Abstract
We investigate generalizations of the ϕ4 and sine-Gordon models, including interactions with Dirac Fermions. We observe new resonance phenomena by taking the fermion back-reaction into account. First, we show that the vibrational mode responsible for the resonance structure of the ϕ4 model has the same frequency as the energy of the fermion excited state when the back-reaction becomes more significant. Second, we consider the sine-Gordon model with the addition of a fermion field and find that a resonant structure appears, despite the absence of a scalar vibrational mode. The vibrational frequency of the mode responsible for the exchange mechanism is again the energy of the fermion excited state. Therefore, we find a new type of resonant energy exchange mechanism which is mediated by fermions.
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References
N. Manton and P. Sutcliffe, Topological solitons, Cambridge University Press (2004).
Y.M. Shnir, Topological and non-topological solitons in scalar field theories, Cambridge University Press (2018).
A. Ustinov, Solitons in Josephson junctions, Physica D 123 (1998) 315.
R.D. Yamaletdinov, V.A. Slipko and Y.V. Pershin, Kinks and antikinks of buckled graphene: a testing ground for the ϕ4 field model, Phys. Rev. B 96 (2017) 094306 [arXiv:1705.10684] [INSPIRE].
M. El-Batanouny, S. Burdick, K.M. Martini and P. Stancioff, Double-sine-Gordon solitons: a model for misfit dislocations on the Au(111) reconstructed surface, Phys. Rev. Lett. 58 (1987) 2762.
L.V. Yakushevich, Nonlinear physics of DNA, John Wiley & Sons (2006).
M. Kardar, Statistical physics of fields, Cambridge University Press (2007).
D.K. Campbell, J.F. Schonfeld and C.A. Wingate, Resonance structure in kink-antikink interactions in ϕ4 theory, Physica D 9 (1983) 1.
D.K. Campbell, M. Peyrard and P. Sodano, Kink-antikink interactions in the double sine-Gordon equation, Physica D 19 (1986) 165.
M. Peyrard and D.K. Campbell, Kink-antikink interactions in a modified sine-Gordon model, Physica D 9 (1983) 33.
N.S. Manton, K. Oleś, T. Romańczukiewicz and A. Wereszczyński, Kink moduli spaces: collective coordinates reconsidered, Phys. Rev. D 103 (2021) 025024 [arXiv:2008.01026] [INSPIRE].
N.S. Manton, K. Oleś, T. Romańczukiewicz and A. Wereszczyński, Collective coordinate model of kink-antikink collisions in ϕ4 theory, Phys. Rev. Lett. 127 (2021) 071601 [arXiv:2106.05153] [INSPIRE].
F.C. Simas, A.R. Gomes, K.Z. Nobrega and J.C.R.E. Oliveira, Suppression of two-bounce windows in kink-antikink collisions, JHEP 09 (2016) 104 [arXiv:1605.05344] [INSPIRE].
R. Fleischer, D.G. Espinosa, R. Jaarsma and G. Tetlalmatzi-Xolocotzi, CP violation in leptonic rare \( {B}_s^0 \) decays as a probe of new physics, Eur. Phys. J. C 78 (2018) 1 [arXiv:1709.04735] [INSPIRE].
A. Demirkaya, R. Decker, P.G. Kevrekidis, I.C. Christov and A. Saxena, Kink dynamics in a parametric ϕ6 system: a model with controllably many internal modes, JHEP 12 (2017) 071 [arXiv:1706.01193] [INSPIRE].
V.A. Gani, V. Lensky and M.A. Lizunova, Kink excitation spectra in the (1 + 1)-dimensional ϕ8 model, JHEP 08 (2015) 147 [arXiv:1506.02313] [INSPIRE].
D. Bazeia, A.R. Gomes, K.Z. Nobrega and F.C. Simas, Kink scattering in a hybrid model, Phys. Lett. B 793 (2019) 26 [arXiv:1805.07017] [INSPIRE].
D. Bazeia, A.R. Gomes, K.Z. Nobrega and F.C. Simas, Oscillons in hyperbolic models, Phys. Lett. B 803 (2020) 135291 [arXiv:1911.03352] [INSPIRE].
V.A. Gani, A.M. Marjaneh, A. Askari, E. Belendryasova and D. Saadatmand, Scattering of the double sine-Gordon kinks, Eur. Phys. J. C 78 (2018) 345 [arXiv:1711.01918] [INSPIRE].
V.A. Gani, A.M. Marjaneh and D. Saadatmand, Multi-kink scattering in the double sine-Gordon model, Eur. Phys. J. C 79 (2019) 620 [arXiv:1901.07966] [INSPIRE].
F.C. Simas, F.C. Lima, K.Z. Nobrega and A.R. Gomes, Solitary oscillations and multiple antikink-kink pairs in the double sine-Gordon model, JHEP 12 (2020) 143 [arXiv:2007.12318] [INSPIRE].
J.G.F. Campos and A. Mohammadi, Wobbling double sine-Gordon kinks, JHEP 09 (2021) 067 [arXiv:2103.04908] [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].
I.C. Christov, R.J. Decker, A. Demirkaya, V.A. Gani, P.G. Kevrekidis and A. Saxena, Kink-antikink collisions and multi-bounce resonance windows in higher-order field theories, Commun. Nonlinear Sci. Numer. Simul. 97 (2021) 105748 [arXiv:2005.00154] [INSPIRE].
A. Nada and A. Ramos, An analysis of systematic effects in finite size scaling studies using the gradient flow, Eur. Phys. J. C 81 (2021) 1 [arXiv:2007.12862] [INSPIRE].
Y.S. Kivshar, Z. Fei and L. Vázquez, Resonant soliton-impurity interactions, Phys. Rev. Lett. 67 (1991) 1177 [INSPIRE].
Z. Fei, Y.S. Kivshar and L. Vázquez, Resonant kink-impurity interactions in the sine-Gordon model, Phys. Rev. A 45 (1992) 6019.
Z. Fei, L. Vázquez and Y.S. Kivshar, Resonant kink impurity interactions in the ϕ4 model, Phys. Rev. A 46 (1992) 5214 [INSPIRE].
R.H. Goodman and R. Haberman, Interaction of sine-Gordon kinks with defects: the two-bounce resonance, Physica D 195 (2004) 303.
R. Arthur, P. Dorey and R. Parini, Breaking integrability at the boundary: the sine-Gordon model with Robin boundary conditions, J. Phys. A 49 (2016) 165205 [arXiv:1509.08448] [INSPIRE].
P. Dorey, A. Halavanau, J. Mercer, T. Romanczukiewicz and Y. Shnir, Boundary scattering in the ϕ4 model, JHEP 05 (2017) 107 [arXiv:1508.02329] [INSPIRE].
F.C. Lima, F.C. Simas, K.Z. Nobrega and A.R. Gomes, Boundary scattering in the ϕ6 model, JHEP 10 (2019) 147 [arXiv:1808.06703] [INSPIRE].
P. Dorey and T. Romańczukiewicz, Resonant kink-antikink scattering through quasinormal modes, Phys. Lett. B 779 (2018) 117 [arXiv:1712.10235] [INSPIRE].
J. Aebischer, C. Bobeth and A.J. Buras, On the importance of NNLO QCD and isospin-breaking corrections in ϵ′/ϵ, Eur. Phys. J. C 80 (2020) 1 [arXiv:1909.05610] [INSPIRE].
C. Adam, D. Ciurla, K. Oleś, T. Romańczukiewicz and A. Wereszczyński, Sphalerons and resonance phenomenon in kink-antikink collisions, Phys. Rev. D 104 (2021) 105022 [arXiv:2109.01834] [INSPIRE].
R. Jackiw and C. Rebbi, Solitons with fermion number 1/2, Phys. Rev. D 13 (1976) 3398 [INSPIRE].
M.F. Atiyah and I.M. Singer, The index of elliptic operators on compact manifolds, Bull. Amer. Math. Soc. 69 (1963) 422.
A.J. Niemi and G.W. Semenoff, Fermion number fractionization in quantum field theory, Phys. Rept. 135 (1986) 99 [INSPIRE].
A. Halavanau, T. Romanczukiewicz and Y. Shnir, Resonance structures in coupled two-component ϕ4 model, Phys. Rev. D 86 (2012) 085027 [arXiv:1206.4471] [INSPIRE].
A. Alonso-Izquierdo, Reflection, transmutation, annihilation and resonance in two-component kink collisions, Phys. Rev. D 97 (2018) 045016 [arXiv:1711.10034] [INSPIRE].
A. Alonso-Izquierdo, Non-topological kink scattering in a two-component scalar field theory model, Commun. Nonlinear Sci. Numer. Simul. 85 (2020) 105251 [arXiv:1906.05040] [INSPIRE].
A. Alonso-Izquierdo, M.A.G. León, J.M. Vaquero and M.d.l.T. Mayado, Kink scattering in a generalized Wess-Zumino model, Commun. Nonlinear Sci. Numer. Simul. 103 (2021) 106011 [arXiv:2105.05750] [INSPIRE].
F. Charmchi and S.S. Gousheh, Complete spectral analysis of the Jackiw-Rebbi model, including its zero mode, Phys. Rev. D 89 (2014) 025002 [arXiv:1402.2444] [INSPIRE].
F. Charmchi and S.S. Gousheh, Massive Jackiw-Rebbi model, Nucl. Phys. B 883 (2014) 256 [arXiv:1404.4263] [INSPIRE].
D. Bazeia and A. Mohammadi, Fermionic bound states in distinct kinklike backgrounds, Eur. Phys. J. C 77 (2017) 203 [arXiv:1702.00891] [INSPIRE].
D. Bazeia, A. Mohammadi and D.C. Moreira, Fermions in the presence of topological structures under geometric constrictions, Phys. Rev. D 103 (2021) 025003 [arXiv:2009.00737] [INSPIRE].
Y.-Z. Chu and T. Vachaspati, Fermions on one or fewer kinks, Phys. Rev. D 77 (2008) 025006 [arXiv:0709.3668] [INSPIRE].
Y. Brihaye and T. Delsate, Remarks on bell-shaped lumps: stability and fermionic modes, Phys. Rev. D 78 (2008) 025014 [arXiv:0803.1458] [INSPIRE].
G. Gibbons, K.-I. Maeda and Y.-I. Takamizu, Fermions on colliding branes, Phys. Lett. B 647 (2007) 1 [hep-th/0610286] [INSPIRE].
P.M. Saffin and A. Tranberg, Particle transfer in braneworld collisions, JHEP 08 (2007) 072 [arXiv:0705.3606] [INSPIRE].
J.G.F. Campos and A. Mohammadi, Fermion transfer in the ϕ4 model with a half-BPS preserving impurity, Phys. Rev. D 102 (2020) 045003 [arXiv:2004.08413] [INSPIRE].
J.G.F. Campos and A. Mohammadi, Fermions on wobbling kinks: normal versus quasinormal modes, JHEP 09 (2021) 103 [arXiv:2106.04712] [INSPIRE].
A. Amado and A. Mohammadi, Coupled fermion-kink system in Jackiw-Rebbi model, Eur. Phys. J. C 77 (2017) 465 [arXiv:1406.1459] [INSPIRE].
V. Klimashonok, I. Perapechka and Y. Shnir, Fermions on kinks revisited, Phys. Rev. D 100 (2019) 105003 [arXiv:1909.12736] [INSPIRE].
I. Perapechka and Y. Shnir, Kinks bounded by fermions, Phys. Rev. D 101 (2020) 021701 [arXiv:1910.09866] [INSPIRE].
I. Perapechka, N. Sawado and Y. Shnir, Soliton solutions of the fermion-skyrmion system in (2 + 1) dimensions, JHEP 10 (2018) 081 [arXiv:1808.07787] [INSPIRE].
I. Perapechka and Y. Shnir, Fermion exchange interaction between magnetic skyrmions, Phys. Rev. D 99 (2019) 125001 [arXiv:1901.06925] [INSPIRE].
J.G.F. Campos and A. Mohammadi, Kink-antikink collision in the supersymmetric ϕ4 model, JHEP 08 (2022) 180 [arXiv:2205.06869] [INSPIRE].
P.M. Morse and H. Feshbach, Methods of theoretical physics, McGraw-Hill (1953).
A. Vanhaverbeke, A. Bischof and R. Allenspach, Control of domain wall polarity by current pulses, Phys. Rev. Lett. 101 (2008) 107202.
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Bazeia, D., Campos, J.G.F. & Mohammadi, A. Resonance mediated by fermions in kink-antikink collisions. J. High Energ. Phys. 2022, 85 (2022). https://doi.org/10.1007/JHEP12(2022)085
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DOI: https://doi.org/10.1007/JHEP12(2022)085