Multiple breaking patterns in the Brout-Englert-Higgs effect beyond perturbation theory. (English) Zbl 1533.81051
Summary: In many BSM theories, especially GUTs, introducing a Brout-Englert-Higgs effect allows for multiple breaking patterns of the gauge symmetry. The possibility to select a particular pattern is usually decisive for the phenomenological viability of a theory. Beyond perturbation theory it is necessary to replace the Brout-Englert-Higgs effect by a manifestly gauge-invariant description. We study the simplest case with multiple breaking patterns, an \(\mathrm{SU}(3)\) Yang-Mills theory coupled to a single scalar ‘Higgs’ field in the adjoint representation, on the lattice. We find that only one pattern remains at fixed parameters and gauge-fixing strategy, and that the associated quantum effective potential emerges from a non-trivial interplay of many aspects.
MSC:
| 81Q35 | Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices |
| 81V22 | Unified quantum theories |
| 81R40 | Symmetry breaking in quantum theory |
| 35B36 | Pattern formations in context of PDEs |
| 70S15 | Yang-Mills and other gauge theories in mechanics of particles and systems |
| 18A40 | Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) |
| 03D45 | Theory of numerations, effectively presented structures |
References:
| [1] | Langacker, P., Phys. Rep., 72, 185 (1981) |
| [2] | O’Raifeartaigh, L., Group Structure of Gauge Theories, 172 (1986), Cambridge University Press: Cambridge University Press Cambridge, Uk · Zbl 0606.22013 |
| [3] | Raby, S.; Dimopoulos, S.; Susskind, L., Nuclear Phys. B, 169, 373-383 (1980) |
| [4] | Böhm, M.; Denner, A.; Joos, H., Gauge Theories of the Strong and Electroweak Interaction, 784 (2001), Stuttgart: Stuttgart Teubner · Zbl 0991.81001 |
| [5] | Fujikawa, K., Nuclear Phys., B223, 218-234 (1983) |
| [6] | Gribov, V. N., Nuclear Phys., B139, 1 (1978) |
| [7] | Singer, I. M., Comm. Math. Phys., 60, 7-12 (1978) · Zbl 0379.53009 |
| [8] | Fröhlich, J.; Morchio, G.; Strocchi, F., Phys. Lett., B97, 249 (1980) |
| [9] | Fröhlich, J.; Morchio, G.; Strocchi, F., Nuclear Phys., B190, 553-582 (1981) |
| [10] | Banks, T.; Rabinovici, E., Nuclear Phys., B160, 349 (1979) |
| [11] | Maas, A., Modern Phys. Lett., A30, 29, Article 1550135 pp. (2015), arXiv:1502.02421 |
| [12] | Maas, A.; Sondenheimer, R.; Törek, P., Ann. Phys., 402, 18-44 (2019), arXiv:1709.07477 · Zbl 1409.81078 |
| [13] | Sondenheimer, R., Phys. Rev. D, 101, 5, Article 056006 pp. (2020), arXiv:1912.08680 |
| [14] | Maas, A.; Sondenheimer, R., Phys. Rev. D, 102, Article 113001 pp. (2020), arXiv:2009.06671 |
| [15] | Dudal, D.; van Egmond, D. M.; Guimaraes, M. S.; Palhares, L. F.; Peruzzo, G.; Sorella, S. P., Eur. Phys. J. C, 81, 3, 222 (2021), arXiv:2008.07813 |
| [16] | Maas, A.; Törek, P., Phys. Rev., D95, 1, Article 014501 pp. (2017), arXiv:1607.05860 |
| [17] | Maas, A.; Törek, P., Ann. Physics, 397, 303-335 (2018), arXiv:1804.04453 · Zbl 1397.81200 |
| [18] | Afferrante, V.; Maas, A.; Törek, P., Phys. Rev. D, 101, 11, Article 114506 pp. (2020), arXiv:2002.08221 |
| [19] | Greensite, J., Phys. Rev. D, 102, 5, Article 054504 pp. (2020), arXiv:2007.11616 |
| [20] | Dobson, E.; Maas, A.; Riederer, B., PoS, LATTICE2021, 207 (2022), arXiv:2110.15670 |
| [21] | Maas, A., Prog. Part. Nucl. Phys., 106, 132-209 (2019), arXiv:1712.04721 |
| [22] | Olynyk, K.; Shigemitsu, J., Nuclear Phys. B, 251, 472-486 (1985) |
| [23] | Lee, I.-H.; Shigemitsu, J., Nuclear Phys., B263, 280-294 (1986) |
| [24] | Olynyk, K.; Shigemitsu, J., Phys. Rev. Lett., 54, 2403 (1985) |
| [25] | Olynyk, K.; Shigemitsu, J., Phys. Lett. B, 154, 278-282 (1985) |
| [26] | Kajantie, K.; Laine, M.; Rajantie, A.; Rummukainen, K.; Tsypin, M., J. High Energy Phys., 11, 011 (1998), Adjoint. arXiv:hep-lat/9811004 |
| [27] | Gies, H.; Sondenheimer, R., Eur. Phys. J., C75, 2, 68 (2015), arXiv:1407.8124. Higgs FRG |
| [28] | Eichhorn, A.; Gies, H.; Jaeckel, J.; Plehn, T.; Scherer, M. M.; Sondenheimer, R., J. High Energy Phys., 04, 022 (2015), arXiv:1501.02812 |
| [29] | A. Rajaraman, 2022. [hep-th] https://arxiv.org/abs/2211.11851. arXiv:2211.11851. |
| [30] | Lee, B.; Zinn-Justin, J., Phys. Rev., D5, 3137-3155 (1972) |
| [31] | Maas, A., Modern Phys. Lett., A27, 38, Article 1250222 pp. (2012), arXiv:1205.0890 · Zbl 1260.81132 |
| [32] | Caudy, W.; Greensite, J., Phys. Rev., D78, Article 025018 pp. (2008), arXiv:0712.0999 |
| [33] | Maas, A., Eur. Phys. J., C71, 1548 (2011), arXiv:1007.0729 |
| [34] | Lenz, F.; Negele, J. W.; O’Raifeartaigh, L.; Thies, M., Ann. Physics, 285, 25-60 (2000), arXiv:hep-th/0004200 · Zbl 1058.81592 |
| [35] | Maas, A., Phys. Rep., 524, 203 (2013), arXiv:1106.3942 |
| [36] | Maas, A.; Mufti, T., J. High Energy Phys., 1404, 006 (2014), arXiv:1312.4873 |
| [37] | Rivers, R. J., Path Integral Methods in Quantum Field Theory, 339 (1987), Cambridge University Press: Cambridge University Press Cambridge, UK · Zbl 0648.46064 |
| [38] | Maas, A.; Zwanziger, D., Phys. Rev., D89, Article 034011 pp. (2014), arXiv:1309.1957 |
| [39] | Cucchieri, A.; Mendes, T., Nuclear Phys., B471, 263-292 (1996), arXiv:hep-lat/9511020 |
| [40] | Montvay, I.; Münster, G., Quantum Fields on a Lattice, 491 (1994), Cambridge University Press: Cambridge University Press Cambridge, UK |
| [41] | Hasenfratz, A.; Hasenfratz, P., Phys. Rev., D34, 3160 (1986) |
| [42] | Cabibbo, N.; Marinari, E., Phys. Lett., B119, 387-390 (1982) |
| [43] | Knechtli, F., The Static potential in the SU(2) Higgs model (1999), arXiv:hep-lat/9910044 · Zbl 1051.81564 |
| [44] | Bonati, C.; Cossu, G.; D’Elia, M.; Di Giacomo, A., Nuclear Phys., B828, 390-403 (2010), arXiv:0911.1721 · Zbl 1203.81189 |
| [45] | Bezanson, J.; Edelman, A.; Karpinski, S.; Shah, V. B., SIAM Rev., 59, 1, 65-98 (2017) · Zbl 1356.68030 |
| [46] | Breloff, T., Plots.jl (2022), Zenodo |
| [47] | Gál, T.; Ling, J. J.; Amin, N., J. Open Source Softw., 7, 76, 4452 (2022) |
| [48] | Inc., W. R., Mathematica (v 12.3.0) (2021), URL https://www.wolfram.com/mathematica. Champaign, IL |
| [49] | Brun, R.; Rademakers, F., Nucl. Instrum. Meth., A389, 81-86 (1997) |
| [50] | Langfeld, K., Quark Confinement and the Hadron Spectrum. Proceedings, 6th Conference, QCHS 2004, Villasimius, Italy, September 21-25, 2004. Quark Confinement and the Hadron Spectrum. Proceedings, 6th Conference, QCHS 2004, Villasimius, Italy, September 21-25, 2004, AIP Conf. Proc., 756, 133-142 (2005), arXiv:hep-th/0412020. Minimal Landau gauge |
| [51] | Kopp, J., Internat. J. Modern Phys. C, 19, 523-548 (2008), arXiv:physics/0610206 · Zbl 1151.65031 |
| [52] | Greensite, J.; Kovalenko, A. V.; Olejnik, S.; Polikarpov, M. I.; Syritsyn, S. N.; Zakharov, V. I., Phys. Rev., D74, Article 094507 pp. (2006), arXiv:hep-lat/0606008 |
| [53] | Ripka, G., (Lect. Notes. Phys., vol. 639 (2003)), arXiv:hep-ph/0310102 |
| [54] | Suman, H.; Schilling, K., A Comparative study of gauge fixing procedures on the connection machines CM2 and CM5 (1993), arXiv:hep-lat/9306018 · Zbl 0809.65051 |
| [55] | Mehta, D.; Sternbeck, A.; von Smekal, L.; Williams, A. G., PoS, QCD-TNT09, 025 (2009), arXiv:0912.0450 |
| [56] | von Smekal, L.; Jorkowski, A.; Mehta, D.; Sternbeck, A., PoS, CONFINEMENT8, 048 (2008), arXiv:0812.2992 |
| [57] | von Smekal, L.; Mehta, D.; Sternbeck, A.; Williams, A. G., PoS, LAT2007, 382 (2007), arXiv:0710.2410 |
| [58] | von Smekal, L.; Maltman, K.; Sternbeck, A., Phys. Lett., B681, 336-342 (2009), arXiv:0903.1696 |
| [59] | Maas, A., J. High Energy Phys., 02, 076 (2011), arXiv:1012.4284 |
| [60] | Osterwalder, K.; Seiler, E., Ann. Physics, 110, 440 (1978) |
| [61] | Fradkin, E. H.; Shenker, S. H., Phys. Rev., D19, 3682-3697 (1979) |
| [62] | Wellegehausen, B. H.; Wipf, A.; Wozar, C., Phys. Rev. D, 83, Article 114502 pp. (2011), arXiv:1102.1900 |
| [63] | Baier, R.; Gavai, R. V.; Lang, C. B., Phys. Lett., B172, 387 (1986) |
| [64] | Greensite, J.; Olejník, Š.; Zwanziger, D., Phys. Rev., D69, Article 074506 pp. (2004), arXiv:hep-lat/0401003 |
| [65] | Endrődi, G.; Kovács, T. G.; Markó, G., Phys. Rev. Lett., 127, 23, Article 232002 pp. (2021), arXiv:2109.03668 |
| [66] | Maas, A.; Mufti, T., Phys. Rev., D91, 11, Article 113011 pp. (2015), arXiv:1412.6440 |
| [67] | Callaway, D. J.E., Phys. Rep., 167, 241 (1988) |
| [68] | Ruegg, H., Phys. Rev., D22, 2040 (1980) |
| [69] | Murphy, T.; O’Raifeartaigh, L., Nuclear Phys., B229, 509-527 (1983) |
| [70] | Dolan, L.; Jackiw, R., Phys. Rev., D9, 2904 (1974) |
| [71] | P.J. Houston, S. Sen, J. Phys. A: Math. Gen. 17 (6) 1163-1171. · Zbl 0547.58018 |
| [72] | Creutz, M., Phys. Rev. D, 21, 2308-2315 (1980) |
| [73] | Bunk, B., Nucl. Phys. B Proc. Suppl., 42, 566-568 (1995) |
| [74] | Gattringer, C.; Lang, C. B., Quantum Chromodynamics on the Lattice, 211 (2010), Lect. notes Phys. |
| [75] | DeGrand, T.; Detar, C. E., Lattice Methods for Quantum Chromodynamics (2006), World Scientific: World Scientific New Jersey, USA · Zbl 1110.81001 |
| [76] | Vairinhos, H., Monte Carlo algorithms for reduced lattices, mixed actions, and double-trace deformations (2010), arXiv:1010.1253 |
| [77] | A. Portelli, R. Bernd, H.B. Rocha, |
| [78] | Ilgenfritz, E.-M.; Menz, C.; Müller-Preussker, M.; Schiller, A.; Sternbeck, A., Phys. Rev., D83, Article 054506 pp. (2011), arXiv:1010.5120. Logarithmic field definition gluon propagator |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
