DOCSLIB.ORG

Physical Parameters of the Electroweak Crossover

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Physical Parameters of the Electroweak Crossover Available online at www.sciencedirect.com Nuclear and Particle Physics Proceedings 273–275 (2016) 2363–2365 www.elsevier.com/locate/nppp Physical parameters of the electroweak crossover Michela D’Onofrio Department of Physics and Helsinki Institute of Physics, PL 64 (Gustaf H¨allstr¨ominkatu 2), FI-00014 University of Helsinki, Finland Kari Rummukainen Department of Physics and Helsinki Institute of Physics, PL 64 (Gustaf H¨allstr¨ominkatu 2), FI-00014 University of Helsinki, Finland Anders Tranberg Faculty of Science and Technology, University of Stavanger, N-4036 Stavanger, Norway Abstract We use large-scale lattice simulations to compute the rate of baryon-number violating processes, the sphaleron rate, the Higgs field expectation value, and the critical temperature of the electroweak phase transition in the Standard Model. Keywords: baryogenesis, sphaleron rate, baryon number, electroweak crossover, lattice simulations, standard model 1. Introduction necessary Sakharov’s conditions of C and CP violation as well as departure from equilibrium. These are not Baryon and lepton numbers are classically conserved naturally satisfied by the Standard Model as-is, but a quantities, but the chiral nature of weak interactions minimal extension is required. gives rise to the anomalous violation of baryon and lep- ton number currents at the quantum level. In practice, Ε however, the processes violating B- and L-numbers are Εsph suppressed below a temperature scale of Tc ∼ 100 GeV, ff N thus making B and L e ectively conserved in the present −2 −1 0 1 2 3 CS Universe. The critical temperature corresponds to the electroweak scale, where it has been suggested [1] that Figure 1: Vacuum structure of the pure-gauge electroweak theory. The baryogenesis might have taken place. In the Standard energy of gauge field configurations as a function of Chern-Simons number [2]. Model, baryon number is violated by the Adler-Bell- Jackiw anomaly At temperatures above the electroweak scale, the rate 2 of the sphaleron transitions is unsuppressed and has μ5 e αβμν ∂μ j = − FαβFμν, (1) been accurately measured using effective theories on the π2 16 lattice. At temperatures substantially below the elec- where jμ5 is the axial vector current, e the gauge cou- troweak scale, the Higgs field expectation value is large pling, and Fij the gauge field strength tensor. Eq. 1 ex- and the sphaleron rate is strongly suppressed. presses the fact that, in gauge theories, gauge invariance The work presented in these proceedings is based on implies axial vector current non-conservation. our previous work [3], where we use an effective elec- However, apart from B-violation, any successful troweak theory on the lattice with multicanonical and model of baryogenesis has also to fulfill the other two real-time simulation methods to calculate the sphaleron http://dx.doi.org/10.1016/j.nuclphysbps.2015.09.392 2405-6014/© 2015 Elsevier B.V. All rights reserved. 2364 M. D’Onofrio et al. / Nuclear and Particle Physics Proceedings 273–275 (2016) 2363–2365 rate through the electroweak crossover with Higgs mass Each transition changes nCS by one unit and the of 125 GeV. baryon number by ng = 3 B(t f ) − B(ti) = ng [nCS (t f ) − nCS (ti)]. 2. Theory The electroweak theory possess a set of infinite non- 3. Theory on the lattice trivial vacua (Fig. 1), each labeled by a Chern-Simons number We use large-scale lattice simulations and compute the sphaleron rate, the Higgs field expectation value and ≡ 3 0 nCS d xjCS the critical temperature of the electroweak phase transi- tion in the Standard Model. g2 g = − 3 ijk + . The thermodynamics of the 4-dimensional elec- π d x Tr AiA jk i AiA jAk 64 3 troweak theory is studied in 3 dimensions through di- μ mensional reduction [5], a perturbative technique giv- The Chern-Simons current jCS is in turn related through the axial anomaly to the baryon- and lepton-number cur- ing the correspondence between 4D and 3D parameters. ff rents The result is a SU(2) e ective theory with the Higgs field φ and gauge field Aμ (Fij) 2 μ μ g αβμν a a ∂μ( j + j ) = ng AαβAμν , (2) B L 16π2 = 1 a a + φ † φ + 2φ†φ + λ φ†φ 2, L FijFij (Di ) (Di ) m3 3( ) (4) ∂ μ = ∂ μ , 4 μ jB ng μ jCS (3) ff 2 λ 2 and 3D e ective parameters g3, 3 and m3. The time where the U(1) part of the theory is omitted. Transitions evolution of this effective SU(2) Higgs model is gov- between vacua are possible by surmounting the poten- erned by Langevin dynamics [6]. The latter, however, sphaleron transitions tial barrier through . The sphaleron is very slow on the lattice and can be substituted by any rate is strongly suppressed at low temperatures, where other dissipative procedure, heat bath in our case. One the potential barrier is high. At temperatures above the heat-bath sweep through the lattice corresponds to the EWPT, though, transitions among vacua are made pos- 2 real-time step Δt = a σel/4[7], where a is the lattice sible because of the availability of thermal energy. spacing and σel is the non-abelian color conductivity, the current response to infrared external fields. The Standard Model 130 4. Methods symmetric phase 120 In the symmetric phase we make use of canoni- perturbation theory cal Monte Carlo simulations and approach the broken phase. At very low temperatures, the rate is highly sup- 110 2nd order pressed and canonical methods do not work anymore. endpoint Here, the computation is performed with multicanon- /GeV c ical methods [8, 9], which make use of a weight func- T 100 tion that compensates the low-temperature suppression in the baryon violation rate. The obtained sphaleron rate is 90 Higgs phase (n (t) − n (0))2 Γ ≡ lim CS CS . (5) t→∞ Vt 80 50 60 70 80 90 5. The sphaleron rate mH/GeV The measured sphaleron rate is shown in Fig. 6 Figure 2: The order of the electroweak phase transition shown in terms of Higgs mass [4]. The phase transition is first order up to with a shaded error band. The freeze-out tem- Γ mH ∼ 70 GeV, where it becomes second order. For higher values perature T∗ is solved from the crossing of and of the Higgs mass, the transition is a crossover. the Hubble rate, shown with the almost horizontal M. D’Onofrio et al. / Nuclear and Particle Physics Proceedings 273–275 (2016) 2363–2365 2365 line. The sphaleron rate in the symmetric phase -10 pure gauge (T > Tc)is Γ/ 4 = ± α5 , T (18 3) W -15 and in the broken phase between 130 GeV < T < Tc can be parametrized as -20 log(Γ/T 4) = (0.83 ± 0.01) T/GeV − (147.7 ± 1.9). 4 -25 The freeze-out temperature in the early Universe, where Γ/Τ log -30 standard the Hubble rate wins over the baryon number violation multicanonical rate, is T∗ = (131.7 ± 2.3) GeV. fit perturbative -35 6. Conclusions α -40 log[ H(T)/T] The discovery of the Higgs particle of mass 125– 126 GeV enables us to fully determine the properties of -45 the symmetry breaking at high temperatures. Using lat- 130 140 150 160 170 tice simulations of a 3D effective theory, we have lo- T / GeV Figure 4: The sphaleron rate as a function of temperature at the cated the crossover range at Tc = (159 ± 1) GeV, de- crossover. Both canonical and multicanonical results are shown and termined the baryon number violation rate both above are in good agreement. The perturbative result is from [10]. Pure and well below the crossover point, and calculated the gauge refers to the rate in hot SU(2) gauge theory [11]. baryon freeze-out temperature in the early Universe, T∗ = (131.7 ± 2.3) GeV. It is the first time that this fundamental parameter of These results represent intrinsic properties of the the Standard Model has been so extensively and pre- Minimal Standard Model, as well as provide input for cisely studied in the full temperature range of the elec- leptogenesis calculations, in particular for models with troweak crossover. The obtained accuracy is the greatest electroweak-scale leptons. The sphaleron rate obtained achievable in the circumstance of exponential suppres- here also provides a benchmark for future computa- sion, which occurs in the broken phase. Significant im- tions of the sphaleron rate in extensions of the Standard provement in this direction is not around the corner any Model. time soon. References [1] V. A. Kuzmin, V. A. Rubakov and M. E. Shaposhnikov, Phys. multicanonical Lett. B 155 (1985) 36 1 standard [2] J. M. Cline, hep-ph/0609145. perturbative [3] M. D’Onofrio, K. Rummukainen and A. Tranberg, Phys. Rev. Lett. 113 (2014) 141602 [arXiv:1404.3565 [hep-ph]]. 0.8 [4] M. Laine and K. Rummukainen, Nucl. Phys. Proc. Suppl. 73 (1999) 180 [hep-lat/9809045]. 2 0.6 [5] K. Kajantie, M. Laine, K. Rummukainen and M. E. Shaposh- nikov, Nucl. Phys. B 458 (1996) 90 [hep-ph/9508379]. (T) / T / 2 [6] D. Bodeker, Phys. Lett. B 426 (1998) 351 [hep-ph 9801430]. v 0.4 [7] G. D. Moore and K. Rummukainen, Phys. Rev. D 63 (2001) 045002 [hep-ph/0009132]. [8] G. D. Moore, Phys. Rev. D 59 (1999) 014503 [hep-ph/9805264]. 0.2 [9] M. D’Onofrio, K. Rummukainen and A. Tranberg, JHEP 1208 (2012) 123 [arXiv:1207.0685 [hep-ph]]. [10] Y. Burnier, M. Laine and M. Shaposhnikov, JCAP 0602 (2006) 0 007 [hep-ph/0511246]. [11] G. D. Moore and K. Rummukainen, Phys.
Load more

Recommended publications
  • Cosmological Relaxation of the Electroweak Scale
    Selected for a Viewpoint in Physics week ending PRL 115, 221801 (2015) PHYSICAL REVIEW LETTERS 27 NOVEMBER 2015 Cosmological Relaxation of the Electroweak Scale Peter W. Graham,1 David E. Kaplan,1,2,3,4 and Surjeet Rajendran3 1Stanford Institute for Theoretical Physics, Department of Physics, Stanford University, Stanford, California 94305, USA 2Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA 3Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, California 94720, USA 4Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa 277-8583, Japan (Received 22 June 2015; published 23 November 2015) A new class of solutions to the electroweak hierarchy problem is presented that does not require either weak-scale dynamics or anthropics. Dynamical evolution during the early Universe drives the Higgs boson mass to a value much smaller than the cutoff. The simplest model has the particle content of the standard model plus a QCD axion and an inflation sector. The highest cutoff achieved in any technically natural model is 108 GeV. DOI: 10.1103/PhysRevLett.115.221801 PACS numbers: 12.60.Fr Introduction.—In the 1970s, Wilson [1] had discovered Our models only make the weak scale technically natural that a fine-tuning seemed to be required of any field theory [9], and we have not yet attempted to UV complete them which completed the standard model Higgs sector, unless for a fully natural theory, though there are promising its new dynamics appeared at the scale of the Higgs mass.
    [Show full text]
  • 10. Electroweak Model and Constraints on New Physics
    1 10. Electroweak Model and Constraints on New Physics 10. Electroweak Model and Constraints on New Physics Revised March 2020 by J. Erler (IF-UNAM; U. of Mainz) and A. Freitas (Pittsburg U.). 10.1 Introduction ....................................... 1 10.2 Renormalization and radiative corrections....................... 3 10.2.1 The Fermi constant ................................ 3 10.2.2 The electromagnetic coupling........................... 3 10.2.3 Quark masses.................................... 5 10.2.4 The weak mixing angle .............................. 6 10.2.5 Radiative corrections................................ 8 10.3 Low energy electroweak observables .......................... 9 10.3.1 Neutrino scattering................................. 9 10.3.2 Parity violating lepton scattering......................... 12 10.3.3 Atomic parity violation .............................. 13 10.4 Precision flavor physics ................................. 15 10.4.1 The τ lifetime.................................... 15 10.4.2 The muon anomalous magnetic moment..................... 17 10.5 Physics of the massive electroweak bosons....................... 18 10.5.1 Electroweak physics off the Z pole........................ 19 10.5.2 Z pole physics ................................... 21 10.5.3 W and Z decays .................................. 25 10.6 Global fit results..................................... 26 10.7 Constraints on new physics............................... 30 10.1 Introduction The standard model of the electroweak interactions (SM) [1–4] is based on the gauge group i SU(2)×U(1), with gauge bosons Wµ, i = 1, 2, 3, and Bµ for the SU(2) and U(1) factors, respectively, and the corresponding gauge coupling constants g and g0. The left-handed fermion fields of the th νi ui 0 P i fermion family transform as doublets Ψi = − and d0 under SU(2), where d ≡ Vij dj, `i i i j and V is the Cabibbo-Kobayashi-Maskawa mixing [5,6] matrix1.
    [Show full text]
  • Lepton Flavor at the Electroweak Scale
    Lepton flavor at the electroweak scale: A complete A4 model Martin Holthausen1(a), Manfred Lindner2(a) and Michael A. Schmidt3(b) (a) Max-Planck Institut f¨urKernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany (b) ARC Centre of Excellence for Particle Physics at the Terascale, School of Physics, The University of Melbourne, Victoria 3010, Australia Abstract Apparent regularities in fermion masses and mixings are often associated with physics at a high flavor scale, especially in the context of discrete flavor symmetries. One of the main reasons for that is that the correct vacuum alignment requires usually some high scale mechanism to be phenomenologically acceptable. Contrary to this expectation, we present in this paper a renormalizable radiative neutrino mass model with an A4 flavor symmetry in the lepton sector, which is broken at the electroweak scale. For that we use a novel way to achieve the VEV alignment via an extended symmetry in the flavon potential proposed before by two of the authors. We discuss various phenomenological consequences for the lepton sector and show how the remnants of the flavor symmetry suppress large lepton flavor violating processes. The model naturally includes a dark matter candidate, whose phenomenology we outline. Finally, we sketch possible extensions to the quark sector and discuss its implications for the LHC, especially how an enhanced diphoton rate for the resonance at 125 GeV can be explained within this model. arXiv:1211.5143v2 [hep-ph] 5 Feb 2013 [email protected] [email protected] [email protected] 1 Introduction Much progress has been achieved in the field of particle physics during the last year.
    [Show full text]
  • Composite Higgs Models with “The Works”
    Composite Higgs models with \the works" James Barnard with Tony Gherghetta, Tirtha Sankar Ray, Andrew Spray and Callum Jones With the recent discovery of the Higgs boson, all elementary particles predicted by the Standard Model have now been observed. But particle physicists remain troubled by several problems. The hierarchy problem Why is the Higgs mass only 126 GeV? Quantum effects naively 16 suggest that mh & 10 GeV would be more natural. Flavour hierarchies Why is the top quark so much heavier than the electron? Dark matter What are the particles that make up most of the matter in the universe? Gauge coupling unification The three gauge couplings in the SM nearly unify, hinting towards a grand unified theory, but they don't quite meet. It feels like we might be missing something. With the recent discovery of the Higgs boson, all elementary particles predicted by the Standard Model have now been observed. However, there is a long history of things that looked like elementary particles turning out not to be Atoms Nuclei Hadrons Splitting the atom Can we really be sure we have reached the end of the line? Perhaps some of the particles in the SM are actually composite. Compositeness in the SM also provides the pieces we are missing The hierarchy problem If the Higgs is composite it is shielded from quantum effects above the compositeness scale. Flavour hierarchies Compositeness in the fermion sector naturally gives mt me . Dark matter Many theories predict other composite states that are stabilised by global symmetries, just like the proton in the SM.
    [Show full text]
  • New Heavy Resonances: from the Electroweak to the Planck Scale
    New heavy resonances : from the electroweak to the planck scale Florian Lyonnet To cite this version: Florian Lyonnet. New heavy resonances : from the electroweak to the planck scale. High Energy Physics - Phenomenology [hep-ph]. Université de Grenoble, 2014. English. NNT : 2014GRENY035. tel-01110759v2 HAL Id: tel-01110759 https://tel.archives-ouvertes.fr/tel-01110759v2 Submitted on 10 Apr 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. THÈSE Pour obtenirle grade de DOCTEUR DE L’UNIVERSITÉ DE GRENOBLE Spécialité:Physique Subatomiqueet Astroparticules Arrêtéministériel:7août2006 Présentéepar FlorianLyonnet ThèsedirigéeparIngoSchienbein préparéeau sein Laboratoirede Physique Subatomiqueet de Cosmolo- gie et de Ecoledoctoralede physique de Grenoble New heavy resonances: from the Electroweak to thePlanck scale ThèsesoutenuepubliquementOH VHSWHPEUH , devant le jurycomposéde : Mr. Aldo,Deandrea Prof., UniversitéClaudeBernardLyon 1, Rapporteur Mr. Jean-Loïc,Kneur DR,LaboratoireCharlesCoulombMontpellier,Rapporteur Mr. Roberto Bonciani Dr., UniversitàdegliStudidi Roma”LaSapienza”,Examinateur Mr. MichaelKlasen Prof., UniversitätMünster,Examinateur Mr. FrançoisMontanet Prof.,UniversitéJosephFourierde Grenoble,3UpVLGHQW Mr. JeanOrloff Prof., UniversitéBlaisePascal de Clermont-Ferrand,Examinateur Mr. IngoSchienbein MCF., UniversitéJosephFourier, Directeurde thèse ACKNOWLEDMENGTS My years at the LPSC have been exciting, intense, and I would like to express my sincere gratitude to all the people that contributed to it on the professional as well as personal level.
    [Show full text]
  • Arxiv:0905.3187V2 [Hep-Ph] 7 Jul 2009 Cie Ataryo Xeietlifrain the Information
    Unanswered Questions in the Electroweak Theory Chris Quigg∗ Theoretical Physics Department, Fermi National Accelerator Laboratory, Batavia, Illinois 60510 USA Institut f¨ur Theoretische Teilchenphysik, Universit¨at Karlsruhe, D-76128 Karlsruhe, Germany Theory Group, Physics Department, CERN, CH-1211 Geneva 23, Switzerland This article is devoted to the status of the electroweak theory on the eve of experimentation at CERN’s Large Hadron Collider. A compact summary of the logic and structure of the electroweak theory precedes an examination of what experimental tests have established so far. The outstanding unconfirmed prediction of the electroweak theory is the existence of the Higgs boson, a weakly interacting spin-zero particle that is the agent of electroweak symmetry breaking, the giver of mass to the weak gauge bosons, the quarks, and the leptons. General arguments imply that the Higgs boson or other new physics is required on the TeV energy scale. Indirect constraints from global analyses of electroweak measurements suggest that the mass of the standard-model Higgs boson is less than 200 GeV. Once its mass is assumed, the properties of the Higgs boson follow from the electroweak theory, and these inform the search for the Higgs boson. Alternative mechanisms for electroweak symmetry breaking are reviewed, and the importance of electroweak symmetry breaking is illuminated by considering a world without a specific mechanism to hide the electroweak symmetry. For all its triumphs, the electroweak theory has many shortcomings. It does not make specific predictions for the masses of the quarks and leptons or for the mixing among different flavors. It leaves unexplained how the Higgs-boson mass could remain below 1 TeV in the face of quantum corrections that tend to lift it toward the Planck scale or a unification scale.
    [Show full text]
  • The Minimal Fermionic Model of Electroweak Baryogenesis
    The minimal fermionic model of electroweak baryogenesis Daniel Egana-Ugrinovic C. N. Yang Institute for Theoretical Physics, Stony Brook, NY 11794 Abstract We present the minimal model of electroweak baryogenesis induced by fermions. The model consists of an extension of the Standard Model with one electroweak singlet fermion and one pair of vector like doublet fermions with renormalizable couplings to the Higgs. A strong first order phase transition is radiatively induced by the singlet- doublet fermions, while the origin of the baryon asymmetry is due to asymmetric reflection of the same set of fermions on the expanding electroweak bubble wall. The singlet-doublet fermions are stabilized at the electroweak scale by chiral symmetries and the Higgs potential is stabilized by threshold corrections coming from a multi-TeV ultraviolet completion which does not play any significant role in the phase transition. We work in terms of background symmetry invariants and perform an analytic semi- classical calculation of the baryon asymmetry, showing that the model may effectively generate the observed baryon asymmetry for percent level values of the unique invari- ant CP violating phase of the singlet-doublet sector. We include a detailed study of electron electric dipole moment and electroweak precision limits, and for one typical benchmark scenario we also recast existing collider constraints, showing that the model arXiv:1707.02306v1 [hep-ph] 7 Jul 2017 is consistent with all current experimental data. We point out that fermion induced electroweak baryogenesis has irreducible phenomenology at the 13 TeV LHC since the new fermions must be at the electroweak scale, have electroweak quantum numbers and couple strongly with the Higgs.
    [Show full text]
  • Electroweak Baryogenesis from Exotic Electroweak Symmetry Breaking
    IPPP-15-23, DCPT-15-46 Electroweak Baryogenesis from Exotic Electroweak Symmetry Breaking Nikita Blinov(a;b), Jonathan Kozaczuk(a), David E. Morrissey(a), and Carlos Tamarit(c) (a) TRIUMF, 4004 Wesbrook Mall, Vancouver, BC V6T 2A3, Canada (b) Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada (c) Institute for Particle Physics Phenomenology, Department of Physics Durham University, Durham DH1 3LE, United Kingdom email: [email protected], [email protected], [email protected], [email protected] August 20, 2015 Abstract We investigate scenarios in which electroweak baryogenesis can occur during an exotic stage of electroweak symmetry breaking in the early Universe. This tran- sition is driven by the expectation value of a new electroweak scalar instead of the standard Higgs field. A later, second transition then takes the system to arXiv:1504.05195v2 [hep-ph] 19 Aug 2015 the usual electroweak minimum, dominated by the Higgs, while preserving the baryon asymmetry created in the first transition. We discuss the general require- ments for such a two-stage electroweak transition to be suitable for electroweak baryogenesis and present a toy model that illustrates the necessary ingredients. We then apply these results to construct an explicit realization of this scenario within the inert two Higgs doublet model. Despite decoupling the Higgs from the symmetry-breaking transition required for electroweak baryogenesis, we find that this picture generically predicts new light states that are accessible experi- mentally. 1 Introduction Electroweak baryogenesis (EWBG) is an elegant mechanism for the generation of the baryon asymmetry during the electroweak phase transition [1{3].
    [Show full text]
  • Probing the Electroweak Phase Transition with Higgs Factories and Gravitational Waves
    Probing the Electroweak Phase Transition with Higgs Factories and Gravitational Waves Peisi Huang,a;b∗ Andrew J. Long,cy and Lian-Tao Wanga;cz aEnrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA. bHigh Energy Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA cKavli Institute for Cosmological Physics, University of Chicago, Chicago, Illinois 60637, USA Abstract After the discovery of the Higgs boson, understanding the nature of electroweak symmetry breaking and the associated electroweak phase transition has become the most pressing question in particle physics. Answering this question is a priority for experimental studies. Data from the LHC and future lepton collider-based Higgs factories may uncover new physics coupled to the Higgs boson, which can induce the electroweak phase transition to become first order. Such a phase transition generates a stochastic background of gravitational waves, which could potentially be detected by a space-based gravitational wave interferometer. In this paper, we survey a few classes of models in which the electroweak phase transition is strongly first order. We identify the observables that would provide evidence of these models at the LHC and next- generation lepton colliders, and we assess whether the corresponding gravitational wave signal could be detected by eLISA. We find that most of the models with first order electroweak phase transition can be covered by the precise measurements of Higgs couplings at the proposed Higgs factories. We also map out the model space that can be probed with gravitational wave detection by eLISA. arXiv:1608.06619v2 [hep-ph] 15 May 2017 ∗[email protected] [email protected] [email protected] Contents 1 Introduction 2 2 Models 4 2.1 Real Scalar Singlet .
    [Show full text]
  • HIGGS BOSONS: THEORY and SEARCHES Updated May 2010 by G
    –1– HIGGS BOSONS: THEORY AND SEARCHES Updated May 2010 by G. Bernardi (LPNHE, CNRS/IN2P3, U. of Paris VI & VII), M. Carena (Fermi National Accelerator Laboratory and the University of Chicago), and T. Junk (Fermi National Accelerator Laboratory). I. Introduction Understanding the mechanism that breaks electroweak sym- metry and generates the masses of all known elementary par- ticles is one of the most fundamental problems in particle physics. The Higgs mechanism [1] provides a general framework to explain the observed masses of the W ± and Z gauge bosons by means of charged and neutral Goldstone bosons that end up as the longitudinal components of the gauge bosons. These Goldstone bosons are generated by the underlying dynamics of electroweak symmetry breaking (EWSB). However, the fun- damental dynamics of the electroweak symmetry breaking are unknown. There are two main classes of theories proposed in the literature, those with weakly coupled dynamics - such as in the Standard Model (SM) [2] - and those with strongly coupled dynamics. In the SM, the electroweak interactions are described by a gauge field theory based on the SU(2)L×U(1)Y symmetry group. The Higgs mechanism posits a self-interacting complex doublet of scalar fields, and renormalizable interactions are arranged such that the neutral component of the scalar doublet acquires a vacuum expectation value v ≈ 246 GeV, which sets the scale of EWSB. Three massless Goldstone bosons are generated, which are absorbed to give masses to the W ± and Z gauge bosons. The remaining component of the complex doublet becomes the Higgs boson - a new fundamental scalar particle.
    [Show full text]
  • Gauged L(Mu)-L(Tau) Symmetry at the Electroweak Scale
    Gauged Lµ − Lτ Symmetry at the Electroweak Scale Julian Heeck∗ and Werner Rodejohanny Max{Planck{Institut f¨urKernphysik, Postfach 103980, D{69029 Heidelberg, Germany The extension of the Standard Model by a spontaneously broken abelian gauge group based on the Lµ − Lτ lepton number can resolve the long-standing discrepancy between experimental and theoretical values for the magnetic moment of the muon. It furthermore naturally generates µ-τ symmetric lepton mixing, introduces neutrino nonstandard interactions, and the associated gauge boson Z0 serves as a mediator to the right-handed neutrino sector. A detailed fit to electroweak data is performed to identify the allowed values for the mass of Z0 and its mixing with the Standard Model Z. An economical new scalar sector is constructed that spontaneously breaks Lµ − Lτ and leads to experimental consequences such as lepton flavor violation and collider signatures. Furthermore we discuss the nonabelian extension to an SU(2)0, particularly the neutrino sector. I. INTRODUCTION Extensions of the Standard Model (SM) of particle physics could either add new particles or represen- tations, or extend the gauge sector. The enormous precision with which the SM has been tested in the last decades, plus the various theoretical consistency conditions which have to be obeyed, require careful addition of new physics. One particularly popular approach is the addition of an abelian gauge symmetry U(1)0. If this symmetry is broken (to avoid an additional force with infinite range), a massive Z0 boson is present, with model-dependent mass and couplings to the SM particles [1]. In this paper we focus on one class of highly interesting U(1)0 models: within the particle content of the SM, it is possible to gauge one of the three differences of lepton flavors Le Lµ, Le Lτ or Lµ Lτ , without introducing an anomaly [2, 3].
    [Show full text]
  • Arxiv:2008.09136V4 [Astro-Ph.CO] 25 May 2021
    SciPost Physics Lecture Notes Submission MPP-2020-163, HIP-2020-27/TH Phase transitions in the early universe Mark Hindmarsh1,2* , Marvin Lüben3** , Johannes Lumma4†, Martin Pauly4‡ 1 Department of Physics and Helsinki Institute of Physics, PL 64, FI-00014 University of Helsinki, Finland 2 Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, United Kingdom 3 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, 80805 Munich, Germany 4 Institut für Theoretische Physik, Ruprecht-Karls-Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany * mark.hindmarsh@helsinki.fi, ** [email protected], †[email protected], ‡[email protected] Abstract These lecture notes are based on a course given by Mark Hindmarsh at the 24th Saalburg Summer School 2018 and written up by Marvin Lüben, Johannes Lumma and Martin Pauly. The aim is to provide the necessary basics to un- derstand first-order phase transitions in the early universe, to outline how they leave imprints in gravitational waves, and advertise how those gravitational waves could be detected in the future. A first-order phase transition at the electroweak scale is a prediction of many theories beyond the Standard Model, and is also motivated as an ingredient of some theories attempting to provide an explanation for the matter-antimatter asymmetry in our Universe. Starting from bosonic and fermionic statistics, we derive Boltzmann’s equation and generalise to a fluid of particles with field dependent mass. We introduce the thermal effective potential for the field in its lowest order approximation, discuss the transition to the Higgs phase in the Standard Model and beyond, and compute the probability for the field to cross a potential barrier.
    [Show full text]