A pedagogical review of electroweak symmetry breaking scenarios

We review different avenues of electroweak symmetry breaking explored over the years. This constitutes a timely exercise as the world's largest and the highest energy particle accelerator, namely, the Large Hadron Collider (LHC) at CERN near Geneva, has started running whose primary mission is to find the Higgs or some phenomena that mimic the effects of the Higgs, i.e. to unravel the mysteries of electroweak phase transition. In the beginning, we discuss the Standard Model Higgs mechanism. After that we review the Higgs sector of the minimal supersymmetric Standard Model. Then we take up three relatively recent ideas: little Higgs, gauge–Higgs unification and Higgsless scenarios. For the latter three cases, we first present the basic ideas and restrict our illustration to some instructive toy models to provide an intuitive feel of the underlying dynamics, and then discuss, for each of the three cases, how more realistic scenarios are constructed and how to decipher their experimental signatures. Wherever possible, we provide pedagogical details, which beginners might find useful.

[1]  Alexandre Alves,et al.  Workshop on CP Studies and Non-Standard Higgs Physics , 2006, hep-ph/0608079.

[2]  Y. Hosotani Dynamical Gauge Symmetry Breaking as the Casimir Effect , 1983 .

[3]  Spencer Chang A ``littlest Higgs'' model with custodial SU(2) symmetry , 2003, hep-ph/0306034.

[4]  C. Hill Topcolor: top quark condensation in a gauge extension of the standard model , 1991 .

[5]  Roberto Contino,et al.  Tasi 2009 lectures: The Higgs as a Composite Nambu-Goldstone Boson , 2010, 1005.4269.

[6]  E. Eichten,et al.  Dynamical breaking of weak interaction symmetries , 1980 .

[7]  S. Weinberg,et al.  Symmetry Breaking and Scalar Bosons , 1976 .

[8]  The Higgs mass and new physics scales in the minimal standard model , 2000, hep-ph/0003170.

[9]  C. Grojean,et al.  Fermions on an interval: Quark and lepton masses without a Higgs , 2003, hep-ph/0310355.

[10]  H. Murayama,et al.  Gauge Theories on an Interval: Unitarity Without a Higgs Boson , 2004 .

[11]  Higgs as a holographic pseudo-Goldstone boson , 2003, hep-ph/0306259.

[12]  B. Jasny,et al.  AIDS 1993: unanswered questions. , 1993, Science.

[13]  J. Bagger Weak-Scale Supersymmetry: Theory and Practice , 1996, hep-ph/9604232.

[14]  Steven Weinberg,et al.  A Model of Leptons , 1967 .

[15]  G. Altarelli New Physics and the LHC , 2008, 0805.1992.

[16]  G. Altarelli,et al.  Vacuum polarization effects of new physics on electroweak processes , 1991 .

[17]  I. Low,et al.  Little Higgs bosons from an antisymmetric condensate , 2002, hep-ph/0207243.

[18]  G. Altarelli,et al.  Lower limit on the Higgs mass in the standard model: An Update , 1994 .

[19]  S. Huber,et al.  The Supersymmetric Standard Model , 1998 .

[20]  Tilman Plehn,et al.  Four generations and Higgs physics , 2007, 0706.3718.

[21]  N. Haba,et al.  Dynamical symmetry breaking in gauge-Higgs unification on an orbifold , 2004, hep-ph/0401183.

[22]  Bando,et al.  Scale-invariant hypercolor model and a dilaton. , 1986, Physical review letters.

[23]  Cyril Hugonie,et al.  The Next-to-Minimal Supersymmetric Standard Model , 2009, 0910.1785.

[24]  The Simplest little Higgs , 2004, hep-ph/0407143.

[25]  Maxim Perelstein Little Higgs models and their phenomenology , 2007 .

[26]  H. Thacker,et al.  Weak interactions at very high energies: The role of the Higgs-boson mass , 1977 .

[27]  J. Maldacena The Large-N Limit of Superconformal Field Theories and Supergravity , 1997, hep-th/9711200.

[28]  Kennedy,et al.  Precision electroweak experiments and heavy physics: A global analysis. , 1990, Physical review letters.

[29]  J. Maldacena The Large N limit of superconformal field theories and supergravity , 1998 .

[30]  D. Volkov,et al.  Is the Neutrino a Goldstone Particle , 1973 .

[31]  Big corrections from a little Higgs , 2002, hep-ph/0211124.

[32]  C. Csáki,et al.  ELECTROWEAK SYMMETRY BREAKING FROM EXTRA DIMENSIONS , 2006 .

[33]  A Supersymmetry Primer , 1997, hep-ph/9709356.

[34]  G. Giudice Naturally Speaking: The Naturalness Criterion and Physics at the LHC , 2008, 0801.2562.

[35]  D. Stolarski,et al.  The bestest little Higgs , 2010, 1006.1356.

[36]  W. Skiba TASI Lectures on Effective Field Theory and Precision Electroweak Measurements , 2010, 1006.2142.

[37]  M. Sher Electroweak Higgs Potentials and Vacuum Stability , 1989 .

[38]  Electroweak symmetry breaking and fermion masses from extra dimensions , 2003, hep-ph/0304220.

[39]  N. Sakai,et al.  Naturalnes in supersymmetric GUTS , 1981 .

[40]  M. Carena,et al.  Collider phenomenology of Gauge-Higgs unification scenarios in warped extra dimensions , 2007, 0712.0095.

[41]  Martin Schmaltz,et al.  LITTLE HIGGS THEORIES , 2005 .

[42]  A. Nelson,et al.  The Littlest Higgs , 2002, hep-ph/0206021.

[43]  C. Collard,et al.  CP Studies and Non-Standard Higgs Physics , 2006 .

[44]  M. Perelstein,et al.  Erratum: Large Hadron Collider Tests of the Little Higgs Model [Phys. Rev. Lett.90, 241802 (2003)] , 2004 .

[45]  R. Godbole,et al.  Theory and phenomenology of sparticles : an account of four-dimensional N=1 supersymmetry in high energy physics , 2004 .

[46]  L. Okun,et al.  On the electroweak one-loop corrections , 1993 .

[47]  Y. Hosotani,et al.  Higgs boson mass and electroweak–gravity hierarchy from dynamical gauge–Higgs unification in the warped spacetime , 2005, hep-ph/0503020.

[48]  N. Arkani-Hamed,et al.  The Minimal Moose for a Little Higgs , 2002 .

[49]  Leonard Susskind,et al.  Dynamics of Spontaneous Symmetry Breaking in the Weinberg-Salam Theory , 1979 .

[50]  M. C. Rodriguez History of Supersymmetric Extensions of the Standard Model , 2009, 0911.5338.

[51]  B. Holdom Raising the sideways scale , 1981 .

[52]  Hill,et al.  Minimal dynamical symmetry breaking of the standard model. , 1990, Physical review. D, Particles and fields.

[53]  L. Randall,et al.  A Large mass hierarchy from a small extra dimension , 1999, hep-ph/9905221.

[54]  N. Okada,et al.  Gauge-Higgs unification at CERN LHC , 2007, 0711.2589.

[55]  S. Dawson Introduction to Electroweak Symmetry Breaking , 1999, hep-ph/9901280.

[56]  M. Schmaltz,et al.  Ultraviolet extension of the simplest little Higgs model , 2004 .

[57]  J. Lykken,et al.  Introduction to Supersymmetry , 1996, hep-th/9612114.

[58]  G. Giudice Theories for the fermi scale , 2007, 0710.3294.

[59]  M. Gell-Mann,et al.  Theory of the Fermi Interaction , 1958 .

[60]  C. Csáki,et al.  Fully radiative electroweak symmetry breaking , 2005, hep-ph/0510366.

[61]  Little hierarchy, little higgses, and a little symmetry , 2004, hep-ph/0405243.

[62]  Tianjun Li,et al.  Coupling unifications in gauge-Higgs unified orbifold models , 2005, hep-ph/0504082.

[63]  J. Hewett,et al.  Electroweak symmetry breaking without a Higgs boson in warped backgrounds: Constraints and signatures , 2004 .

[64]  M. Serone Holographic methods and gauge–Higgs unification in flat extra dimensions , 2009, 0909.5619.

[65]  N. Okada,et al.  Higgs boson mass from gauge-Higgs unification , 2007, 0705.3035.

[66]  Electroweak precision constraints on the littlest Higgs model with T parity , 2005, hep-ph/0506042.

[67]  A. Kundu,et al.  Multijet discriminators for new physics in leptonic signals at the LHC , 2009, 0910.4082.

[68]  M. Maniatis,et al.  The Next-to-Minimal Supersymmetric extension of the Standard Model reviewed , 2009, 0906.0777.

[69]  Edward Witten,et al.  Dynamical Breaking of Supersymmetry , 1981 .

[70]  J. Wacker,et al.  Little Higgs models and custodial SU ( 2 ) , 2003, hep-ph/0303001.

[71]  Y. Hosotani Dynamical Mass Generation by Compact Extra Dimensions , 1983 .

[72]  A. Djouadi The anatomy of electroweak symmetry breaking Tome II: The Higgs bosons in the Minimal Supersymmetric Model , 2005, hep-ph/0503173.

[73]  R. L. Mills,et al.  Conservation of Isotopic Spin and Isotopic Gauge Invariance , 1954 .

[74]  Pierre Fayet,et al.  Supergauge invariant extension of the Higgs mechanism and a model for the electron and its neutrino , 1975 .

[75]  N. Okada,et al.  Gauge-Higgs Unification at LHC , 2010, 1002.1835.

[76]  A. Hektor,et al.  Testing neutrino masses in little Higgs models via discovery of doubly charged Higgs at LHC , 2007, 0705.1495.

[77]  R. Rattazzi,et al.  Weakly coupled Higgsless theories and precision electroweak tests , 2003, hep-ph/0310285.

[78]  Roberto Contino,et al.  The Minimal Composite Higgs Model , 2005 .

[79]  S. Dawson Susy and Such , 1996, hep-ph/9612229.

[80]  W. Marciano,et al.  Erratum: `` Parity violation as a probe of new physics [Phys. Rev. Lett. 65, 2963 (1990)] , 1992 .

[81]  R. Kaul Gauge hierarchy in a supersymmetric model , 1982 .

[82]  L. Susskind,et al.  Mass Without Scalars , 1979 .

[83]  Antonio Delgado,et al.  RS1, custodial isospin and precision tests , 2003 .

[84]  B. Zumino,et al.  A lagrangian model invariant under supergauge transformations , 1974 .

[85]  D. Roy Higgs and SUSY Searches at LHC : An Overview , 2003, hep-ph/0303106.

[86]  S. Nandi,et al.  Unification of gauge, Higgs and matter in extra dimensions , 2003, hep-ph/0302176.

[87]  H. Baer,et al.  Beyond the Standard Model , 2004, Inference: International Review of Science.

[88]  Riccardo Barbieri,et al.  Searching for new physics at future accelerators , 2004, hep-ph/0410223.

[89]  M. Lechowski,et al.  Exploring Little Higgs models with ATLAS at the LHC- , 2004, The European Physical Journal C.

[90]  C. Hill Topcolor assisted technicolor , 1994, hep-ph/9411426.

[91]  B. Zumino,et al.  Supergauge Invariant Extension of Quantum Electrodynamics , 1974 .

[92]  Savas Dimopoulos,et al.  Softly Broken Supersymmetry and SU(5) , 1981 .

[93]  A Three site Higgsless model , 2006, hep-ph/0607124.

[94]  Ulrich Ellwanger Radiative corrections to the neutral Higgs spectrum in supersymmetry with a gauge singlet , 1993 .

[95]  Eldad Gildener,et al.  Gauge Symmetry Hierarchies , 1976 .

[96]  S. Glashow Partial Symmetries of Weak Interactions , 1961 .

[97]  R. Rattazzi,et al.  Strong double higgs production at the LHC , 2010, 1002.1011.

[98]  R. Kaul Supersymmetry and Supergravity , 1989 .

[99]  Riccardo Barbieri,et al.  Electroweak symmetry breaking after LEP1 and LEP2 , 2004, hep-ph/0405040.

[100]  Marciano,et al.  Atomic parity violation as a probe of new physics. , 1990, Physical review letters.

[101]  S. Pokorski,et al.  Gauge Field Theories: Spontaneous and explicit global symmetry breaking , 1987 .

[102]  C. Csáki,et al.  TASI Lectures on Electroweak Symmetry Breaking from Extra Dimensions , 2005, hep-ph/0510275.

[103]  Manuel Drees,et al.  SUPERSYMMETRIC MODELS WITH EXTENDED HIGGS SECTOR , 1989 .

[104]  C. Grojean,et al.  The Strongly-Interacting Light Higgs , 2007, hep-ph/0703164.

[105]  P. Pandita One-loop radiative corrections to the lightest Higgs scalar mass in the non-minimal supersymmetric standard model , 1993 .

[106]  H. Logan,et al.  Phenomenology of the little Higgs model , 2003, hep-ph/0301040.

[107]  Y. Golfand,et al.  EXTENSION OF THE ALGEBRA OF POINCARE GROUP GENERATORS AND VIOLATION OF P INVARIANCE. , 1971 .

[108]  P. Roy,et al.  Developments in high energy theory , 2009, 0905.1793.

[109]  The Hosotani Mechanism in Bulk Gauge Theories with an Orbifold Extra Space S 1 /Z 2 , 2001, hep-ph/0111327.

[110]  R. Kaul Supersymmetric solution of gauge hierarchy problem , 1982 .

[111]  N. Okada,et al.  Window for Higgs boson mass from gauge-Higgs unification , 2007, 0708.2503.

[112]  The little Higgs from a simple group , 2003, hep-ph/0302049.

[113]  R. Godbole CP violation in supersymmetry, Higgs sector and the large hadron collider , 2006 .

[114]  Howard Georgi,et al.  Electroweak symmetry breaking from dimensional deconstruction , 2001, hep-ph/0105239.

[115]  J. Espinosa,et al.  Standard model stability bounds for new physics within LHC reach , 1996, hep-ph/9603227.

[116]  Takeuchi,et al.  New constraint on a strongly interacting Higgs sector. , 1990, Physical review letters.

[117]  C. Csáki The Minimal Supersymmetric Standard Model (MSSM) , 1996, hep-ph/9606414.

[118]  Romesh K. Kaul,et al.  Cancellation of quadratically divergent mass corrections in globally supersymmetric spontaneously broken gauge theories , 1982 .

[119]  Steven Weinberg,et al.  Implications of Dynamical Symmetry Breaking , 1976 .

[120]  Roy,et al.  Oblique electroweak corrections and new physics. , 1992, Physical review. D, Particles and fields.

[121]  Constraining the littlest Higgs , 2002, hep-ph/0211218.

[122]  C. Csáki,et al.  Towards a realistic model of Higgsless electroweak symmetry breaking. , 2003, Physical Review Letters.

[123]  B. Zumino,et al.  Supergauge Transformations in Four-Dimensions , 1974 .

[124]  M. Peskin,et al.  Top quarks and electroweak symmetry breaking in little Higgs models , 2003, hep-ph/0310039.

[125]  Jay G. Wacker,et al.  Phenomenology of Electroweak Symmetry Breaking from Theory Space , 2002 .

[126]  H. Haber Present status and future prospects for a Higgs boson discovery at the Tevatron and LHC , 2010, 1011.1038.

[127]  Hsin-Chia Cheng Little Higgs, Non-standard Higgs, No Higgs and All That , 2007, 0710.3407.

[128]  Ignatios Antoniadis,et al.  A Possible new dimension at a few TeV , 1990 .

[129]  Supersymmetry Structure and Phenomena , 2001, hep-ph/0108236.

[130]  Robert E. Marshak,et al.  Chirality invariance and the universal Fermi interaction , 1958 .

[131]  Alan D. Martin,et al.  Review of Particle Physics , 2010 .

[132]  T. Appelquist,et al.  Chiral hierarchies and flavor-changing neutral currents in hypercolor. , 1986, Physical review letters.

[133]  Martin Schmaltz Physics beyond the standard model (Theory): Introducing the Little Higgs , 2002 .

[134]  H. Georgi,et al.  (De)constructing dimensions. , 2001, Physical review letters.

[135]  C. Chiang,et al.  A six-dimensional gauge-Higgs unification model based on E6 gauge symmetry , 2010, 1006.4446.

[136]  J. L. Lopes,et al.  A model for leptons , 1977 .