The electroweak standard model

Authors

  • Jose Ignacio Illana University of Granada

DOI:

https://doi.org/10.31349/SuplRevMexFis.3.020721

Keywords:

Electroweak standard model

Abstract

After introducing the basic symmetry principles, the full Lagrangian is derived in detail and the most relevant aspects of the electroweak phenomenology are discussed with special emphasis on the determination of the input parameters and the consistency checks of the model.

References

S. Weinberg, The Quantum Theory of Fields. Vol. 1: Foundations, Cambridge University Press, 2005.

M. Schwartz, Quantum Field Theory and the Standard Model, Cambridge University Press, 2014.

M. Maggiore, A Modern Introduction to Quantum Field Theory, Oxford University Press, 2005.

A. Lahiri, P. B. Pal, A first book of Quantum Field Theory, Narosa Publishing House, 2nd edition, 2005.

M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory, Addison-Wesley, 1995.

S. Pokorski, Gauge Field Theories, Cambridge University Press, 2nd edition, 2000.

Y. Nambu, Quasiparticles and Gauge Invariance in the Theory of Superconductivity, Phys. Rev. 117 (1960) 648, https://doi.org/10.1103/PhysRev.117.648.

J. Goldstone, Field Theories with Superconductor Solutions, Nuovo Cim. 19 (1961) 154, https://doi.org/10.1007/BF02812722.

P. W. Anderson, Plasmons, Gauge Invariance, and Mass, Phys. Rev. 130 (1963) 439, https://doi.org/10.1103/PhysRev.130.439.

F. Englert and R. Brout, Broken Symmetry and the Mass of Gauge Vector Mesons, Phys. Rev. Lett. 13 (1964) 321, https://doi.org/10.1103/PhysRevLett.13.321.

P. W. Higgs, Broken symmetries, massless particles and gauge fields, Phys. Lett. 12 (1964) 132, https://doi.org/10.1016/0031-9163(64)91136-9.

P. W. Higgs, Broken Symmetries and the Masses of Gauge Bosons, Phys. Rev. Lett. 13 (1964) 508, https://doi.org/10.1103/PhysRevLett.13.508.

G. S. Guralnik, C. R. Hagen and T. W. B. Kibble, Global Conservation Laws and Massless Particles, Phys. Rev. Lett. 13 (1964) 585, https://doi.org/10.1103/PhysRevLett.13.585.

P. W. Higgs, Spontaneous Symmetry Breakdown without Massless Bosons, Phys. Rev. 145 (1966) 1156, https://doi.org/10.1103/PhysRev.145.1156.

T. W. B. Kibble, Symmetry breaking in nonAbelian gauge theories, Phys. Rev. 155 (1967) 1554, https://doi.org/10.1103/PhysRev.155.1554.

G. ’t Hooft and M. J. G. Veltman, Regularization and Renormalization of Gauge Fields, Nucl. Phys. B 44 (1972) 189, https://doi.org/10.1016/0550-3213(72)90279-9.

S. L. Glashow, Partial Symmetries of Weak Interactions, Nucl. Phys. 22 (1961) 579, https://doi.org/10.1016/0029-5582(61)90469-2.

S. Weinberg, A Model of Leptons, Phys. Rev. Lett. 19 (1967) 1264, https://doi.org/10.1103/PhysRevLett.19.1264.

A. Salam, Weak and Electromagnetic Interactions, Proceedings of the 8th Nobel Symposium, 367-377 (1968). https://doi.org/10.1142/9789812795915.0034.

M. Gell-Mann, A Schematic Model of Baryons and Mesons, Phys. Lett. 8 (1964) 214, https://doi.org/10.1016/S0031-9163(64)92001-3.

G. Zweig, An SU(3) model for strong interaction symmetry and its breaking. Version 2, Preprint CERN-TH-412 (1964).

H. Fritzsch, M. Gell-Mann and H. Leutwyler, Advantages of the Color Octet Gluon Picture, Phys. Lett. B 47 (1973) 365, https://doi.org/10.1016/0370-2693(73)90625-4.

N. Cabibbo, Unitary Symmetry and Leptonic Decays, Phys. Rev. Lett. 10 (1963) 531.

M. Kobayashi and T. Maskawa, CP Violation in the Renormalizable Theory of Weak Interaction, Prog. Theor. Phys. 49 (1973) 652, https://doi.org/10.1143/PTP.49.652

S. L. Glashow, J. Iliopoulos and L. Maiani, Weak Interactions with Lepton-Hadron Symmetry, Phys. Rev. D 2 (1970) 1285, https://doi.org/10.1103/PhysRevD.2.1285.

P. A. Zyla et al. [Particle Data Group], Review of Particle Physics, PTEP 2020 (2020) 083C01, https://doi.org/10.1093/ptep/ptaa104.

C. Jarlskog, Commutator of the Quark Mass Matrices in the Standard Electroweak Model and a Measure of Maximal CP Violation, Phys. Rev. Lett. 55 (1985) 1039. https://doi.org/10.1103/PhysRevLett.55.1039.

R. N. Mohapatra and P. B. Pal, Massive neutrinos in physics and astrophysics. Second edition, World Sci. Lect. Notes Phys. 60 (1998) 1; 72 1 (2004).

M. Gell-Mann, P. Ramond and R. Slansky, Complex Spinors and Unified Theories, Conf. Proc. C 790927 (1979) 315.

T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, Conf. Proc. C 7902131 (1979) 95.

G. Hernandez-Tome, J. I. Illana and M. Masip, The ρ parameter and H 0 → `i`j in models with TeV sterile neutrinos, Phys. Rev. D 102 (2020) 113006 https://doi.org/10.1103/PhysRevD.102.113006.

B. Pontecorvo, Mesonium and anti-mesonium, Sov. Phys. JETP 6 (1957), 429.

Z. Maki, M. Nakagawa and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28 (1962), 870-880. https://doi.org/10.1143/PTP.28.870.

B. Pontecorvo, Neutrino Experiments and the Problem of Conservation of Leptonic Charge, Zh. Eksp. Teor. Fiz. 53 (1967) 1717.

E. K. Akhmedov, Do charged leptons oscillate?, JHEP 09 (2007) 116 https://doi.org/10.1088/1126-6708/ 2007/09/116.

P. F. de Salas, D. V. Forero, S. Gariazzo, P. Martınez-Mirave, O. Mena, C. A. Ternes, M. Tortola and J. W. F. Valle, 2020 global reassessment of the neutrino oscillation picture, JHEP 02 (2021), 071 https://doi.org/10.1007/JHEP02(2021)071.

S. M. Bilenky and C. Giunti, Neutrinoless Double-Beta Decay: a Probe of Physics Beyond the Standard Model, Int. J. Mod. Phys. A 30 (2015) no.04n05, 1530001 https://doi.org/10.1142/S0217751X1530001X.

T. Hahn and M. Perez-Victoria, Automatized one loop calculations in four-dimensions and D-dimensions, Comput. Phys. Commun. 118 (1999) 153 The FeynArts package can be downloaded from http://www.feynarts.de. https://doi.org/10.1016/S0010-4655(98)00173-8.

T. Aoyama, T. Kinoshita and M. Nio, Revised and Improved Value of the QED Tenth-Order Electron Anomalous Magnetic Moment, Phys. Rev. D 97 (2018) 036001 https://doi.org/10.1103/PhysRevD.97.036001.

R. H. Parker, C. Yu, W. Zhong, B. Estey and H. Müller, Measurement of the fine-structure constant as a test of the Standard Model, Science 360 (2018) 191 https://doi.org/10.1126/science.aap7706.

L. Morel, Z. Yao, P. Clade and S. Guellati-Khelifa, Determination of the fine-structure constant with an accuracy of 81 parts per trillion, Nature 588 (2020) 61-65. https://doi.org/10.1038/s41586-020-2964-7.

G. Arnison et al. [UA1], Experimental Observation of Isolated Large Transverse Energy Electrons with Associated Missing Energy at √ s = 540 GeV, Phys. Lett. B 122 (1983), 103, https://doi.org/10.1016/0370-2693(83)91177-2.

M. Banner et al. [UA2], Observation of Single Isolated Electrons of High Transverse Momentum in Events with Missing Transverse Energy at the CERN anti-p p Collider, Phys. Lett. B 122 (1983) 476, https://doi.org/10.1016/0370-2693(83)91605-2.

G. Arnison et al. [UA1], Experimental Observation of Lepton Pairs of Invariant Mass Around 95 GeV/c 2 at the CERN SPS Collider, Phys. Lett. B 126 (1983) 398, https://doi.org/ 10.1016/0370-2693(83)90188-0.

P. Bagnaia et al. [UA2], Evidence for Z 0 → e +e − at the CERN pp¯ Collider, Phys. Lett. B 129 (1983) 130, https://doi.org/10.1016/0370-2693(83)90744-X.

F. Abe et al. [CDF], Observation of top quark production in pp¯ collisions, Phys. Rev. Lett. 74 (1995) 2626, https://doi.org/10.1103/PhysRevLett.74.2626.

S. Abachi et al. [D0], Observation of the top quark, Phys. Rev. Lett. 74 (1995) 2632, https://doi.org/10.1103/PhysRevLett.74.2632.

G. Aad et al. [ATLAS], 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, https://doi.org/10.1103/PhysRevLett.74.2632.

S. Chatrchyan et al. [CMS], Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC, Phys. Lett. B 716 (2012) 30, https://doi.org/10.1016/j.physletb.2012.08.021.

F. J. Hasert et al. [Gargamelle Neutrino], Observation of Neutrino Like Interactions Without Muon Or Electron in the Gargamelle Neutrino Experiment, Phys. Lett. B 46 (1973), 138, https://doi.org/10.1016/0370-2693(73)90499-1.

R. L. Garwin, L. M. Lederman and M. Weinrich, Observations of the Failure of Conservation of Parity and Charge Conjugation in Meson Decays: The Magnetic Moment of the Free Muon, Phys. Rev. 105 (1957) 1415, https://doi.org/10.1103/PhysRev.105.1415.

C. S. Wu, E. Ambler, R. W. Hayward, D. D. Hoppes and R. P. Hudson, Experimental Test of Parity Conservation in β Decay, Phys. Rev. 105 (1957) 1413, https://doi.org/10.1103/PhysRev.105.1413.

T. D. Lee and C. N. Yang, Question of Parity Conservation in Weak Interactions, Phys. Rev. 104 (1956), 254, https://doi.org/10.1103/PhysRev.104.254.

E. Fermi, An attempt of a theory of beta radiation. 1., Z. Phys. 88 (1934) 161, https://doi.org/10.1007/BF01351864.

S. Schael et al. [ALEPH, DELPHI, L3, OPAL, SLD, LEP Electroweak Working Group, SLD Electroweak Group and SLD Heavy Flavour Group], Precision electroweak measurements on the Z resonance, Phys. Rept. 427 (2006) 257, https://doi.org/10.1016/j.physrep.2005.12.006.

P. Janot and S. Jadach, Improved Bhabha cross section at LEP and the number of light neutrino species, Phys. Lett. B 803 (2020) 135319, https://doi.org/10.1016/j.physletb.2020.135319.

S. Schael et al. [ALEPH, DELPHI, L3, OPAL and LEP Electroweak], Electroweak Measurements in ElectronPositron Collisions at W-Boson-Pair Energies at LEP, Phys. Rept. 532 (2013) 119, https://doi.org/10.1016/j.physrep.2013.07.004.

S. Weinberg, On the Development of Effective Field Theory, Eur. Phys. J. H 46 (2021) 6, https://doi.org/10.1140/epjh/s13129-021-00004-x.

C. H. Llewellyn Smith, High-Energy Behavior and Gauge Symmetry, Phys. Lett. B 46 (1973) 233, https://doi.org/10.1016/0370-2693(73)90692-8.

A. Djouadi, The Anatomy of electro-weak symmetry breaking. I: The Higgs boson in the standard model, Phys. Rept. 457 (2008) 1, https://doi.org/10.1016/j.physrep.2007.10.004.

D. de Florian et al. [LHC Higgs Cross Section Working Group], Handbook of LHC Higgs Cross Sections: 4. Deciphering the Nature of the Higgs Sector, https://doi.org/10.23731/CYRM-2017-002.

M. Aaboud et al. [ATLAS], Observation of H → b ¯b decays and V H production with the ATLAS detector, Phys. Lett. B 786 (2018) 59. https://doi.org/10.1016/j.physletb.2018.09.013.

A. M. Sirunyan et al. [CMS], Evidence for Higgs boson decay to a pair of muons, JHEP 01 (2021) 148, https://doi.org/10.1007/JHEP01(2021)148.

[ATLAS], Measurements of Higgs boson properties in the diphoton decay channel with 36.1 fb−1 pp collision data at the center-of-mass energy of 13 TeV with the ATLAS detector, ATLAS-CONF-2017-045 (2017).

[CMS], Measurements of properties of the Higgs boson in the four-lepton final state in proton-proton collisions at √ s = 13 TeV, CMS-PAS-HIG-19-001 (2019).

M. Awramik, M. Czakon and A. Freitas, Electroweak two-loop corrections to the effective weak mixing angle, JHEP 11 (2006) 048, https://doi.org/10.1088/1126-6708/2006/11/048.

G. W. Bennett et al. [Muon g-2], Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL, Phys. Rev. D 73 (2006) 072003, https://doi.org/10.1103/PhysRevD.73.072003.

T. Aoyama, N. Asmussen, M. Benayoun, J. Bijnens, T. Blum, M. Bruno, I. Caprini, C. M. Carloni Calame, M. Ce` and G. Colangelo, et al. The anomalous magnetic moment of the muon in the Standard Model, Phys. Rept. 887 (2020) 1, https://doi.org/10.1016/j.physrep.2020.07.006.

B. Abi et al. [Muon g-2], Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm, Phys. Rev. Lett. 126 (2021) 141801, https://doi.org/10.1103/PhysRevLett.126.141801.

R. Aaij et al. [LHCb], Test of lepton universality in beautyquark decays,

J. Albrecht, D. van Dyk and C. Langenbruch, Flavour anomalies in heavy quark decays, Prog. Part. Nucl. Phys. 120 (2021) 103885, https://doi.org/10.1016/j.ppnp.2021.103885.

E. Kou et al. [Belle-II], The Belle II Physics Book, PTEP 2019 (2019) 123C01, [erratum: PTEP 2020 (2020) 029201], https://doi.org/10.1093/ptep/ptz106.

J. Haller, A. Hoecker, R. Kogler, K. Monig, T. Peiffer and J. Stelzer, Update of the global electroweak fit and constraints on two-Higgs-doublet models, Eur. Phys. J. C 78 (2018) 675, https://doi.org/10.1140/epjc/s10052-018-6131-3.

V. A. Kuzmin, V. A. Rubakov and M. E. Shaposhnikov, On the Anomalous Electroweak Baryon Number Nonconservation in the Early Universe, Phys. Lett. B 155 (1985) 36, https://doi.org/10.1016/0370-2693(85)91028-7.

S. Davidson, E. Nardi and Y. Nir, Leptogenesis, Phys. Rept. 466 (2008) 105, https://doi.org/10.1016/j.physrep.2008.06.002.

G. Bertone, D. Hooper and J. Silk, Particle dark matter: Evidence, candidates and constraints, Phys. Rept. 405 (2005) 279, https://doi.org/10.1016/j.physrep.2004.08.031.

S. Clesse and J. Garcıa-Bellido, Seven Hints for Primordial Black Hole Dark Matter, Phys. Dark Univ. 22 (2018), 137, https://doi.org/10.1016/j.dark.2018.08.004.

R. D. Peccei, The Strong CP problem and axions, Lect. Notes Phys. 741 (2008) 3, https://doi.org/10.1007/978-3-540-73518-2 1.

P. J. E. Peebles and B. Ratra, The Cosmological Constant and Dark Energy, Rev. Mod. Phys. 75 (2003) 559, https://doi.org/10.1103/RevModPhys.75.559.

N. Aghanim et al. [Planck], Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641 (2020) A6; [erratum: Astron. Astrophys. 652 (2021) C4] https://doi.org/10.1051/0004-6361/201833910.

S. P. Martin, A Supersymmetry primer, Adv. Ser. Direct. High Energy Phys. 18 (1998) 1, https://doi.org/10.1142/9789812839657 0001.

N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali, The Hierarchy problem and new dimensions at a millimeter, Phys. Lett. B 429 (1998) 263, https://doi.org/10.1016/S0370-2693(98)00466-3.

L. Randall and R. Sundrum, A Large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370, https://doi.org/10.1103/PhysRevLett.83.3370.

W. Buchmuller and D. Wyler, Effective Lagrangian Analysis of New Interactions and Flavor Conservation, Nucl. Phys. B 268 (1986) 621, https://doi.org/10.1016/0550-3213(86)90262-2.

B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-Six Terms in the Standard Model Lagrangian, JHEP 10 (2010) 085, https://doi.org/10.1007/JHEP10(2010)085.

J. Ellis, M. Madigan, K. Mimasu, V. Sanz and T. You, Top, Higgs, Diboson and Electroweak Fit to the Standard Model Effective Field Theory, JHEP 04 (2021) 279, https://doi.org/10.1007/JHEP04(2021)279.

Downloads

Published

2022-06-23

How to Cite

1.
Illana JI. The electroweak standard model. Supl. Rev. Mex. Fis. [Internet]. 2022 Jun. 23 [cited 2022 Oct. 4];3(2):020721 1-30. Available from: https://rmf.smf.mx/ojs/index.php/rmf-s/article/view/6169