DOCSLIB.ORG

Dilaton As the Higgs Particle

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Dilaton As the Higgs Particle Dilaton as the Higgs Particle by Hassan Saadi A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF Master of Science in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Mathematics) The University of British Columbia (Vancouver) December 2016 c Hassan Saadi,2016 Abstract This essay focuses on exploring dilatons as an alternate model to the Higgs mechanism. An introductory analysis to the Higgs mechanism, effective potential method, and dilatons is provided. Then, three different models are explored on how to obtain a light dilaton that emerges as a pseudo Goldstone boson because of the spontaneously broken approximate scale invariance. This light dilaton is shown to have properties that are, in general, similar to the Higgs boson with minor differences that can differentiate between the two models in collider experiments. ii Preface This dissertation is original, unpublished, independent work by the author, Hassan Saadi. iii Table of Contents Abstract......................................... ii Preface......................................... iii Acknowledgements................................... vi 1 Introduction......................................1 1.1 The Higgs Mechanism..............................2 1.2 The Effective Potential Description.......................5 1.2.1 Formalism.................................6 1.2.2 Renormalization Group.........................8 1.2.3 Application to φ4 Theory........................ 10 2 Dilatons........................................ 13 2.1 Introduction.................................... 13 2.2 Model 1: Distinguishing the Higgs Boson from the Dilaton at the Large Hadron Collider.................................. 16 2.2.1 Electroweak Sector............................ 17 2.2.2 Dilaton Self-coupling........................... 18 2.2.3 Couplings to Massless Gauge Bosons.................. 19 2.3 Model 2: Effective Theory of a Light Dilaton................. 22 2.3.1 Effective Theory of a Dilaton...................... 22 2.3.2 Dilaton Interactions in a Conformal SM................ 29 iv 2.4 Model 3: A Very Light Dilaton......................... 33 2.4.1 The Model................................ 34 2.4.2 Dilaton.................................. 39 2.4.3 Phase Structure............................. 41 3 Conclusion....................................... 43 Bibliography...................................... 43 Appendices....................................... 46 A Dirac and Gell-Mann Matrices......................... 46 B Integral with a Cutoff.............................. 49 C Beta Function for the Gauge Coupling..................... 51 D The Renormalized Mass in Fermions...................... 52 v Acknowledgments I would like to thank my supervisor, Professor Gordon Semenoff, in the Physics Depart- ment for introducing me to the field and helping me in my thesis. I am really glad that I got the opportunity to work on this interesting project. I would also like to thank my su- pervisor Professor Nassif Ghoussoub in the Mathematics Department for his support and help. Moreover, I express my sincere appreciation to all the helpful staff of the Institute of Applied Mathematics, the Mathematics Department, and the Physics Department. And finally, I would like to thank my parents for supporting me in pursuing my dreams. vi Chapter 1 Introduction The Standard Model (SM) in particle physics consists of three generations of quarks and 1 leptons, four bosons, and the Higgs boson. The quarks are spin- 2 particles with 6 flavors: up, down, charm, strange, top, and bottom 0 1 0 1 0 1 u c t @ A ; @ A ; @ A (1.1) d s b L L L And the leptons also with 6 flavors: electron, electron neutrino, muon, muon neutrino, tau, and tau neutrino 0 1 0 1 0 1 νe νµ ντ @ A ; @ A ; @ A (1.2) e− µ− τ − L L L where the subscript L denotes left-handed components. The SM has been consistent with experiment. However, the SM does not explain some phenomena such as dark matter, dark energy, gravity, neutrino oscillations, and the hierarchy problem (why the Higgs' mass is small and doesn't receive radiative corrections). In this chapter, how the Higgs mechanism gives mass to the particles of SM is demonstrated. Then, the effective potential description is derived. 1 1.1 The Higgs Mechanism Let's define 0 1 νe Le = @ A (1.3) e− L 0 1 u Lq = @ A (1.4) d L In the following equations, one generation of quarks and leptons is considered and the neutrino is massless. The generalization to any number of generations is straightforward. The Lagrangian of the SM consists of four parts: gauge, fermion, Yukawa, and Higgs (or scalar) LSM = Lgauge + Lfermion + LY + LHiggs (1.5) 1 1 1 L = − B Bµν − (W a )2 − T r(G Gµν) (1.6) gauge 4 µν 4 µν 2 µν i i L = ¯ iγµ @ − g0B + gτ W a +e ¯ iγµ @ − ig0B e fermion Le µ 2 µ 2 a µ Le R µ µ R i i + ¯ iγ @ + g0B + τ W a + ig λ Ga Lq µ 6 µ 2 a µ s a µ Lq 2i +u ¯ iγµ @ + g0B + ig λ Gµa u R µ 3 µ s a R i + d¯ iγµ @ − g0B + ig λ Ga (1.7) R µ 3 µ s a µ h y ¯ i h ¯ y ¯ i LY = −ζe e¯Rφ Le + Le φeR − ζd dRφ Lq + Lq φdR h ¯y ¯ ¯ i − ζu u¯Rφ Lq + Lq φuR (1.8) y 2 y y 2 LHiggs = (Dµφ) (Dµφ) − µ φ φ − λ(φ φ) (1.9) 2 where Bµν = @µBν − @νBµ =) U(1)Y gauge field (1.10) a a a b c Wµν = @µWν − @νWµ + gabcWµWν =) SU(2)L gauge fields (1.11) a a a b c Gµν = @µGν − @νGµ + gsabcGµGν =) SU(3)c gauge fields (1.12) 0 p 1 3 + a Wµ 2Wµ τaWµ = @p A (1.13) − 3 2Wµ −Wµ i i D φ = @ + g0B + gτ W a φ (1.14) µ µ 2 µ 2 a µ 0 1 0 1 φ+ φ0∗ ¯ ∗ φ ≡ @ A ! φ = iτ2φ = @ A (1.15) φ0 −φ+∗ µ and ζ is Yukawa's coupling, abc is an antisymmetric three-index symbol, γ are Dirac matrices, τa are Pauli matrices, and λa are Gell-mann matrices listed in appendix A. Now let's modify the potential by assuming that µ2 < 0 so that we have a Mexican- hat potential. Spontaneous symmetry breaking occurs when the vacuum picks up an expectation value. Let's choose the vacuum expectation value of the scalar field to be 0 1 0 hφi0 = @ A (1.16) pν 2 where ν = p−µ2/λ. When the vacuum picks up an expectation value it breaks the symmetries of SU(2)L and U(1)Y , but it preserves U(1)EM symmetry. φ can be expressed in a new gauge φ0 without a phase as 0 1 a π τa 0 φ(x) = exp i @ A (1.17) 2ν νp+ρ 2 0 1 a 0 π τa 0 φ (x) = exp − i φ = @ A (1.18) 2ν νp+ρ 2 where ρ(x) and π(x) are associated with the radial and angular axises respectively in the Mexican hat potential of the Higgs, τa are pauli matrices, and πa are real fields (would-be 3 Goldstone). Expressing (1.14) after φ picking up an expectation value 0 p 1 + ρ+ν 1 −i 2gWµ 2 Dµφ = p @ A (1.19) 2 0 3 ρ+ν @µρ − i(g Bµ − gWµ ) 2 Expanding the Higgs Lagrangian (1.9) about the minimum of the Higgs potential by using (1.13) and (1.19) yields g2 1 L = W µW +(ρ + ν)2 + (g0Bµ − gW µ)(g0B − gW 3)(ρ + ν)2 Higgs 4 − µ 8 3 µ µ 1 1 1 + @µρ∂ ρ + µ2(ν + ρ)2 − λ(ν + ρ)4 (1.20) 2 µ 2 4 3 We rotate Bµ and Wµ so that the photon is massless 0 1 0 1 0 1 0 Zµ sin(θW ) − cos(θW ) Bµ @ A = @ A @ A (1.21) 3 Aµ cos(θW ) sin(θW ) Wµ where g0 sin(θW ) = (1.22) pg2 + g02 g cos(θW ) = (1.23) pg2 + g02 and the masses of the particle can be read off the Lagrangian (1.20)(Quigg, 2013) ν p M = g2 + g02 ' 91:2 GeV (1.24) Z 2 1 M ± = gν ' 80:4 GeV (1.25) W 2 MW ± ) = cos(θW ) (1.26) MZ p p −1=2 0 −1=2 and ν = (GF 2) ' 246 GeV , so φ 0 = (GF 8) ' 174 GeV where GF = −5 −2 1:663787(6) × 10 GeV is Fermi constant and sin(θW ) = 0:2122 is the weak mixing parameter. The Yukawa Lagrangian (1.8) becomes ρ + ν h i ρ + ν h ¯ ¯ i LY = −ζe p e¯ReL +e ¯LeR − ζd p dRdL + dLdR 2 2 ρ + ν h i − ζu p u¯RuL +u ¯LuR (1.27) 2 4 and the masses of the electron, up and down quarks can be read off ζeν me = p (1.28) 2 ζdν md = p (1.29) 2 ζuν mu = p (1.30) 2 It has been shown above how gauge bosons, leptons, and quarks acquire mass when the symmetry of the Higgs potential is broken when it picks up a vacuum expectation value. This mechanism is called Glashow-Salam-Weinberg model (GSW) when applied to the electroweak theory. Hence, the GSW model describes how the group SU(2)L ⊗ U(1)Y breaks to the electromagnetic gauge group U(1)EM Higgs SU(3)c ⊗ SU(2)L ⊗ U(1)Y −−−! SU(3)c ⊗ U(1)EM (1.31) | {z } GSW U(1)EM The original four generators (τa;Y ) are broken, but the electric charge operator Q = 1 2 (τ3 + Y ) is not. Hence, by Goldstone theorem the photon and the gluons are massless. One of the problems with the Higgs model is that it's not a dynamical model, that's to say, it does not explain why the symmetry was broken in the first place. The Higgs model suffers from the hierarchy problem that implies that the square mass of the Higgs should be finely tuned (to cancel radiative quantum corrections) with the correct sign in order to produce the scale ν.
Load more

Recommended publications
  • 2-Loop $\Beta $ Function for Non-Hermitian PT Symmetric $\Iota
    2-Loop β Function for Non-Hermitian PT Symmetric ιgφ3 Theory Aditya Dwivedi1 and Bhabani Prasad Mandal2 Department of Physics, Institute of Science, Banaras Hindu University Varanasi-221005 INDIA Abstract We investigate Non-Hermitian quantum field theoretic model with ιgφ3 interaction in 6 dimension. Such a model is PT-symmetric for the pseudo scalar field φ. We analytically calculate the 2-loop β function and analyse the system using renormalization group technique. Behavior of the system is studied near the different fixed points. Unlike gφ3 theory in 6 dimension ιgφ3 theory develops a new non trivial fixed point which is energetically stable. 1 Introduction Over the past two decades a new field with combined Parity(P)-Time rever- sal(T) symmetric non-Hermitian systems has emerged and has been one of the most exciting topics in frontier research. It has been shown that such theories can lead to the consistent quantum theories with real spectrum, unitary time evolution and probabilistic interpretation in a different Hilbert space equipped with a positive definite inner product [1]-[3]. The huge success of such non- Hermitian systems has lead to extension to many other branches of physics and interdisciplinary areas. The novel idea of such theories have been applied in arXiv:1912.07595v1 [hep-th] 14 Dec 2019 numerous systems leading huge number of application [4]-[21]. Several PT symmetric non-Hermitian models in quantum field theory have also been studied in various context [16]-[26]. Deconfinment to confinment tran- sition is realised by PT phase transition in QCD model using natural but uncon- ventional hermitian property of the ghost fields [16].
    [Show full text]
  • Effective Quantum Field Theories Thomas Mannel Theoretical Physics I (Particle Physics) University of Siegen, Siegen, Germany
    Generating Functionals Functional Integration Renormalization Introduction to Effective Quantum Field Theories Thomas Mannel Theoretical Physics I (Particle Physics) University of Siegen, Siegen, Germany 2nd Autumn School on High Energy Physics and Quantum Field Theory Yerevan, Armenia, 6-10 October, 2014 T. Mannel, Siegen University Effective Quantum Field Theories: Lecture 1 Generating Functionals Functional Integration Renormalization Overview Lecture 1: Basics of Quantum Field Theory Generating Functionals Functional Integration Perturbation Theory Renormalization Lecture 2: Effective Field Thoeries Effective Actions Effective Lagrangians Identifying relevant degrees of freedom Renormalization and Renormalization Group T. Mannel, Siegen University Effective Quantum Field Theories: Lecture 1 Generating Functionals Functional Integration Renormalization Lecture 3: Examples @ work From Standard Model to Fermi Theory From QCD to Heavy Quark Effective Theory From QCD to Chiral Perturbation Theory From New Physics to the Standard Model Lecture 4: Limitations: When Effective Field Theories become ineffective Dispersion theory and effective field theory Bound Systems of Quarks and anomalous thresholds When quarks are needed in QCD É. T. Mannel, Siegen University Effective Quantum Field Theories: Lecture 1 Generating Functionals Functional Integration Renormalization Lecture 1: Basics of Quantum Field Theory Thomas Mannel Theoretische Physik I, Universität Siegen f q f et Yerevan, October 2014 T. Mannel, Siegen University Effective Quantum
    [Show full text]
  • Theoretical and Experimental Aspects of the Higgs Mechanism in the Standard Model and Beyond Alessandra Edda Baas University of Massachusetts Amherst
    University of Massachusetts Amherst ScholarWorks@UMass Amherst Masters Theses 1911 - February 2014 2010 Theoretical and Experimental Aspects of the Higgs Mechanism in the Standard Model and Beyond Alessandra Edda Baas University of Massachusetts Amherst Follow this and additional works at: https://scholarworks.umass.edu/theses Part of the Physics Commons Baas, Alessandra Edda, "Theoretical and Experimental Aspects of the Higgs Mechanism in the Standard Model and Beyond" (2010). Masters Theses 1911 - February 2014. 503. Retrieved from https://scholarworks.umass.edu/theses/503 This thesis is brought to you for free and open access by ScholarWorks@UMass Amherst. It has been accepted for inclusion in Masters Theses 1911 - February 2014 by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contact [email protected]. THEORETICAL AND EXPERIMENTAL ASPECTS OF THE HIGGS MECHANISM IN THE STANDARD MODEL AND BEYOND A Thesis Presented by ALESSANDRA EDDA BAAS Submitted to the Graduate School of the University of Massachusetts Amherst in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE September 2010 Department of Physics © Copyright by Alessandra Edda Baas 2010 All Rights Reserved THEORETICAL AND EXPERIMENTAL ASPECTS OF THE HIGGS MECHANISM IN THE STANDARD MODEL AND BEYOND A Thesis Presented by ALESSANDRA EDDA BAAS Approved as to style and content by: Eugene Golowich, Chair Benjamin Brau, Member Donald Candela, Department Chair Department of Physics To my loving parents. ACKNOWLEDGMENTS Writing a Thesis is never possible without the help of many people. The greatest gratitude goes to my supervisor, Prof. Eugene Golowich who gave my the opportunity of working with him this year.
    [Show full text]
  • Hep-Th] 27 May 2021
    Higher order curvature corrections and holographic renormalization group flow Ahmad Ghodsi∗and Malihe Siahvoshan† Department of Physics, Faculty of Science, Ferdowsi University of Mashhad, Mashhad, Iran September 3, 2021 Abstract We study the holographic renormalization group (RG) flow in the presence of higher-order curvature corrections to the (d+1)-dimensional Einstein-Hilbert (EH) action for an arbitrary interacting scalar matter field by using the superpotential approach. We find the critical points of the RG flow near the local minima and maxima of the potential and show the existence of the bounce solutions. In contrast to the EH gravity, regarding the values of couplings of the bulk theory, superpoten- tial may have both upper and lower bounds. Moreover, the behavior of the RG flow controls by singular curves. This study may shed some light on how a c-function can exist in the presence of these corrections. arXiv:2105.13208v1 [hep-th] 27 May 2021 ∗[email protected] †[email protected] Contents 1 Introduction1 2 The general setup4 3 Holographic RG flow: κ1 = 0 theories5 3.1 Critical points for κ2 < 0...........................7 3.1.1 Local maxima of the potential . .7 3.1.2 Local minima of potential . .9 3.1.3 Bounces . .9 3.2 Critical points for κ2 > 0........................... 11 3.2.1 Critical points for W 6= WE ..................... 12 3.2.2 Critical points near W = WE .................... 13 4 Holographic RG flow: General case 15 4.1 Local maxima of potential . 18 4.2 Local minima of potential . 22 4.3 Bounces .
    [Show full text]
  • The Euler Legacy to Modern Physics
    ENTE PER LE NUOVE TECNOLOGIE, L'ENERGIA E L'AMBIENTE THE EULER LEGACY TO MODERN PHYSICS G. DATTOLI ENEA -Dipartimento Tecnologie Fisiche e Nuovi Materiali Centro Ricerche Frascati M. DEL FRANCO - ENEA Guest RT/2009/30/FIM This report has been prepared and distributed by: Servizio Edizioni Scientifiche - ENEA Centro Ricerche Frascati, C.P. 65 - 00044 Frascati, Rome, Italy The technical and scientific contents of these reports express the opinion of the authors but not necessarily the opinion of ENEA. THE EULER LEGACY TO MODERN PHYSICS Abstract Particular families of special functions, conceived as purely mathematical devices between the end of XVIII and the beginning of XIX centuries, have played a crucial role in the development of many aspects of modern Physics. This is indeed the case of the Euler gamma function, which has been one of the key elements paving the way to string theories, furthermore the Euler-Riemann Zeta function has played a decisive role in the development of renormalization theories. The ideas of Euler and later those of Riemann, Ramanujan and of other, less popular, mathematicians have therefore provided the mathematical apparatus ideally suited to explore, and eventually solve, problems of fundamental importance in modern Physics. The mathematical foundations of the theory of renormalization trace back to the work on divergent series by Euler and by mathematicians of two centuries ago. Feynman, Dyson, Schwinger… rediscovered most of these mathematical “curiosities” and were able to develop a new and powerful way of looking at physical phenomena. Keywords: Special functions, Euler gamma function, Strin theories, Euler-Riemann Zeta function, Mthematical curiosities Riassunto Alcune particolari famiglie di funzioni speciali, concepite come dispositivi puramente matematici tra la fine del XVIII e l'inizio del XIX secolo, hanno svolto un ruolo cruciale nello sviluppo di molti aspetti della fisica moderna.
    [Show full text]
  • Arxiv:1102.4624V1 [Hep-Th] 22 Feb 2011 (Sec
    Renormalisation group and the Planck scale Daniel F. Litim∗ Department of Physics and Astronomy, University of Sussex, Brighton, BN1 9QH, U.K. I discuss the renormalisation group approach to gravity, its link to S. Weinberg's asymptotic safety scenario, and give an overview of results with applications to particle physics and cosmology. I. INTRODUCTION Einstein's theory of general relativity is the remarkably successful classical theory of the gravitational force, charac- −11 3 2 terised by Newton's coupling constant GN = 6:67×10 m =(kg s ) and a small cosmological constant Λ. Experimen- tally, its validity has been confirmed over many orders of magnitude in length scales ranging from the sub-millimeter regime up to solar system size. At larger length scales, the standard model of cosmology including dark matter and dark energy components fits the data well. At shorter length scales, quantum effects are expected to become impor- tant. An order of magnitude estimate for the quantum scale of gravity { the Planck scale { is obtained by dimensional p 3 −33 analysis leading to the Planck length `Pl ≈ ~GN =c of the order of 10 cm, with c the speed of light. In particle physics units this translates into the Planck mass 19 MPl ≈ 10 GeV : (1) While this energy scale is presently out of reach for earth-based particle accelerator experiments, fingerprints of Planck-scale physics can nevertheless become accessible through cosmological data from the very early universe. From a theory perspective, it is widely expected that a fundamental understanding of Planck scale physics requires a quantum theory of gravity.
    [Show full text]
  • Exploring Models for New Physics on the Lattice
    Exploring Models for New Physics on the Lattice Ethan T. Neil∗ Fermi National Accelerator Laboratory E-mail: [email protected] Strongly-coupled gauge theories are an important ingredient in the construction of many exten- sions of the standard model, particularly for models of electroweak symmetry breaking in which the Higgs boson is a composite object. There is a large parameter space of such gauge theories with a rich phase structure, particularly in the presence of large numbers of fermionic degrees of freedom. Lattice simulation provides a non-perturbative way to explore this space of strongly- coupled theories, and to search for interesting dynamical features. Here I review recent progress in the simulation of such theories, with an eye towards applications to dynamical electroweak symmetry breaking. XXIX International Symposium on Lattice Field Theory July 10-16, 2011 Squaw Valley, Lake Tahoe, California ∗Speaker. c Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/ Exploring Models for New Physics on the Lattice Ethan T. Neil 1. Introduction Lattice gauge theory has enjoyed considerable success as a non-perturbative method to study and understand quantum chromodynamics (QCD), the only example of a strongly coupled gauge theory observed in nature thus far. With modern computers and computational techniques, lattice QCD is attaining high levels of precision, with simulation parameters approaching the physical point. However, the success enjoyed by lattice QCD is no reason for us to restrict the attention of our lattice studies to that theory alone. QCD is far from unique as an example of an asymptotically free Yang-Mills gauge theory, inhabiting a large space of models, all of which are well-suited to numerical study on the lattice.
    [Show full text]
  • HIGGS BOSONS: THEORY and SEARCHES Updated May 2012 by G
    – 1– HIGGS BOSONS: THEORY AND SEARCHES Updated May 2012 by G. Bernardi (CNRS/IN2P3, LPNHE/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 II. The Standard Model (SM) Higgs Boson II.1. Indirect Constraints on the SM Higgs Boson II.2. Searches for the SM Higgs Boson at LEP II.3. Searches for the SM Higgs Boson at the Tevatron II.4. SM Higgs Boson Searches at the LHC II.5. Models with a Fourth Generation of SM-Like Fermions III. Higgs Bosons in the Minimal Supersymmetric Standard Model (MSSM) III.1. Radiatively-Corrected MSSM Higgs Masses and Couplings III.2. Decay Properties and Production Mechanisms of MSSM Higgs Bosons III.3. Searches for Neutral Higgs Bosons in the CP-Conserving CP C Scenario III.3.1. Searches for Neutral MSSM Higgs Bosons at LEP III.3.2. Searches for Neutral MSSM Higgs Bosons at Hadron Colliders III.4. Searches for Charged MSSM Higgs Bosons III.5. Effects of CP Violation on the MSSM Higgs Spectrum III.6. Searches for Neutral Higgs Bosons in CP V Scenarios III.7. Indirect Constraints on Supersymmetric Higgs Bosons IV. Other Model Extensions V. Searches for Higgs Bosons Beyond the MSSM VI. Outlook VII. Addendum NOTE: The 4 July 2012 update on the Higgs search from ATLAS and CMS is described in the Addendum at the end of this review. CITATION: J. Beringer et al. (Particle Data Group), PR D86, 010001 (2012) (URL: http://pdg.lbl.gov) July 25, 2012 15:44 – 2– I.
    [Show full text]
  • Higgs-Like Boson at 750 Gev and Genesis of Baryons
    BNL-112543-2016-JA Higgs-like boson at 750 GeV and genesis of baryons Hooman Davoudiasl, Pier Paolo Giardino, Cen Zhang Submitted to Physical Review D July 2016 Physics Department Brookhaven National Laboratory U.S. Department of Energy USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25) Notice: This manuscript has been co-authored by employees of Brookhaven Science Associates, LLC under Contract No. DE-SC0012704 with the U.S. Department of Energy. The publisher by accepting the manuscript for publication acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or any third party’s use or the results of such use of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof or its contractors or subcontractors. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
    [Show full text]
  • Spontaneous Symmetry Breaking in the Higgs Mechanism
    Spontaneous symmetry breaking in the Higgs mechanism August 2012 Abstract The Higgs mechanism is very powerful: it furnishes a description of the elec- troweak theory in the Standard Model which has a convincing experimental ver- ification. But although the Higgs mechanism had been applied successfully, the conceptual background is not clear. The Higgs mechanism is often presented as spontaneous breaking of a local gauge symmetry. But a local gauge symmetry is rooted in redundancy of description: gauge transformations connect states that cannot be physically distinguished. A gauge symmetry is therefore not a sym- metry of nature, but of our description of nature. The spontaneous breaking of such a symmetry cannot be expected to have physical e↵ects since asymmetries are not reflected in the physics. If spontaneous gauge symmetry breaking cannot have physical e↵ects, this causes conceptual problems for the Higgs mechanism, if taken to be described as spontaneous gauge symmetry breaking. In a gauge invariant theory, gauge fixing is necessary to retrieve the physics from the theory. This means that also in a theory with spontaneous gauge sym- metry breaking, a gauge should be fixed. But gauge fixing itself breaks the gauge symmetry, and thereby obscures the spontaneous breaking of the symmetry. It suggests that spontaneous gauge symmetry breaking is not part of the physics, but an unphysical artifact of the redundancy in description. However, the Higgs mechanism can be formulated in a gauge independent way, without spontaneous symmetry breaking. The same outcome as in the account with spontaneous symmetry breaking is obtained. It is concluded that even though spontaneous gauge symmetry breaking cannot have physical consequences, the Higgs mechanism is not in conceptual danger.
    [Show full text]
  • Annual Report 2018 Annual Report 2018 Annual Report 2018 Helsinki Institute of Physics
    Helsinki office CERN office P.O. Box 64 (Gustaf Hällströmin katu 2) CERN/PH FI-00014 University of Helsinki, Finland CH-1211 Geneva 23, Switzerland tel. +358-2-941 50557 tel. +41-22-76 73027 Annual Report 2018 www.hip.fi Annual Report 2018 Annual Report 2018 Helsinki Institute of Physics Vice-Rector Sari Lindblom unveiling the portrait of the former HIP Director, Vice-Rector Paula Eerola. Annual Report 2018 Helsinki Institute of Physics CONTENTS 1. Preface 4 2. Highlights of Research Results 6 3. Theory Programme 10 4. CMS Programme 16 5. Nuclear Matter Programme 22 6. Technology Programme 26 7. Detector Laboratory 32 8. CLOUD 34 9. Planck-Euclid 36 10. Education and Open Data 38 11. Joint Activities 39 12. Organization and Personnel 40 13. Seminars 43 14. Visitors 44 15. Conference participation, Talks and Visits by Personnel 45 16. Publications 53 17. Preprints 66 Annual Report 2018 Helsinki Institute of Physics, Preface PREFACE The Helsinki Institute of Physics (HIP) is a joint research institute of the Universities of Helsinki and Jyväskylä, Aalto University, Tampere University of Technology, and Lappeenranta-Lahti University of Technology LUT. The Finnish Radiation and Nuclear Safety Authority is an interim member of HIP for 2018–2019. The University of Helsinki is the host organisation of HIP. HIP addresses fundamental science questions from quarks to the Cosmos as well as technologies from semiconductors to medical applications and climate research. The Institute serves as a national institute for Finnish physics and related technology research and development at international accelerator laboratories. By mandate of the Finnish Ministry of KATRI HUITU Education and Culture, HIP is responsible for the Finnish research collaboration Helsinki Institute of Physics director with the European Organization for Nuclear Research CERN and the Facility for Antiproton and Ion Research FAIR GmbH, which is under construction at the GSI Accelerator Laboratory in Darmstadt.
    [Show full text]
  • Dimensional Reduction, Regularisation
    PoS(LL2012)011 Dimensional Reduction (and all that) Tim Jones∗ Liverpool University E-mail: [email protected] I summarise the salient features of regularisation by dimensional reduction, and its relationship with the original form of dimensional regularisation. “Loops and Legs in Quantum Field Theory", 11th DESY Workshop on Elementary Particle Physics April 15-20, 2012 Wernigerode, Germany ∗Speaker. c Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/ Dimensional Reduction (and all that) Tim Jones 1. Introduction Siegel [1] introduced regularisation by dimensional reduction (DRED) as a variation of di- mensional regularisation, DREG [2], to maintain the equality of Bose-Fermi degrees of freedom characteristic of supersymmetry, an equality not preserved by DREG. As a consequence, for exam- ple, the relationship between the quark-quark-gluon and quark-squark-gluino couplings in SQCD is not preserved when DREG is used. Which is not to say that DREG cannot be used in supersym- metric theories; but it lacks convenience. For a formal discussion of the equivalence of DRED and DREG (modulo DRED ambiguities to be discussed below) see [3],[4]. A pedagogical introduction PoS(LL2012)011 to Siegel’s proposal, and a first discussion of its application to the non-supersymmetric case appears in Ref. [5]. Essentially DRED amounts to defining xµ ≡ (xi,0) pµ ≡ (pi,0) j j Wµ ≡ Wi(x ),Wσ (x ) (1.1) where µ and i, j are 4-dimensional and D-dimensional indices respectively, and D < 4. It is useful to define hatted quantities with µ,ν ··· indices whose only non-vanishing components are in the D-dimensional subspace; in particular,g ˆµν = (gi j,0).
    [Show full text]