Abstract
We study the crossover phase transition of the SU(2) Georgi-Glashow model in three dimensions. In this model, a confining condensate of topological ’t Hooft-Polyakov monopoles exists in the Higgs regime. We use lattice Monte Carlo simulations to study the monopole gas across a crossover transition, and demonstrate that gradient flow can be used to renormalize the otherwise divergent monopole number density. The condensation of the monopoles means that the theory admits also a massive photon-like excitation. We show that the renormalized monopole number density is approximately proportional to the square of the photon mass, in agreement with semiclassical results. Our results give insight into behaviour of the Higgs regime near crossover, which has boarder implications for beyond the Standard Model theories containing adjoint scalar fields.
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References
H. Georgi and S.L. Glashow, Unity of all elementary particle forces, Phys. Rev. Lett. 32 (1974) 438 [INSPIRE].
T. Appelquist and R.D. Pisarski, High-temperature Yang-Mills theories and three-dimensional quantum chromodynamics, Phys. Rev. D 23 (1981) 2305 [INSPIRE].
K. Kajantie, M. Laine, K. Rummukainen and M.E. Shaposhnikov, 3D SU(N) + adjoint Higgs theory and finite temperature QCD, Nucl. Phys. B 503 (1997) 357 [hep-ph/9704416] [INSPIRE].
G. ’t Hooft, Magnetic monopoles in unified gauge theories, Nucl. Phys. B 79 (1974) 276 [INSPIRE].
A.M. Polyakov, Particle spectrum in quantum field theory, JETP Lett. 20 (1974) 194 [INSPIRE].
A.M. Polyakov, Quark confinement and topology of gauge groups, Nucl. Phys. B 120 (1977) 429 [INSPIRE].
S. Nadkarni, The SU(2) adjoint Higgs model in three-dimensions, Nucl. Phys. B 334 (1990) 559 [INSPIRE].
A. Hart, O. Philipsen, J.D. Stack and M. Teper, On the phase diagram of the SU(2) adjoint Higgs model in (2 + 1)-dimensions, Phys. Lett. B 396 (1997) 217 [hep-lat/9612021] [INSPIRE].
A.C. Davis, A. Hart, T.W.B. Kibble and A. Rajantie, The monopole mass in the three-dimensional Georgi-Glashow model, Phys. Rev. D 65 (2002) 125008 [hep-lat/0110154] [INSPIRE].
I.-H. Lee and J. Shigemitsu, Spectrum calculations in the lattice Georgi-Glashow model, Nucl. Phys. B 263 (1986) 280 [INSPIRE].
V. Afferrante, A. Maas and P. Törek, Composite massless vector boson, Phys. Rev. D 101 (2020) 114506 [arXiv:2002.08221] [INSPIRE].
M. Lüscher, Properties and uses of the Wilson flow in lattice QCD, JHEP 08 (2010) 071 [Erratum ibid. 03 (2014) 092] [arXiv:1006.4518] [INSPIRE].
L. Niemi, K. Rummukainen, R. Seppä and D. Weir, Infrared physics of the SU(2) Georgi-Glashow crossover transition, PoS LATTICE2021 (2022) 041 [arXiv:2111.09097] [INSPIRE].
H.H. Patel and M.J. Ramsey-Musolf, Stepping into electroweak symmetry breaking: phase transitions and Higgs phenomenology, Phys. Rev. D 88 (2013) 035013 [arXiv:1212.5652] [INSPIRE].
L. Niemi, M.J. Ramsey-Musolf, T.V.I. Tenkanen and D.J. Weir, Thermodynamics of a two-step electroweak phase transition, Phys. Rev. Lett. 126 (2021) 171802 [arXiv:2005.11332] [INSPIRE].
P. McFadden and K. Skenderis, Holography for cosmology, Phys. Rev. D 81 (2010) 021301 [arXiv:0907.5542] [INSPIRE].
K. Kajantie, M. Laine, T. Neuhaus, J. Peisa, A. Rajantie and K. Rummukainen, Vortex tension as an order parameter in three-dimensional U(1) + Higgs theory, Nucl. Phys. B 546 (1999) 351 [hep-ph/9809334] [INSPIRE].
P. Forgacs, N. Obadia and S. Reuillon, Numerical and asymptotic analysis of the ’t Hooft-Polyakov magnetic monopole, Phys. Rev. D 71 (2005) 035002 [Erratum ibid. 71 (2005) 119902] [hep-th/0412057] [INSPIRE].
K. Dietz and T. Filk, Critical Higgs mass for the (2 + 1)-dimensional Georgi-Glashow model, Nucl. Phys. B 164 (1980) 536 [INSPIRE].
M. Laine, Exact relation of lattice and continuum parameters in three-dimensional SU(2) + Higgs theories, Nucl. Phys. B 451 (1995) 484 [hep-lat/9504001] [INSPIRE].
M. Laine and A. Rajantie, Lattice continuum relations for 3D SU(N) + Higgs theories, Nucl. Phys. B 513 (1998) 471 [hep-lat/9705003] [INSPIRE].
G.D. Moore, O(a) errors in 3D SU(N) Higgs theories, Nucl. Phys. B 523 (1998) 569 [hep-lat/9709053] [INSPIRE].
G.D. Moore and N. Schlusser, Full O(a) improvement in electrostatic QCD, Phys. Rev. D 100 (2019) 034510 [arXiv:1905.09708] [INSPIRE].
A.C. Davis, T.W.B. Kibble, A. Rajantie and H. Shanahan, Topological defects in lattice gauge theories, JHEP 11 (2000) 010 [hep-lat/0009037] [INSPIRE].
A.S. Kronfeld and U.J. Wiese, SU(N) gauge theories with C periodic boundary conditions. 1. Topological structure, Nucl. Phys. B 357 (1991) 521 [INSPIRE].
S. Edwards, D.B. Mehta, A. Rajantie and L. von Smekal, ’t Hooft-Polyakov monopoles in lattice SU(N) + adjoint Higgs theory, Phys. Rev. D 80 (2009) 065030 [arXiv:0906.5531] [INSPIRE].
A. Rajantie, Mass of a quantum ’t Hooft-Polyakov monopole, JHEP 01 (2006) 088 [hep-lat/0512006] [INSPIRE].
G.D. Moore, Measuring the broken phase sphaleron rate nonperturbatively, Phys. Rev. D 59 (1999) 014503 [hep-ph/9805264] [INSPIRE].
A.D. Kennedy and B.J. Pendleton, Improved heat bath method for Monte Carlo calculations in lattice gauge theories, Phys. Lett. B 156 (1985) 393 [INSPIRE].
K. Kajantie, M. Laine, K. Rummukainen and M.E. Shaposhnikov, The electroweak phase transition: a nonperturbative analysis, Nucl. Phys. B 466 (1996) 189 [hep-lat/9510020] [INSPIRE].
F.D.R. Bonnet, D.B. Leinweber, A.G. Williams and J.M. Zanotti, Improved smoothing algorithms for lattice gauge theory, Phys. Rev. D 65 (2002) 114510 [hep-lat/0106023] [INSPIRE].
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Niemi, L., Rummukainen, K., Seppä, R. et al. Infrared physics of the 3D SU(2) adjoint Higgs model at the crossover transition. J. High Energ. Phys. 2023, 212 (2023). https://doi.org/10.1007/JHEP02(2023)212
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DOI: https://doi.org/10.1007/JHEP02(2023)212