Abstract
Contrary to the standard model that does not admit topologically nontrivial solitons, two Higgs doublet models admit topologically stable vortex strings and domain walls. We numerically confirm the existence of a topological Z-string confining fractional Z-flux inside. We show that topological strings at sin θW = 0 limit reduce to non-Abelian strings which possess non-Abelian moduli S2 associated with spontaneous breakdown of the SU(2) custodial symmetry. We numerically solve the equations of motion for various parameter choices. It is found that a gauging U(1)Y always lowers the tension of the Z-string while it keeps that of the W-string. On the other hand, a deformation of the Higgs potential is either raising or lowering the tensions of the Z-string and W-string. We numerically obtain an effective potential for the non-Abelian moduli S2 for various parameter deformations under the restriction tan β = 1. It is the first time to show that there exists a certain parameter region where the topological W-string can be the most stable topological excitation, contrary to conventional wisdom of electroweak theories. We also obtain numerical solutions of composites of the string and domain walls in a certain condition.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher and J.P. Silva, Theory and phenomenology of two-Higgs-doublet models, Phys. Rept. 516 (2012) 1 [arXiv:1106.0034] [INSPIRE].
S. Kanemura, K. Tsumura, K. Yagyu and H. Yokoya, Fingerprinting nonminimal Higgs sectors, Phys. Rev. D 90 (2014) 075001 [arXiv:1406.3294] [INSPIRE].
S. Kanemura, M. Kikuchi and K. Yagyu, Fingerprinting the extended Higgs sector using one-loop corrected Higgs boson couplings and future precision measurements, Nucl. Phys. B 896 (2015) 80 [arXiv:1502.07716] [INSPIRE].
J. Bernon, J.F. Gunion, H.E. Haber, Y. Jiang and S. Kraml, Scrutinizing the alignment limit in two-Higgs-doublet models: m h = 125 GeV, Phys. Rev. D 92 (2015) 075004 [arXiv:1507.00933] [INSPIRE].
F. Kling, J.M. No and S. Su, Anatomy of exotic Higgs decays in 2HDM, JHEP 09 (2016) 093 [arXiv:1604.01406] [INSPIRE].
J. Haller, A. Hoecker, R. Kogler, K. Mönig, T. Peiffer and J. Stelzer, Update of the global electroweak fit and constraints on two-Higgs-doublet models, arXiv:1803.01853 [INSPIRE].
H.P. Nilles, Supersymmetry, supergravity and particle physics, Phys. Rept. 110 (1984) 1 [INSPIRE].
H.E. Haber and G.L. Kane, The search for supersymmetry: probing physics beyond the Standard Model, Phys. Rept. 117 (1985) 75 [INSPIRE].
Y. Nambu, String-like configurations in the Weinberg-Salam theory, Nucl. Phys. B 130 (1977) 505 [INSPIRE].
T. Vachaspati and A. Achucarro, Semilocal cosmic strings, Phys. Rev. D 44 (1991) 3067 [INSPIRE].
M. Hindmarsh, Existence and stability of semilocal strings, Phys. Rev. Lett. 68 (1992) 1263 [INSPIRE].
A. Achucarro, K. Kuijken, L. Perivolaropoulos and T. Vachaspati, Dynamical simulations of semilocal strings, Nucl. Phys. B 388 (1992) 435 [INSPIRE].
T. Vachaspati, Vortex solutions in the Weinberg-Salam model, Phys. Rev. Lett. 68 (1992) 1977 [Erratum ibid. 69 (1992) 216] [INSPIRE].
T. Vachaspati, Electroweak strings, Nucl. Phys. B 397 (1993) 648 [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].
A. Achucarro and T. Vachaspati, Semilocal and electroweak strings, Phys. Rept. 327 (2000) 347 [hep-ph/9904229] [INSPIRE].
R.H. Brandenberger and A.-C. Davis, Electroweak baryogenesis with electroweak strings, Phys. Lett. B 308 (1993) 79 [astro-ph/9206001] [INSPIRE].
M. Barriola, Electroweak strings that produce baryons, Phys. Rev. D 51 (1995) 300 [hep-ph/9403323] [INSPIRE].
M. Nagasawa and J. Yokoyama, Are nontopological strings produced at the electroweak phase transition?, Phys. Rev. Lett. 77 (1996) 2166 [hep-ph/9608263] [INSPIRE].
T. Vachaspati, Estimate of the primordial magnetic field helicity, Phys. Rev. Lett. 87 (2001) 251302 [astro-ph/0101261] [INSPIRE].
R. Poltis and D. Stojkovic, Can primordial magnetic fields seeded by electroweak strings cause an alignment of quasar axes on cosmological scales?, Phys. Rev. Lett. 105 (2010) 161301 [arXiv:1004.2704] [INSPIRE].
F.R. Klinkhamer and N.S. Manton, A saddle point solution in the Weinberg-Salam theory, Phys. Rev. D 30 (1984) 2212 [INSPIRE].
H. La, Vortex solutions in two Higgs systems and tan β, hep-ph/9302220 [INSPIRE].
M.A. Earnshaw and M. James, Stability of two doublet electroweak strings, Phys. Rev. D 48 (1993) 5818 [hep-ph/9308223] [INSPIRE].
L. Perivolaropoulos, Existence of double vortex solutions, Phys. Lett. B 316 (1993) 528 [hep-ph/9309261] [INSPIRE].
G. Bimonte and G. Lozano, Vortex solutions in two Higgs doublet systems, Phys. Lett. B 326 (1994) 270 [hep-ph/9401313] [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].
C. Bachas and T.N. Tomaras, Membranes in the two Higgs standard model, Phys. Rev. Lett. 76 (1996) 356 [hep-ph/9508395] [INSPIRE].
A. Riotto and O. Tornkvist, CP violating solitons in the minimal supersymmetric standard model, Phys. Rev. D 56 (1997) 3917 [hep-ph/9704371] [INSPIRE].
C. Bachas, P. Tinyakov and T.N. Tomaras, On spherically symmetric solutions in the two Higgs standard model, Phys. Lett. B 385 (1996) 237 [hep-ph/9606348] [INSPIRE].
J. Grant and M. Hindmarsh, Sphalerons with CP-violating Higgs potentials, Phys. Rev. D 59 (1999) 116014 [hep-ph/9811289] [INSPIRE].
J. Grant and M. Hindmarsh, Sphalerons in two Higgs doublet theories, Phys. Rev. D 64 (2001) 016002 [hep-ph/0101120] [INSPIRE].
Y. Brihaye, Sphaleron-bisphaleron bifurcations in a custodial-symmetric two-doublets model, J. Phys. A 41 (2008) 405401 [hep-th/0412276] [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].
G.D. Brawn, Symmetries and topological defects of the two Higgs doublet model, Ph.D. thesis, The University of Manchester, Manchester, U.K., (2011).
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].
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].
M. Eto, M. Kurachi and M. Nitta, Constraints on two Higgs doublet models from domain walls, arXiv:1803.04662 [INSPIRE].
A. Hanany and D. Tong, Vortices, instantons and branes, JHEP 07 (2003) 037 [hep-th/0306150] [INSPIRE].
R. Auzzi, S. Bolognesi, J. Evslin, K. Konishi and A. Yung, Non-Abelian superconductors: vortices and confinement in N = 2 SQCD, Nucl. Phys. B 673 (2003) 187 [hep-th/0307287] [INSPIRE].
R. Auzzi, S. Bolognesi, J. Evslin and K. Konishi, Non-Abelian monopoles and the vortices that confine them, Nucl. Phys. B 686 (2004) 119 [hep-th/0312233] [INSPIRE].
A. Hanany and D. Tong, Vortex strings and four-dimensional gauge dynamics, JHEP 04 (2004) 066 [hep-th/0403158] [INSPIRE].
M. Shifman and A. Yung, Non-Abelian string junctions as confined monopoles, Phys. Rev. D 70 (2004) 045004 [hep-th/0403149] [INSPIRE].
A. Gorsky, M. Shifman and A. Yung, Non-Abelian Meissner effect in Yang-Mills theories at weak coupling, Phys. Rev. D 71 (2005) 045010 [hep-th/0412082] [INSPIRE].
M. Eto, Y. Isozumi, M. Nitta, K. Ohashi and N. Sakai, Moduli space of non-Abelian vortices, Phys. Rev. Lett. 96 (2006) 161601 [hep-th/0511088] [INSPIRE].
M. Eto et al., Non-Abelian vortices of higher winding numbers, Phys. Rev. D 74 (2006) 065021 [hep-th/0607070] [INSPIRE].
M. Eto, K. Hashimoto, G. Marmorini, M. Nitta, K. Ohashi and W. Vinci, Universal reconnection of non-Abelian cosmic strings, Phys. Rev. Lett. 98 (2007) 091602 [hep-th/0609214] [INSPIRE].
D. Tong, TASI lectures on solitons: instantons, monopoles, vortices and kinks, in Theoretical Advanced Study Institute in Elementary Particle Physics: many dimensions of string theory (TASI 2005), Boulder, CO, U.S.A., 5 June–1 July 2005 [hep-th/0509216] [INSPIRE].
M. Eto, Y. Isozumi, M. Nitta, K. Ohashi and N. Sakai, Solitons in the Higgs phase: the moduli matrix approach, J. Phys. A 39 (2006) R315 [hep-th/0602170] [INSPIRE].
M. Shifman and A. Yung, Supersymmetric solitons and how they help us understand non-Abelian gauge theories, Rev. Mod. Phys. 79 (2007) 1139 [hep-th/0703267] [INSPIRE].
A.P. Balachandran, S. Digal and T. Matsuura, Semi-superfluid strings in high density QCD, Phys. Rev. D 73 (2006) 074009 [hep-ph/0509276] [INSPIRE].
E. Nakano, M. Nitta and T. Matsuura, Non-Abelian strings in high density QCD: zero modes and interactions, Phys. Rev. D 78 (2008) 045002 [arXiv:0708.4096] [INSPIRE].
E. Nakano, M. Nitta and T. Matsuura, Non-Abelian strings in hot or dense QCD, Prog. Theor. Phys. Suppl. 174 (2008) 254 [arXiv:0805.4539] [INSPIRE].
M. Eto and M. Nitta, Color magnetic flux tubes in dense QCD, Phys. Rev. D 80 (2009) 125007 [arXiv:0907.1278] [INSPIRE].
M. Eto, E. Nakano and M. Nitta, Effective world-sheet theory of color magnetic flux tubes in dense QCD, Phys. Rev. D 80 (2009) 125011 [arXiv:0908.4470] [INSPIRE].
M. Eto, M. Nitta and N. Yamamoto, Instabilities of non-Abelian vortices in dense QCD, Phys. Rev. Lett. 104 (2010) 161601 [arXiv:0912.1352] [INSPIRE].
Y. Hirono, T. Kanazawa and M. Nitta, Topological interactions of non-Abelian vortices with quasi-particles in high density QCD, Phys. Rev. D 83 (2011) 085018 [arXiv:1012.6042] [INSPIRE].
S. Yasui, K. Itakura and M. Nitta, Fermion structure of non-Abelian vortices in high density QCD, Phys. Rev. D 81 (2010) 105003 [arXiv:1001.3730] [INSPIRE].
T. Fujiwara, T. Fukui, M. Nitta and S. Yasui, Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor, Phys. Rev. D 84 (2011) 076002 [arXiv:1105.2115] [INSPIRE].
M. Eto, M. Nitta and N. Yamamoto, Confined monopoles induced by quantum effects in dense QCD, Phys. Rev. D 83 (2011) 085005 [arXiv:1101.2574] [INSPIRE].
W. Vinci, M. Cipriani and M. Nitta, Spontaneous magnetization through non-Abelian vortex formation in rotating dense quark matter, Phys. Rev. D 86 (2012) 085018 [arXiv:1206.3535] [INSPIRE].
M. Cipriani, W. Vinci and M. Nitta, Colorful boojums at the interface of a color superconductor, Phys. Rev. D 86 (2012) 121704 [arXiv:1208.5704] [INSPIRE].
M. Kobayashi, E. Nakano and M. Nitta, Color magnetism in non-Abelian vortex matter, JHEP 06 (2014) 130 [arXiv:1311.2399] [INSPIRE].
C. Chatterjee and M. Nitta, Aharonov-Bohm phase in high density quark matter, Phys. Rev. D 93 (2016) 065050 [arXiv:1512.06603] [INSPIRE].
M.G. Alford, S.K. Mallavarapu, T. Vachaspati and A. Windisch, Stability of superfluid vortices in dense quark matter, Phys. Rev. C 93 (2016) 045801 [arXiv:1601.04656] [INSPIRE].
C. Chatterjee, M. Cipriani and M. Nitta, Coupling between Majorana fermions and Nambu-Goldstone bosons inside a non-Abelian vortex in dense QCD, Phys. Rev. D 93 (2016) 065046 [arXiv:1602.01677] [INSPIRE].
C. Chatterjee and M. Nitta, Low-energy effective worldsheet theory of a non-Abelian vortex in high-density QCD revisited: a regular gauge construction, Phys. Rev. D 95 (2017) 085013 [arXiv:1612.09419] [INSPIRE].
M.G. Alford, G. Baym, K. Fukushima, T. Hatsuda and M. Tachibana, Continuity of vortices from the hadronic to the color-flavor locked phase in dense matter, arXiv:1803.05115 [INSPIRE].
M. Eto, Y. Hirono, M. Nitta and S. Yasui, Vortices and other topological solitons in dense quark matter, PTEP 2014 (2014) 012D01 [arXiv:1308.1535] [INSPIRE].
C. Chatterjee, M. Kurachi and M. Nitta, Topological defects in the Georgi-Machacek model, Phys. Rev. D 97 (2018) 115010 [arXiv:1801.10469] [INSPIRE].
T.W.B. Kibble, Topology of cosmic domains and strings, J. Phys. A 9 (1976) 1387 [INSPIRE].
T.W.B. Kibble, G. Lazarides and Q. Shafi, Walls bounded by strings, Phys. Rev. D 26 (1982) 435 [INSPIRE].
A. Vilenkin and A.E. Everett, Cosmic strings and domain walls in models with Goldstone and pseudo-Goldstone bosons, Phys. Rev. Lett. 48 (1982) 1867 [INSPIRE].
A.E. Everett and A. Vilenkin, Left-right symmetric theories and vacuum domain walls and strings, Nucl. Phys. B 207 (1982) 43 [INSPIRE].
A. Vilenkin and E.P.S. Shellard, Cosmic strings and other topological defects, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, U.K., (2000) [INSPIRE].
M. Kawasaki and K. Nakayama, Axions: theory and cosmological role, Ann. Rev. Nucl. Part. Sci. 63 (2013) 69 [arXiv:1301.1123] [INSPIRE].
M. Eto, Y. Hirono and M. Nitta, Domain walls and vortices in chiral symmetry breaking, PTEP 2014 (2014) 033B01 [arXiv:1309.4559] [INSPIRE].
J.F. Gunion and H.E. Haber, The CP conserving two Higgs doublet model: the approach to the decoupling limit, Phys. Rev. D 67 (2003) 075019 [hep-ph/0207010] [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].
K. Saikawa, A review of gravitational waves from cosmic domain walls, Universe 3 (2017) 40 [arXiv:1703.02576] [INSPIRE].
R. Jackiw and P. Rossi, Zero modes of the vortex-fermion system, Nucl. Phys. B 190 (1981) 681 [INSPIRE].
R. Jackiw and C. Rebbi, Solitons with fermion number 1/2, Phys. Rev. D 13 (1976) 3398 [INSPIRE].
T. Vachaspati and R. Watkins, Bound states can stabilize electroweak strings, Phys. Lett. B 318 (1993) 163 [hep-ph/9211284] [INSPIRE].
M.A. Earnshaw and W.B. Perkins, Stability of an electroweak string with a fermion condensate, Phys. Lett. B 328 (1994) 337 [hep-ph/9402218] [INSPIRE].
J. Garriga and T. Vachaspati, Zero modes on linked strings, Nucl. Phys. B 438 (1995) 161 [hep-ph/9411375] [INSPIRE].
J.M. Moreno, D.H. Oaknin and M. Quirós, Fermions on the electroweak string, Phys. Lett. B 347 (1995) 332 [hep-ph/9411411] [INSPIRE].
S.G. Naculich, Fermions destabilize electroweak strings, Phys. Rev. Lett. 75 (1995) 998 [hep-ph/9501388] [INSPIRE].
H. Liu and T. Vachaspati, Perturbed electroweak strings and fermion zero modes, Nucl. Phys. B 470 (1996) 176 [hep-ph/9511216] [INSPIRE].
G.D. Starkman, D. Stojkovic and T. Vachaspati, Neutrino zero modes on electroweak strings, Phys. Rev. D 63 (2001) 085011 [hep-ph/0007071] [INSPIRE].
G. Starkman, D. Stojkovic and T. Vachaspati, Zero modes of fermions with a general mass matrix, Phys. Rev. D 65 (2002) 065003 [hep-th/0103039] [INSPIRE].
N. Graham, M. Quandt and H. Weigel, Fermion energies in the background of a cosmic string, Phys. Rev. D 84 (2011) 025017 [arXiv:1105.1112] [INSPIRE].
M.G. Alford, K. Rajagopal and F. Wilczek, Color flavor locking and chiral symmetry breaking in high density QCD, Nucl. Phys. B 537 (1999) 443 [hep-ph/9804403] [INSPIRE].
M.G. Alford, K. Rajagopal and F. Wilczek, QCD at finite baryon density: nucleon droplets and color superconductivity, Phys. Lett. B 422 (1998) 247 [hep-ph/9711395] [INSPIRE].
R. Rapp, T. Schäfer, E.V. Shuryak and M. Velkovsky, Diquark Bose condensates in high density matter and instantons, Phys. Rev. Lett. 81 (1998) 53 [hep-ph/9711396] [INSPIRE].
R. Rapp, T. Schäfer, E.V. Shuryak and M. Velkovsky, High density QCD and instantons, Annals Phys. 280 (2000) 35 [hep-ph/9904353] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1805.07015
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Eto, M., Kurachi, M. & Nitta, M. Non-Abelian strings and domain walls in two Higgs doublet models. J. High Energ. Phys. 2018, 195 (2018). https://doi.org/10.1007/JHEP08(2018)195
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2018)195