Abstract
We study the axion strings with the electroweak gauge flux in the DFSZ axion model and show that these strings, called the electroweak axion strings, can exhibit superconductivity without fermionic zeromodes. We construct three types of electroweak axion string solutions. Among them, the string with W-flux can be lightest in some parameter space, which leads to a stable superconducting cosmic string. We also show that a large electric current can flow along the string due to the Peccei-Quinn scale much higher than the electroweak scale. This large current induces a net attractive force between the axion strings with the same topological charge, which opens a novel possibility that the axion strings form Y-junctions in the early universe.
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References
R.D. Peccei and H.R. Quinn, Constraints Imposed by CP Conservation in the Presence of Instantons, Phys. Rev. D 16 (1977) 1791 [INSPIRE].
R.D. Peccei and H.R. Quinn, CP Conservation in the Presence of Instantons, Phys. Rev. Lett. 38 (1977) 1440 [INSPIRE].
S. Weinberg, A New Light Boson?, Phys. Rev. Lett. 40 (1978) 223 [INSPIRE].
F. Wilczek, Problem of Strong P and T Invariance in the Presence of Instantons, Phys. Rev. Lett. 40 (1978) 279 [INSPIRE].
J. Preskill, M.B. Wise and F. Wilczek, Cosmology of the Invisible Axion, Phys. Lett. B 120 (1983) 127 [INSPIRE].
L.F. Abbott and P. Sikivie, A Cosmological Bound on the Invisible Axion, Phys. Lett. B 120 (1983) 133 [INSPIRE].
M. Dine and W. Fischler, The Not So Harmless Axion, Phys. Lett. B 120 (1983) 137 [INSPIRE].
P. Sikivie, Axion Cosmology, Lect. Notes Phys. 741 (2008) 19 [astro-ph/0610440] [INSPIRE].
D.J.E. Marsh, Axion Cosmology, Phys. Rept. 643 (2016) 1 [arXiv:1510.07633] [INSPIRE].
A. Ringwald, Exploring the Role of Axions and Other WISPs in the Dark Universe, Phys. Dark Univ. 1 (2012) 116 [arXiv:1210.5081] [INSPIRE].
O. Wantz and E.P.S. Shellard, Axion Cosmology Revisited, Phys. Rev. D 82 (2010) 123508 [arXiv:0910.1066] [INSPIRE].
J.E. Kim and G. Carosi, Axions and the Strong CP Problem, Rev. Mod. Phys. 82 (2010) 557 [Erratum ibid. 91 (2019) 049902] [arXiv:0807.3125] [INSPIRE].
A.R. Zhitnitsky, On Possible Suppression of the Axion Hadron Interactions (in Russian), Sov. J. Nucl. Phys. 31 (1980) 260 [INSPIRE].
M. Dine, W. Fischler and M. Srednicki, A Simple Solution to the Strong CP Problem with a Harmless Axion, Phys. Lett. B 104 (1981) 199 [INSPIRE].
J.E. Kim, Weak Interaction Singlet and Strong CP Invariance, Phys. Rev. Lett. 43 (1979) 103 [INSPIRE].
M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Can Confinement Ensure Natural CP Invariance of Strong Interactions?, Nucl. Phys. B 166 (1980) 493 [INSPIRE].
Planck collaboration, Planck 2018 results. X. Constraints on inflation, Astron. Astrophys. 641 (2020) A10 [arXiv:1807.06211] [INSPIRE].
G.B. Gelmini, M. Gleiser and E.W. Kolb, Cosmology of Biased Discrete Symmetry Breaking, Phys. Rev. D 39 (1989) 1558 [INSPIRE].
S.E. Larsson, S. Sarkar and P.L. White, Evading the cosmological domain wall problem, Phys. Rev. D 55 (1997) 5129 [hep-ph/9608319] [INSPIRE].
P. Sikivie, Of Axions, Domain Walls and the Early Universe, Phys. Rev. Lett. 48 (1982) 1156 [INSPIRE].
S. Chang, C. Hagmann and P. Sikivie, Studies of the motion and decay of axion walls bounded by strings, Phys. Rev. D 59 (1999) 023505 [hep-ph/9807374] [INSPIRE].
A. Vilenkin, Gravitational Field of Vacuum Domain Walls and Strings, Phys. Rev. D 23 (1981) 852 [INSPIRE].
R.D. Peccei, T.T. Wu and T. Yanagida, A viable axion model, Phys. Lett. B 172 (1986) 435 [INSPIRE].
L.M. Krauss and F. Wilczek, A shortlived axion variant, Phys. Lett. B 173 (1986) 189 [INSPIRE].
G. Lazarides and Q. Shafi, Axion Models with No Domain Wall Problem, Phys. Lett. B 115 (1982) 21 [INSPIRE].
C. Chatterjee, T. Higaki and M. Nitta, Note on a solution to domain wall problem with the Lazarides-Shafi mechanism in axion dark matter models, Phys. Rev. D 101 (2020) 075026 [arXiv:1903.11753] [INSPIRE].
M. Kawasaki, F. Takahashi and M. Yamada, Suppressing the QCD Axion Abundance by Hidden Monopoles, Phys. Lett. B 753 (2016) 677 [arXiv:1511.05030] [INSPIRE].
R. Sato, F. Takahashi and M. Yamada, Unified Origin of Axion and Monopole Dark Matter, and Solution to the Domain-wall Problem, Phys. Rev. D 98 (2018) 043535 [arXiv:1805.10533] [INSPIRE].
R.L. Davis, Cosmic Axions from Cosmic Strings, Phys. Lett. B 180 (1986) 225 [INSPIRE].
T.W.B. Kibble, Some Implications of a Cosmological Phase Transition, Phys. Rept. 67 (1980) 183 [INSPIRE].
W.H. Zurek, Cosmological Experiments in Superfluid Helium?, Nature 317 (1985) 505 [INSPIRE].
H. Murayama and J. Shu, Topological Dark Matter, Phys. Lett. B 686 (2010) 162 [arXiv:0905.1720] [INSPIRE].
A. Vilenkin and E.S. Shellard, Cosmic Strings and Other Topological Defects, Cambridge University Press (2000) [INSPIRE].
E. Witten, Superconducting Strings, Nucl. Phys. B 249 (1985) 557 [INSPIRE].
G. Lazarides and Q. Shafi, Superconducting Strings in Axion Models, Phys. Lett. B 151 (1985) 123 [INSPIRE].
A. Iwazaki, Spontaneous magnetization of axion domain wall and primordial magnetic field, Phys. Rev. Lett. 79 (1997) 2927 [hep-ph/9705456] [INSPIRE].
N. Ganoulis and G. Lazarides, Fermionic Zero Modes for Cosmic Strings, Nucl. Phys. B 316 (1989) 443 [INSPIRE].
G. Lazarides, C. Panagiotakopoulos and Q. Shafi, Cosmic superconducting strings and colliders, Nucl. Phys. B 296 (1988) 657 [INSPIRE].
R. Jackiw and P. Rossi, Zero Modes of the Vortex - Fermion System, Nucl. Phys. B 190 (1981) 681 [INSPIRE].
C.G. Callan Jr. and J.A. Harvey, Anomalies and Fermion Zero Modes on Strings and Domain Walls, Nucl. Phys. B 250 (1985) 427 [INSPIRE].
A.A. Abrikosov, On the Magnetic properties of superconductors of the second group, Sov. Phys. JETP 5 (1957) 1174 [INSPIRE].
H.B. Nielsen and P. Olesen, Vortex Line Models for Dual Strings, Nucl. Phys. B 61 (1973) 45 [INSPIRE].
Y. Nambu, String-Like Configurations in the Weinberg-Salam Theory, Nucl. Phys. B 130 (1977) 505 [INSPIRE].
T. Vachaspati, Electroweak strings, Nucl. Phys. B 397 (1993) 648 [INSPIRE].
T. Vachaspati, Vortex solutions in the Weinberg-Salam model, Phys. Rev. Lett. 68 (1992) 1977 [Erratum ibid. 69 (1992) 216] [INSPIRE].
M. James, L. Perivolaropoulos and T. Vachaspati, Stability of electroweak strings, Phys. Rev. D 46 (1992) R5232 [INSPIRE].
M. James, L. Perivolaropoulos and T. Vachaspati, Detailed stability analysis of electroweak strings, Nucl. Phys. B 395 (1993) 534 [hep-ph/9212301] [INSPIRE].
T. Vachaspati and G.B. Field, Electroweak string configurations with baryon number, Phys. Rev. Lett. 73 (1994) 373 [hep-ph/9401220] [INSPIRE].
M. Barriola, T. Vachaspati and M. Bucher, Embedded defects, Phys. Rev. D 50 (1994) 2819 [hep-th/9306120] [INSPIRE].
M. Barriola, Electroweak strings that produce baryons, Phys. Rev. D 51 (1995) 300 [hep-ph/9403323] [INSPIRE].
M. Eto, K. Konishi, M. Nitta and Y. Ookouchi, Brane Realization of Nambu Monopoles and Electroweak Strings, Phys. Rev. D 87 (2013) 045006 [arXiv:1211.2971] [INSPIRE].
A. Achucarro and T. Vachaspati, Semilocal and electroweak strings, Phys. Rept. 327 (2000) 347 [hep-ph/9904229] [INSPIRE].
L. Perivolaropoulos, Existence of double vortex solutions, Phys. Lett. B 316 (1993) 528 [hep-ph/9309261] [INSPIRE].
H. La, Vortex solutions in two Higgs systems and tanβ, hep-ph/9302220 [INSPIRE].
G.R. Dvali and G. Senjanović, Topologically stable electroweak flux tubes, Phys. Rev. Lett. 71 (1993) 2376 [hep-ph/9305278] [INSPIRE].
G.R. Dvali and G. Senjanović, Topologically stable Z strings in the supersymmetric Standard Model, Phys. Lett. B 331 (1994) 63 [hep-ph/9403277] [INSPIRE].
G. Bimonte and G. Lozano, Vortex solutions in two Higgs doublet systems, Phys. Lett. B 326 (1994) 270 [hep-ph/9401313] [INSPIRE].
C. Bachas, B. Rai and T.N. Tomaras, New string excitations in the two Higgs standard model, Phys. Rev. Lett. 82 (1999) 2443 [hep-ph/9801263] [INSPIRE].
I.P. Ivanov, Minkowski space structure of the Higgs potential in 2HDM. II. Minima, symmetries, and topology, Phys. Rev. D 77 (2008) 015017 [arXiv:0710.3490] [INSPIRE].
R.A. Battye, G.D. Brawn and A. Pilaftsis, Vacuum Topology of the Two Higgs Doublet Model, JHEP 08 (2011) 020 [arXiv:1106.3482] [INSPIRE].
M. Eto, Y. Hamada, M. Kurachi and M. Nitta, Topological Nambu monopole in two Higgs doublet models, Phys. Lett. B 802 (2020) 135220 [arXiv:1904.09269] [INSPIRE].
M. Eto, Y. Hamada, M. Kurachi and M. Nitta, Dynamics of Nambu monopole in two Higgs doublet models. Cosmological Monopole Collider, JHEP 07 (2020) 004 [arXiv:2003.08772] [INSPIRE].
M. Eto, M. Kurachi and M. Nitta, Constraints on two Higgs doublet models from domain walls, Phys. Lett. B 785 (2018) 447 [arXiv:1803.04662] [INSPIRE].
M. Eto, M. Kurachi and M. Nitta, Non-Abelian strings and domain walls in two Higgs doublet models, JHEP 08 (2018) 195 [arXiv:1805.07015] [INSPIRE].
M.G. Alford, K. Benson, S.R. Coleman, J. March-Russell and F. Wilczek, The Interactions and Excitations of Nonabelian Vortices, Phys. Rev. Lett. 64 (1990) 1632 [Erratum ibid. 65 (1990) 668] [INSPIRE].
M.G. Alford, K. Benson, S.R. Coleman, J. March-Russell and F. Wilczek, Zero modes of nonabelian vortices, Nucl. Phys. B 349 (1991) 414 [INSPIRE].
B. Grzadkowski, M. Maniatis and J. Wudka, The bilinear formalism and the custodial symmetry in the two-Higgs-doublet model, JHEP 11 (2011) 030 [arXiv:1011.5228] [INSPIRE].
A. Pomarol and R. Vega, Constraints on CP-violation in the Higgs sector from the ρ parameter, Nucl. Phys. B 413 (1994) 3 [hep-ph/9305272] [INSPIRE].
M. Eto, Y. Hamada and M. Nitta, Topological structure of a Nambu monopole in two-Higgs-doublet models: Fiber bundle, Dirac’s quantization, and a dyon, Phys. Rev. D 102 (2020) 105018 [arXiv:2007.15587] [INSPIRE].
L.M.A. Bettencourt, P. Laguna and R.A. Matzner, Nonintercommuting cosmic strings, Phys. Rev. Lett. 78 (1997) 2066 [hep-ph/9612350] [INSPIRE].
L.M.A. Bettencourt and T.W.B. Kibble, Nonintercommuting configurations in the collisions of type-I U(1) cosmic strings, Phys. Lett. B 332 (1994) 297 [hep-ph/9405221] [INSPIRE].
E.J. Copeland, T.W.B. Kibble and D.A. Steer, Collisions of strings with Y junctions, Phys. Rev. Lett. 97 (2006) 021602 [hep-th/0601153] [INSPIRE].
E.J. Copeland, T.W.B. Kibble and D.A. Steer, Constraints on string networks with junctions, Phys. Rev. D 75 (2007) 065024 [hep-th/0611243] [INSPIRE].
P. Salmi, A. Achucarro, E.J. Copeland, T.W.B. Kibble, R. de Putter and D.A. Steer, Kinematic constraints on formation of bound states of cosmic strings: Field theoretical approach, Phys. Rev. D 77 (2008) 041701 [arXiv:0712.1204] [INSPIRE].
N. Bevis and P.M. Saffin, Cosmic string Y-junctions: A Comparison between field theoretic and Nambu-Goto dynamics, Phys. Rev. D 78 (2008) 023503 [arXiv:0804.0200] [INSPIRE].
N. Bevis et al., Evolution and stability of cosmic string loops with Y-junctions, Phys. Rev. D 80 (2009) 125030 [arXiv:0904.2127] [INSPIRE].
T. Hiramatsu, M. Eto, K. Kamada, T. Kobayashi and Y. Ookouchi, Instability of colliding metastable strings, JHEP 01 (2014) 165 [arXiv:1304.0623] [INSPIRE].
T. Hiramatsu, Y. Sendouda, K. Takahashi, D. Yamauchi and C.-M. Yoo, Type-I cosmic string network, Phys. Rev. D 88 (2013) 085021 [arXiv:1307.0308] [INSPIRE].
E.N. Parker, Hydromagnetic Dynamo Models, Astrophys. J. 122 (1955) 293 [INSPIRE].
R. Durrer and A. Neronov, Cosmological Magnetic Fields: Their Generation, Evolution and Observation, Astron. Astrophys. Rev. 21 (2013) 62 [arXiv:1303.7121] [INSPIRE].
A. Neronov and I. Vovk, Evidence for strong extragalactic magnetic fields from Fermi observations of TeV blazars, Science 328 (2010) 73 [arXiv:1006.3504] [INSPIRE].
K. Jedamzik and A. Saveliev, Stringent Limit on Primordial Magnetic Fields from the Cosmic Microwave Background Radiation, Phys. Rev. Lett. 123 (2019) 021301 [arXiv:1804.06115] [INSPIRE].
E.J. Copeland and N. Turok, Cosmic String Interactions, Imperial College Preprint (1986).
E.P.S. Shellard, Cosmic String Interactions, Nucl. Phys. B 283 (1987) 624 [INSPIRE].
E.P.S. Shellard, Understanding intercommuting, in Yale Workshop: Cosmic Strings: The Current Status (1988) [INSPIRE].
J. Ambjørn and P. Olesen, Electroweak magnetism, W condensation and antiscreening, in 4th Hellenic School on Elementary Particle Physics, (1992) [hep-ph/9304220] [INSPIRE].
J. Ambjørn and P. Olesen, Electroweak Magnetism: Theory and Application, Int. J. Mod. Phys. A 5 (1990) 4525 [INSPIRE].
J. Ambjørn and P. Olesen, A Condensate Solution of the Electroweak Theory Which Interpolates Between the Broken and the Symmetric Phase, Nucl. Phys. B 330 (1990) 193 [INSPIRE].
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Abe, Y., Hamada, Y. & Yoshioka, K. Electroweak axion string and superconductivity. J. High Energ. Phys. 2021, 172 (2021). https://doi.org/10.1007/JHEP06(2021)172
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DOI: https://doi.org/10.1007/JHEP06(2021)172