Slavnov--Taylor Identities in Spontaneously Broken Non-Abelian Effective Gauge Theories

A. Quadri

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematical and theoretical physics, Tome 309 (2020), pp. 257-268.

Résumé

We study the solution to the Slavnov–Taylor identities in spontaneously broken effective gauge theories for a non-Abelian gauge group. The procedure to extract the $\beta $-functions of the theory in the presence of (generalized) non-polynomial field redefinitions is elucidated.

Bibliographie

[1] Aad G. et al. (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, 716:1 (2012), 1–29

[2] Alonso R., Jenkins E.E., Manohar A.V., “Holomorphy without supersymmetry in the Standard Model Effective Field Theory”, Phys. Lett. B, 739 (2014), 95–98 | MR | Zbl

[3] Alonso R., Jenkins E.E., Manohar A.V., Trott M., “Renormalization group evolution of the Standard Model dimension six operators. III: Gauge coupling dependence and phenomenology”, J. High Energy Phys., 2014:04 (2014), 159 | MR

[4] Anselmi D., “A general field-covariant formulation of quantum field theory”, Eur. Phys. J. C, 73:3 (2013), 2338

[5] Anselmi D., “Master functional and proper formalism for quantum gauge field theory”, Eur. Phys. J. C, 73:3 (2013), 2363

[6] Anselmi D., “A master functional for quantum field theory”, Eur. Phys. J. C, 73:4 (2013), 2385

[7] Barnich G., Brandt F., Henneaux M., “Local BRST cohomology in gauge theories”, Phys. Rep., 338:5 (2000), 439–569 | MR | Zbl

[8] Becchi C., “Lectures on the renormalization of gauge theories”, Relativité, groupes et topologie II, Les Houches Éc. d'Été Phys. Théor. Sess. 40, 1983, North-Holland, Amsterdam, 1984, 787–821 | MR

[9] Becchi C., Rouet A., Stora R., “The abelian Higgs Kibble model, unitarity of the $S$-operator”, Phys. Lett. B, 52:3 (1974), 344–346 | MR

[10] Bettinelli D., Ferrari R., Quadri A., “Massive Yang–Mills theory based on the nonlinearly realized gauge group”, Phys. Rev. D, 77:4 (2008), 045021 | MR

[11] Bettinelli D., Ferrari R., Quadri A., “One-loop self-energy and counterterms in a massive Yang–Mills theory based on the nonlinearly realized gauge group”, Phys. Rev. D, 77:10 (2008), 105012 ; “Erratum”, Phys. Rev. D, 85:12 (2012), 129901 | MR

[12] Bettinelli D., Ferrari R., Quadri A., “The $\mathrm {SU}(2)\otimes \mathrm {U}(1)$ electroweak model based on the nonlinearly realized gauge group”, Int. J. Mod. Phys. A, 24:14 (2009), 2639–2654 ; “Erratum”, Int. J. Mod. Phys. A, 27:7 (2012), 1292004 | Zbl

[13] Bettinelli D., Ferrari R., Quadri A., “The $\mathrm {SU}(2)\otimes \mathrm {U}(1)$ electroweak model based on the nonlinearly realized gauge group. II: Functional equations and the weak power-counting”, Acta phys. Polon. B, 41:3 (2010), 597–628 ; “Erratum”, Acta phys. Polon. B, 43:3 (2012), 483 | MR

[14] Binosi D., Quadri A., “Off-shell renormalization in Higgs effective field theories”, J. High Energy Phys., 2018:04 (2018), 050 | MR

[15] Binosi D., Quadri A., “Off-shell renormalization in the presence of dimension 6 derivative operators. I: General theory”, J. High Energy Phys., 2019:09 (2019), 032 | MR

[16] Binosi D., Quadri A., Off-shell renormalization in the presence of dimension 6 derivative operators. II: UV coefficients, E-print, 2019, arXiv: 1904.06693 | MR | Zbl

[17] Buchmüller W., Wyler D., “Effective lagrangian analysis of new interactions and flavour conservation”, Nucl. Phys. B, 268:3–4 (1986), 621–653

[18] Chatrchyan S. et al. (CMS Collaboration)., “Observation of a new boson at a mass of 125\;GeV with the CMS experiment at the LHC”, Phys. Lett. B, 716:1 (2012), 30–61

[19] Cheung C., Shen C.-H., “Nonrenormalization theorems without supersymmetry”, Phys. Rev. Lett., 115:7 (2015), 071601

[20] Curci G., Ferrari R., “An alternative approach to the proof of unitarity for gauge theories”, Nuovo Cimento A, 35 (1976), 273–279

[21] Elias-Miró J., Espinosa J.R., Pomarol A., “One-loop non-renormalization results in EFTs”, Phys. Lett. B, 747 (2015), 272–280 | Zbl

[22] Ferrari R., Grassi P.A., Quadri A., “Direct algebraic restoration of Slavnov–Taylor identities in the Abelian Higgs–Kibble model”, Phys. Lett. B, 472:3–4 (2000), 346–356 | MR | Zbl

[23] Ferrari R., Quadri A., “Physical unitarity for massive non-abelian gauge theories in the Landau gauge: Stückelberg Higgs”, J. High Energy Phys., 2004:11 (2004), 019

[24] Ferrari R., Quadri A., “Weak power-counting theorem for the renormalization of the nonlinear sigma model in four dimensions”, Int. J. Theor. Phys., 45:12 (2006), 2497–2515 | Zbl

[25] Glashow S.L., “Partial-symmetries of weak interactions”, Nucl. Phys., 22:4 (1961), 579–588

[26] Gomis J., París J., Samuel S., “Antibracket, antifields and gauge-theory quantization”, Phys. Rep., 259:1–2 (1995), 1–145 | MR

[27] Gomis J., Weinberg S., “Are nonrenormalizable gauge theories renormalizable?”, Nucl. Phys. B, 469:3 (1996), 473–487 | MR | Zbl

[28] Grassi P.A., “Algebraic renormalization of Yang–Mills theory with background field method”, Nucl. Phys. B, 462:2–3 (1996), 524–550 | MR

[29] Grassi P.A., Hurth T., Steinhauser M., “Practical algebraic renormalization”, Ann. Phys., 288:1 (2001), 197–248 | MR | Zbl

[30] Grassi P.A., Hurth T., Steinhauser M., “The algebraic method”, Nucl. Phys. B, 610:1–2 (2001), 215–250 | MR | Zbl

[31] Grzadkowski B., Iskrzyński M., Misiak M., Rosiek J., “Dimension-six terms in the Standard Model Lagrangian”, J. High Energy Phys., 2010:10 (2010), 085 | Zbl

[32] Handbook of LHC Higgs cross sections. 4: Deciphering the nature of the Higgs sector, CERN Yellow Rep.: Monogr., 2/2017, ed. by D. de Florian et al., CERN, Geneva, 2017

[33] Hollik W., Kraus E., Roth M., Rupp C., Sibold K., Stöckinger D., “Renormalization of the minimal supersymmetric standard model”, Nucl. Phys. B, 639:1–2 (2002), 3–65 | MR

[34] Jenkins E.E., Manohar A.V., Trott M., “Renormalization group evolution of the standard model dimension six operators. I: Formalism and $\lambda $ dependence”, J. High Energy Phys., 2013:10 (2013), 087 | MR | Zbl

[35] Jenkins E.E., Manohar A.V., Trott M., “Renormalization group evolution of the standard model dimension six operators. II: Yukawa dependence”, J. High Energy Phys., 2014:01 (2014), 035 | MR

[36] Kraus E., “Renormalization of the electroweak standard model to all orders”, Ann. Phys., 262:2 (1998), 155–259 | MR | Zbl

[37] Kugo T., Ojima I., “Manifestly covariant canonical formulation of Yang–Mills theories: Physical state subsidiary conditions and physical $S$-matrix unitarity”, Phys. Lett. B, 73:4–5 (1978), 459–462

[38] Kugo T., Ojima I., “Manifestly covariant canonical formulation of the Yang–Mills field theories. I: General formalism”, Prog. Theor. Phys., 60:6 (1978), 1869–1889 | MR

[39] Lee B.W., Zinn-Justin J., “Spontaneously broken gauge symmetries. IV: General gauge formulation”, Phys. Rev. D, 7:4 (1973), 1049–1056

[40] Picariello M., Quadri A., “Refined chiral Slavnov–Taylor identities: Renormalization and local physics”, Int. J. Theor. Phys., 41:3 (2002), 393–408 | MR | Zbl

[41] Piguet O., Sorella S.P., Algebraic renormalization: Perturbative renormalization, symmetries and anomalies, Lect. Notes Phys. Monogr., 28, Springer, Berlin, 1995 | MR

[42] Quadri A., “Algebraic properties of BRST coupled doublets”, J. High Energy Phys., 2002:05 (2002), 051 | MR

[43] Quadri A., “Slavnov–Taylor parameterization for the quantum restoration of BRST symmetries in anomaly-free gauge theories”, J. High Energy Phys., 2003:04 (2003), 017 | MR

[44] Quadri A., “Higher order non-symmetric counterterms in pure Yang–Mills theory”, J. Phys. G, 30:5 (2004), 677–689

[45] Quadri A., “Slavnov–Taylor parameterization of Yang–Mills theory with massive fermions in the presence of singlet axial-vector currents”, J. High Energy Phys., 2005:06 (2005), 068

[46] Quadri A., “Abelian embedding formulation of the Stueckelberg model and its power-counting renormalizable extension”, Phys. Rev. D, 73:6 (2006), 065024

[47] Quadri A., “Higgs potential from derivative interactions”, Int. J. Mod. Phys. A, 32:16 (2017), 1750089 | MR | Zbl

[48] Salam A., Ward J.C., “Electromagnetic and weak interactions”, Phys. Lett., 13:2 (1964), 168–171 | MR | Zbl

[49] A. A. Slavnov, “Ward identities in gauge theories”, Theor. Math. Phys., 10:2 (1972), 99–104

[50] 'T Hooft G., Veltman M., “Regularization and renormalization of gauge fields”, Nucl. Phys. B, 44:1 (1972), 189–213 | MR

[51] Vagnoni V.M., “QCD and high energy interactions: Experimental summary”, 2019 QCD and high energy interactions, Proc. 54th Rencontres de Moriond (La Thuile, Italy, 2019), ARISF, Paris, 2019, 261–274

[52] Weinberg S., “A model of leptons”, Phys. Rev. Lett., 19:21 (1967), 1264–1266

[53] Wess J., Zumino B., “Consequences of anomalous Ward identities”, Phys. Lett. B, 37:1 (1971), 95–97 | MR