Abstract
At leading order, there are three inelastic scattering processes beginning with a quantum kink and a fundamental meson. Meson multiplication, in which the final state is a kink and two mesons, was treated recently. In this note we treat the other two, (anti)-Stokes scattering, in which the kink’s shape mode is (de-)excited and the final state contains one meson. In the case of a general scalar kink, we find analytic formulas for the forward and backward scattering amplitudes and probabilities as functions of the momentum of the incident meson. The general results are then specialized to the kink of the ϕ4 double-well model.
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Y. Zhong et al., Collision of two kinks with inner structure, JHEP 02 (2020) 153 [arXiv:1906.02920] [INSPIRE].
H. Yan, Y. Zhong, Y.-X. Liu and K.-I. Maeda, Kink-antikink collision in a Lorentz-violating ϕ4 model, Phys. Lett. B 807 (2020) 135542 [arXiv:2004.13329] [INSPIRE].
M. Mohammadi and E. Momeni, Scattering of kinks in the Bφ4 model, Chaos Solitons Fractals 165 (2022) 112834 [arXiv:2207.00655] [INSPIRE].
I. Takyi et al., Kink collision in the noncanonical φ6 model: A model with localized inner structures, Results Phys. 44 (2023) 106197 [arXiv:2209.05902] [INSPIRE].
D.K. Campbell, J.F. Schonfeld and C.A. Wingate, Resonance structure in kink-antikink interactions in ϕ4 theory, Physica D9 (1983) 1.
N.S. Manton, K. Oles, T. Romanczukiewicz and A. Wereszczynski, Collective Coordinate Model of Kink-Antikink Collisions in ϕ4 Theory, Phys. Rev. Lett. 127 (2021) 071601 [arXiv:2106.05153] [INSPIRE].
A. Moradi Marjaneh, F.C. Simas and D. Bazeia, Collisions of kinks in deformed φ4 and φ6 models, Chaos Solitons Fractals 164 (2022) 112723 [arXiv:2207.00835] [INSPIRE].
A. Alonso-Izquierdo, D. Miguélez-Caballero, L.M. Nieto and J. Queiroga-Nunes, Wobbling kinks in a two-component scalar field theory: Interaction between shape modes, Physica D 443 (2023) 133590 [arXiv:2207.10989] [INSPIRE].
P. Dorey, K. Mersh, T. Romanczukiewicz and Y. Shnir, Kink-antikink collisions in the ϕ6 model, Phys. Rev. Lett. 107 (2011) 091602 [arXiv:1101.5951] [INSPIRE].
C. Adam et al., Multikink scattering in the ϕ6 model revisited, Phys. Rev. D 106 (2022) 125003 [arXiv:2209.08849] [INSPIRE].
C. Adam et al., Sphalerons and resonance phenomenon in kink-antikink collisions, Phys. Rev. D 104 (2021) 105022 [arXiv:2109.01834] [INSPIRE].
C. Adam, K. Oles, T. Romanczukiewicz and A. Wereszczynski, Spectral Walls in Soliton Collisions, Phys. Rev. Lett. 122 (2019) 241601 [arXiv:1903.12100] [INSPIRE].
J.G.F. Campos et al., Fermionic spectral walls in kink collisions, JHEP 01 (2023) 071 [arXiv:2211.07754] [INSPIRE].
J. Evslin, C. Halcrow, T. Romanczukiewicz and A. Wereszczynski, Spectral walls at one loop, Phys. Rev. D 105 (2022) 125002 [arXiv:2202.08249] [INSPIRE].
H. Segur and M.D. Kruskal, Nonexistence of Small Amplitude Breather Solutions in ϕ4 Theory, Phys. Rev. Lett. 58 (1987) 747 [INSPIRE].
G. Fodor, P. Forgacs, P. Grandclement and I. Racz, Oscillons and Quasi-breathers in the ϕ4 Klein-Gordon model, Phys. Rev. D 74 (2006) 124003 [hep-th/0609023] [INSPIRE].
M.P. Hertzberg, Quantum Radiation of Oscillons, Phys. Rev. D 82 (2010) 045022 [arXiv:1003.3459] [INSPIRE].
A. Hayashi, S. Saito and M. Uehara, Pion-nucleon scattering in the Skyrme model and the P wave Born amplitudes, Phys. Rev. D 43 (1991) 1520 [INSPIRE].
A. Hayashi, S. Saito and M. Uehara, Pion-nucleon scattering in the soliton model, Prog. Theor. Phys. Suppl. 109 (1992) 45 [INSPIRE].
J. Evslin, Manifestly Finite Derivation of the Quantum Kink Mass, JHEP 11 (2019) 161 [arXiv:1908.06710] [INSPIRE].
J. Evslin and H. Guo, Two-Loop Scalar Kinks, Phys. Rev. D 103 (2021) 125011 [arXiv:2012.04912] [INSPIRE].
J.-L. Gervais, A. Jevicki and B. Sakita, Collective Coordinate Method for Quantization of Extended Systems, Phys. Rept. 23 (1976) 281 [INSPIRE].
J.-L. Gervais and A. Jevicki, Point Canonical Transformations in Path Integral, Nucl. Phys. B 110 (1976) 93 [INSPIRE].
J. Evslin, H. Liu and B. Zhang, Kinks Multiply Mesons, arXiv:2211.01794 [INSPIRE].
H. Weigel, Quantum Instabilities of Solitons, AIP Conf. Proc. 2116 (2019) 170002 [arXiv:1907.10942] [INSPIRE].
K.E. Cahill, A. Comtet and R.J. Glauber, Mass Formulas for Static Solitons, Phys. Lett. B 64 (1976) 283 [INSPIRE].
J. Evslin and H. Liu, A reduced inner product for kink states, JHEP 03 (2023) 070 [arXiv:2212.10344] [INSPIRE].
T. Romanczukiewicz, Interaction between kink and radiation in ϕ4 model, Acta Phys. Polon. B 35 (2004) 523 [hep-th/0303058] [INSPIRE].
T. Romanczukiewicz, Interaction between topological defects and radiation, Acta Phys. Polon. B 36 (2005) 3877 [INSPIRE].
P. Forgacs, A. Lukacs and T. Romanczukiewicz, Negative radiation pressure exerted on kinks, Phys. Rev. D 77 (2008) 125012 [arXiv:0802.0080] [INSPIRE].
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Evslin, J., Liu, H. (Anti-)Stokes scattering on kinks. J. High Energ. Phys. 2023, 95 (2023). https://doi.org/10.1007/JHEP03(2023)095
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DOI: https://doi.org/10.1007/JHEP03(2023)095