions in the background field of a topological soliton of the modified $$(2 + 1)$$ ( 2 + 1 ) -dimensional $$\mathbb{C}\mathbb{P}^{1}$$ C P 1 model is studied here both analytically and numerically. Unlike the original $$\mathbb{C}\mathbb{P}^{1}$$ C P 1 model, the Lagrangian of the modified model contains a potential term. Due to this, a dilatation zero mode of the topological soliton disappears, which results in stability of the fermion-soliton system. The symmetry properties of the fermion-soliton system are established, and the asymptotic forms of fermionic radial wave functions are studied. Questions related to the bound states of the fermion-soliton system are then discussed. General formulae describing the scattering of fermions are presented. The amplitudes of the fermion-soliton scattering are obtained in an analytical form within the framework of the Born approximation, and their symmetry properties and asymptotic forms are studied. The energy levels of the fermionic bound states and the partial phase shifts of fermionic scattering are obtained by numerical methods, and the ultrarelativistic limits of the partial phase shifts are found.

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Fermion scattering on topological solitons in theCPN−1model

Cited by 3 publications

References 30 publications

Spectral flow of fermions in the ℂP2 (anti-)instanton, and the sphaleron with vanishing topological charge

Spectral flow of fermions in the ℂP2 (anti-)instanton, and the sphaleron with vanishing topological charge

Asymptotic states for kink–meson scattering

Fermion-soliton scattering in a modified $$\mathbb{C}\mathbb{P}^{1}$$ model

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