Spontaneous symmetry breaking in particle physics: a case of cross fertilization. Giovanni Jona-Lasinio
|
|
- Donna Shona Sutton
- 5 years ago
- Views:
Transcription
1 Spontaneous symmetry breaking in particle physics: a case of cross fertilization Giovanni Jona-Lasinio QUARK MATTER ITALIA, aprile / 38
2 Spontaneous (dynamical) symmetry breaking Figure: Elastic rod compressed by a force of increasing strength 2 / 38
3 Other examples physical system ferromagnets crystals superconductors superfluid 4 He broken symmetry rotational invariance translational invariance local gauge invariance global gauge invariance When spontaneous symmetry breaking takes place, the ground state of the system is degenerate 3 / 38
4 Quasi-particles in superconductivity Electrons near the Fermi surface are described by the following equation Eψ p,+ = ɛ p ψ p,+ + φψ p, Eψ p, = ɛ pψ p, + φψ p,+ with eigenvalues E = ± ɛ 2 p + φ 2 Here, ψ p,+ and ψ p, are the wavefunctions for an electron and a hole of momentum p and spin + 4 / 38
5 Analogy with the Dirac equation In the Weyl representation, the Dirac equations reads Eψ 1 = σ pψ 1 + mψ 2 Eψ 2 = σ pψ 2 + mψ 1 with eigenvalues E = ± p 2 + m 2 Here, ψ 1 and ψ 2 are the eigenstates of the chirality operator γ 5 5 / 38
6 Nambu-Goldstone boson in superconductivity Y. Nambu, Phys. Rev. 117, 648 (1960) Approximate expressions for the charge density and the current associated to a quasi-particle in a BCS superconductor ρ(x, t) ρ α 2 tf j(x, t) j 0 f where ρ 0 = eψ σ 3 ZΨ and j 0 = eψ (p/m)y Ψ with Y, Z and α constants and f satisfies the wave equation ( 2 1α 2 t 2 ) f 2eΨ σ 2 φψ Here, Ψ = (ψ 1, ψ 2) 6 / 38
7 Plasmons The Fourier transform of the wave equation for f gives f 1 q 2 0 α2 q 2 The pole at q 2 0 = α2 q 2 describes the excitation spectrum of the Nambu-Goldstone boson. A better approximation reveals that, due to the Coulomb force, this spectrum is shifted to the plasma frequency e 2 n, where n is the number of electrons per unit volume. In this way the field f acquires a mass. 7 / 38
8 The Goldstone theorem J. Goldstone, Nuovo Cimento 19, 154 (1961) Whenever the original Lagrangian has a continuous symmetry group, which does not leave the ground state invariant, massless bosons appear in the spectrum of the theory. physical system broken symmetry massless bosons ferromagnets rotational invariance spin waves crystals translational invariance phonons 8 / 38
9 The axial vector current Y. Nambu, Phys. Rev. Lett. 4, 380 (1960) Electromagnetic current ψγ µ ψ Axial current ψγ5 γ µ ψ The axial current is the analog of the electromagnetic current in BCS theory. In the hypothesis of exact conservation, the matrix elements of the axial current between nucleon states of four-momentum p and p have the form Γ A µ (p, p) = ( iγ 5 γ µ 2mγ 5 q µ /q 2) F (q 2 ) q = p p Conservation is compatible with a finite nucleon mass m provided there exists a massless pseudoscalar particle, the Nambu-Goldstone boson. 9 / 38
10 In Nature, the axial current is only approximately conserved. Nambu s hypothesis was that the small violation of axial current conservation gives a mass to the N-G boson, which is then identified with the π meson. Under this hypothesis, one can write ( Γµ A (p, p) iγ 5 γ µ 2mγ ) 5q µ q 2 + m 2 F (q 2 ) q = p p π This expression implies a relationship between the pion nucleon coupling constant G π, the pion decay coupling g π and the axial current β-decay constant g A 2mg A 2G π g π This is the Goldberger Treiman relation 10 / 38
11 An encouraging calculation Y. Nambu, G. Jona-Lasinio, Phys. Rev. 124, 246 (1961), Appendix It was experimentally known that the ratio between the axial vector and vector β-decay constants R = g A /g V was slightly greater than 1 and about The following two hypotheses were then natural: 1. under strict axial current conservation there is no renormalization of g A ; 2. the violation of the conservation gives rise to the finite pion mass as well as to the ratio R > 1 so that there is some relation between these quantities. Under these assumptions a perturbative calculation gave a value of R close to the experimental one. More important, the renormalization effect due to a positive pion mass went in the right direction. 11 / 38
12 12 / 38
13 The NJL model: an informal presentation 1960 Midwest Conference in Theoretical Physics, Purdue University 13 / 38
14 14 / 38
15 The Nambu Jona-Lasinio (NJL) model Y. Nambu, G. Jona-Lasinio, Phys. Rev. 122, 345 (1961) The Lagrangian of the model is L = ψγ µ µ ψ + g [ ( ψψ) 2 ( ψγ 5 ψ) 2] It is invariant under ordinary and γ 5 gauge transformations ψ e iα ψ, ψ ψe iα ψ e iαγ 5 ψ, ψ ψe iαγ 5 15 / 38
16 Mean field approximation x = m = g 0mi 2π 4 d 4 p p 2 m 2 iε F (p, Λ) 16 / 38
17 The spectrum of the NJL model Mass equation 2π 2 ) (1 gλ 2 = 1 m2 Λ 2 ln + Λ2 m 2 where Λ is the invariant cut-off Spectrum of bound states nucleon mass µ spin-parity spectroscopic number notation S 0 0 2m P 0 0 µ 2 > 8 3 m2 1 ±2 µ 2 > 2m P 1 S 0 17 / 38
18 Other examples of BCS type SSB 3 He superfluidity Nuleon pairing in nuclei Fermion mass generation in the electro-weak sector of the standard model Nambu calls the last entry my biased opinion, there being other interpretations as to the nature of the Higgs field 18 / 38
19 Broken symmetry and the mass of gauge vector mesons P. W. Anderson, Phys. Rev. 130, 439 (1963) F. Englert, R. Brout, Phys. Rev. Lett. 13, 321 (1964) P. W. Higgs, Phys. Rev. Lett. 13, 508 (1964) A simple example (Englert, Brout). Consider a complex scalar field ϕ = (ϕ 1 + iϕ 2 )/ 2 interacting with an abelian gauge field A µ H int = iea µ ϕ µ ϕ e 2 ϕ ϕa µ A µ If the vacuum expectation value of ϕ is 0, e.g. ϕ = ϕ 1 / 2, the polarization loop Π µν for the field A µ in lowest order perturbation theory is Π µν (q) = (2π) 4 ie 2 ϕ 1 2 [ g µν ( q µ q ν /q 2)] Therefore the A µ field acquires a mass µ 2 = e 2 ϕ 1 2 and gauge invariance is preserved, q µ Π µν = / 38
20 Electroweak unification S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967) Leptons interact only with photons, and with the intermediate bosons that presumably mediate weak interaction. What could be more natural than to unite these spin-one bosons into a multiplet of gauge fields? Standing in the way of this synthesis are the obvious differences in the masses of the photon and intermediate meson, and in their couplings. We might hope to understand these differences by imagining that the symmetries relating the weak and the electromagnetic interactions are exact symmetries of the Lagrangian but are broken by the vacuum. 20 / 38
21 The NJL model as a low-energy effective theory of QCD e.g. T. Hatsuda, T. Kunihiro, Phys. Rep. 247, 221 (1994) The NJL model has been reinterpreted in terms of quark variables. One is interested in the low energy degrees of freedom on a scale smaller than some cut-off Λ 1 Gev. The short distance dynamics above Λ is dictated by perturbative QCD and is treated as a small perturbation. Confinement is also treated as a small perturbation. The total Lagrangian is then L QCD L NJL + L KMT + ε (L conf + L OGE ) where the Kobayashi Maskawa t Hooft term L KMT = g D det i,j [ q i(1 γ 5 )q j + h.c.] mimics the axial anomaly and L OGE is the one gluon exchange potential. 21 / 38
22 Analysis of the mean field approximation x = m = g 0mi 2π 4 d 4 p p 2 m 2 iε F (p, Λ) This equation has the obvious solution m = 0 but if 2π 2 g 0 Λ 2 < 1 there is a second non zero solution which lowers the energy of the vacuum. 22 / 38
23 The Bogolubov-Valatin transformation 23 / 38
24 Structure of the vacuum Since the sum in expoment is negative and divergent we have (Ω (0), Ω (m) ) = 0 24 / 38
25 Chiral transformations of the vacuum the sum in the exponent is negative and divergent so that (Ω (m) α, Ω (m) α ) = 0 25 / 38
26 Nucleon-nucleon scattering 26 / 38
27 Due to the mass self-consistency equation J P (0) = 1 27 / 38
28 Summary 28 / 38
29 Chirality conservation and soft pion production Y. Nambu, D. Lurie, Phys. Rev. 125, 1429 (1962). An effective model consisting of a nucleon field ψ of mass m and a massless pseudoscalar field varφ(pion) coupled through 29 / 38
30 Chirality is defined by One verifies that < in χ in >=< out χ out > 30 / 38
31 A small fermion bare mass For the observed value of µ 2 /4m 2 1 1/200 we have m0 1 5Mev. 31 / 38
32 The effective action G. Jona-Lasinio, Nuovo Cimento 34, 1790 (1964) Define the partition function Z[J] = 0 T exp i[ dx(l I + J i Φ i )] 0 where the fields Φ i transform, e.g., according to the fundamental representation of the orthogonal group. Then G[J] = i log Z[J] is the generator of the time ordered vacuum expectation values (in statistical mechanics G is the free energy in the presence of an external field J) δg δj = Φ = φ The effective action is the dual functional Γ[φ] defined by the Legendre transformation δγ δφ = J 32 / 38
33 The vacuum of the theory is defined by the variational principle δγ δφ = 0 Γ[φ] is the generator of the vertex functions and can be constructed by simple diagrammatic rules. Its general form is Γ[φ] = L cl [φ] + Q[φ] 33 / 38
34 Proof of the Goldstone theorem Consider an infinitesimal transformation of the group δφ = t ij φ j. Due to the invariance of the effective action Γ we find which implies 1 ij (q = 0)t jkφ k = 0 det[ 1 ij (q = 0)] = 0 34 / 38
35 The mass hierarchy problem Y. Nambu, Masses as a problem and as a clue, May 2004 Unlike the internal quantum numbers like charge and spin, mass is not quantized in regular manner Mass receives contributions from interactions. In other words, it is dynamical. The masses form hierarchies. Hierarchical structure is an outstanding feature of the universe in terms of size as well of mass. Elementary particles are no exception. 35 / 38
36 Einstein used to express dissatisfaction with his famous equation of gravity G µν = 8πGT µν His point was that, from an aesthetic point of view, the left hand side of the equation which describes the gravitational field is based on a beautiful geometrical principle, whereas the right hand side, which describes everything else,... looks arbitrary and ugly.... [today] Since gauge fields are based on a beautiful geometrical principle, one may shift them to the left hand side of Einstein s equation. What is left on the right are the matter fields which act as the source for the gauge fields... Can one geometrize the matter fields and shift everything to the left? 36 / 38
37 Hierarchical spontaneous symmetry breaking Y. Nambu, Masses as a problem and as a clue, May 2004 The BCS mechanism is most relevant to the mass problem because introduces an energy (mass) gap for fermions, and the Goldstone and Higgs modes as low-lying bosonic states. An interesting feature of the SSB is the possibility of hierarchical SSB or tumbling. Namely an SSB can be a cause for another SSB at lower energy scale.... [examples are] 1. the chain crystal phonon superconductivity.... Its NG mode is the phonon which then induces the Cooper pairing of electrons to cause superconductivity. 2. the chain QCD chiral SSB of quarks and hadrons π and σ mesons nuclei formation and nucleon pairing nuclear π and σ modes nuclear collective modes. 37 / 38
38 Chiral molecules 3 ed ) 0.8 ND 3 a- an 4) t), le a- h ν (cm 1 ) NH 3 0 c / 38
Nobel Lecture: Spontaneous Symmetry Breaking In Particle Physics: A Case of Cross Fertilization
EJTP 12, No. 33 (2015) 171 178 Electronic Journal of Theoretical Physics Nobel Lecture: Spontaneous Symmetry Breaking In Particle Physics: A Case of Cross Fertilization Yoichiro Nambu University of Chicago,
More informationThe Phases of QCD. Thomas Schaefer. North Carolina State University
The Phases of QCD Thomas Schaefer North Carolina State University 1 Motivation Different phases of QCD occur in the universe Neutron Stars, Big Bang Exploring the phase diagram is important to understanding
More informationAnomaly. Kenichi KONISHI University of Pisa. College de France, 14 February 2006
Anomaly Kenichi KONISHI University of Pisa College de France, 14 February 2006 Abstract Symmetry and quantization U A (1) anomaly and π 0 decay Origin of anomalies Chiral and nonabelian anomaly Anomally
More informationThe mass of the Higgs boson
The mass of the Higgs boson LHC : Higgs particle observation CMS 2011/12 ATLAS 2011/12 a prediction Higgs boson found standard model Higgs boson T.Plehn, M.Rauch Spontaneous symmetry breaking confirmed
More informationThe Standard Model of Electroweak Physics. Christopher T. Hill Head of Theoretical Physics Fermilab
The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab Lecture I: Incarnations of Symmetry Noether s Theorem is as important to us now as the Pythagorean Theorem
More informationThe Phases of QCD. Thomas Schaefer. North Carolina State University
The Phases of QCD Thomas Schaefer North Carolina State University 1 Plan of the lectures 1. QCD and States of Matter 2. The High Temperature Phase: Theory 3. Exploring QCD at High Temperature: Experiment
More informationQCD and the Nambu Jona-Lasinio Model
Lecture 1 QCD and the Nambu Jona-Lasinio Model Ian Cloët The University of Adelaide & Argonne National Laboratory CSSM Summer School Non-perturbative Methods in Quantum Field Theory 11 th 15 th February
More informationη π 0 γγ decay in the three-flavor Nambu Jona-Lasinio model
TIT/HEP-38/NP INS-Rep.-3 η π 0 γγ decay in the three-flavor Nambu Jona-Lasinio model arxiv:hep-ph/96053v 8 Feb 996 Y.Nemoto, M.Oka Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 5,
More informationQCD Symmetries in eta and etaprime mesic nuclei
QCD Symmetries in eta and etaprime mesic nuclei Steven Bass Chiral symmetry, eta and eta physics: the masses of these mesons are 300-400 MeV too big for them to be pure Goldstone bosons Famous axial U(1)
More informationQuark matter and the high-density frontier. Mark Alford Washington University in St. Louis
Quark matter and the high-density frontier Mark Alford Washington University in St. Louis Outline I Quarks at high density Confined, quark-gluon plasma, color superconducting II Color superconducting phases
More informationMay 7, Physics Beyond the Standard Model. Francesco Fucito. Introduction. Standard. Model- Boson Sector. Standard. Model- Fermion Sector
- Boson - May 7, 2017 - Boson - The standard model of particle physics is the state of the art in quantum field theory All the knowledge we have developed so far in this field enters in its definition:
More informationSuperfluidity and Symmetry Breaking. An Unfinished Symphony
Superfluidity and Symmetry Breaking An Unfinished Symphony The Classics The simplest model for superfluidity involves a complex scalar field that supports a phase (U(1)) symmetry in its fundamental equations,
More informationQuantum Field Theory. and the Standard Model. !H Cambridge UNIVERSITY PRESS MATTHEW D. SCHWARTZ. Harvard University
Quantum Field Theory and the Standard Model MATTHEW D. Harvard University SCHWARTZ!H Cambridge UNIVERSITY PRESS t Contents v Preface page xv Part I Field theory 1 1 Microscopic theory of radiation 3 1.1
More informationStandard Model & Beyond
XI SERC School on Experimental High-Energy Physics National Institute of Science Education and Research 13 th November 2017 Standard Model & Beyond Lecture III Sreerup Raychaudhuri TIFR, Mumbai 2 Fermions
More informationEDMs from the QCD θ term
ACFI EDM School November 2016 EDMs from the QCD θ term Vincenzo Cirigliano Los Alamos National Laboratory 1 Lecture II outline The QCD θ term Toolbox: chiral symmetries and their breaking Estimate of the
More informationIntroduction to gauge theory
Introduction to gauge theory 2008 High energy lecture 1 장상현 연세대학교 September 24, 2008 장상현 ( 연세대학교 ) Introduction to gauge theory September 24, 2008 1 / 72 Table of Contents 1 Introduction 2 Dirac equation
More informationThe Big Picture. Thomas Schaefer. North Carolina State University
The Big Picture Thomas Schaefer North Carolina State University 1 Big Questions What is QCD? What is a Phase of QCD? What is a Plasma? What is a (perfect) Liquid? What is a wqgp/sqgp? 2 What is QCD (Quantum
More informationThe Scale-Symmetric Theory as the Origin of the Standard Model
Copyright 2017 by Sylwester Kornowski All rights reserved The Scale-Symmetric Theory as the Origin of the Standard Model Sylwester Kornowski Abstract: Here we showed that the Scale-Symmetric Theory (SST)
More informationCritical lines and points. in the. QCD phase diagram
Critical lines and points in the QCD phase diagram Understanding the phase diagram Phase diagram for m s > m u,d quark-gluon plasma deconfinement quark matter : superfluid B spontaneously broken nuclear
More informationCold and dense QCD matter
Cold and dense QCD matter GCOE sympodium Feb. 15, 2010 Yoshimasa Hidaka Quantum ChromoDynamics Atom Electron 10-10 m Quantum ChromoDynamics Atom Nucleon Electron 10-10 m 10-15 m Quantum ElectroDynamics
More informationHunting New Physics in the Higgs Sector
HS Hunting New Physics in the Higgs Sector SM Higgs Sector - Test of the Higgs Mechanism Oleg Kaikov KIT, Seminar WS 2015/16 Prof. Dr. M. Margarete Mühlleitner, Dr. Roger Wolf, Dr. Hendrik Mantler Advisor:
More informationIntroduction to Particle Physics. HST July 2016 Luis Alvarez Gaume 1
Introduction to Particle Physics HST July 2016 Luis Alvarez Gaume 1 Basics Particle Physics describes the basic constituents of matter and their interactions It has a deep interplay with cosmology Modern
More informationAxions. Kerstin Helfrich. Seminar on Theoretical Particle Physics, / 31
1 / 31 Axions Kerstin Helfrich Seminar on Theoretical Particle Physics, 06.07.06 2 / 31 Structure 1 Introduction 2 Repetition: Instantons Formulae The θ-vacuum 3 The U(1) and the strong CP problem The
More informationBethe Salpeter studies of mesons beyond rainbow-ladder
Bethe Salpeter studies of mesons beyond rainbow-ladder Richard Williams 1 st June 2010 12th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon College of William and Mary,
More informationPions are Special Contents Chiral Symmetry and Its Breaking Symmetries and Conservation Laws Goldstone Theorem The Potential Linear Sigma Model Wigner
Lecture 3 Pions as Goldstone Bosons of Chiral Symmetry Breaking Adnan Bashir, IFM, UMSNH, Mexico August 2013 Hermosillo Sonora Pions are Special Contents Chiral Symmetry and Its Breaking Symmetries and
More informationQCD Phase Transitions and Quark Quasi-particle Picture
QCD Phase Transitions and Quark Quasi-particle Picture Teiji Kunihiro (YITP, Kyoto) YITP workshop New Developments on Nuclear Self-consistent Mean-field Theories May 30 June 1, 2005 YITP, Kyoto 1.Introduction
More informationAn Introduction to the Standard Model of Particle Physics
An Introduction to the Standard Model of Particle Physics W. N. COTTINGHAM and D. A. GREENWOOD Ж CAMBRIDGE UNIVERSITY PRESS Contents Preface. page xiii Notation xv 1 The particle physicist's view of Nature
More informationchapter 3 Spontaneous Symmetry Breaking and
chapter 3 Spontaneous Symmetry Breaking and Nambu-Goldstone boson History 1961 Nambu: SSB of chiral symmetry and appearance of zero mass boson Goldstone s s theorem in general 1964 Higgs (+others): consider
More informationSpeculations on extensions of symmetry and interctions to GUT energies Lecture 16
Speculations on extensions of symmetry and interctions to GUT energies Lecture 16 1 Introduction The use of symmetry, as has previously shown, provides insight to extensions of present physics into physics
More informationLecture 03. The Standard Model of Particle Physics. Part II The Higgs Boson Properties of the SM
Lecture 03 The Standard Model of Particle Physics Part II The Higgs Boson Properties of the SM The Standard Model So far we talked about all the particles except the Higgs If we know what the particles
More informationHiggs Boson Phenomenology Lecture I
iggs Boson Phenomenology Lecture I Laura Reina TASI 2011, CU-Boulder, June 2011 Outline of Lecture I Understanding the Electroweak Symmetry Breaking as a first step towards a more fundamental theory of
More informationQCD in the light quark (up & down) sector (QCD-light) has two mass scales M(GeV)
QCD in the light quark (up & down) sector (QCD-light) has two mass scales M(GeV) 1 m N m ρ Λ QCD 0 m π m u,d In a generic physical system, there are often many scales involved. However, for a specific
More informationOutline. Charged Leptonic Weak Interaction. Charged Weak Interactions of Quarks. Neutral Weak Interaction. Electroweak Unification
Weak Interactions Outline Charged Leptonic Weak Interaction Decay of the Muon Decay of the Neutron Decay of the Pion Charged Weak Interactions of Quarks Cabibbo-GIM Mechanism Cabibbo-Kobayashi-Maskawa
More informationWeak interactions and vector bosons
Weak interactions and vector bosons What do we know now about weak interactions? Theory of weak interactions Fermi's theory of weak interactions V-A theory Current - current theory, current algebra W and
More informationPHASE TRANSITIONS AND SPONTANEOUSLY BROKEN SYMMETRIES 1
PHASE TRANSITIONS AND SPONTANEOUSLY BROKEN SYMMETRIES 1 Roelof Bijker Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico Keywords: Spontaneously broken symmetries, global
More informationPhysics 4213/5213 Lecture 1
August 28, 2002 1 INTRODUCTION 1 Introduction Physics 4213/5213 Lecture 1 There are four known forces: gravity, electricity and magnetism (E&M), the weak force, and the strong force. Each is responsible
More informationThe BEH Mechanism and its Scalar Boson
Le Boson H, Séminaire Poincaré XIX (2014) 27 45 Séminaire Poincaré The BEH Mechanism and its Scalar Boson François Englert Service de Physique Théorique CP225 Université Libre de Bruxelles Boulevard du
More informationQuantum Field Theory 2 nd Edition
Quantum Field Theory 2 nd Edition FRANZ MANDL and GRAHAM SHAW School of Physics & Astromony, The University of Manchester, Manchester, UK WILEY A John Wiley and Sons, Ltd., Publication Contents Preface
More informationOn the Higgs mechanism in the theory of
On the Higgs mechanism in the theory of superconductivity* ty Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften D-85748 Garching Outline Phenomenological
More informationIntroduction to the Standard Model New Horizons in Lattice Field Theory IIP Natal, March 2013
Introduction to the Standard Model New Horizons in Lattice Field Theory IIP Natal, March 2013 Rogerio Rosenfeld IFT-UNESP Lecture 1: Motivation/QFT/Gauge Symmetries/QED/QCD Lecture 2: QCD tests/electroweak
More informationPart III The Standard Model
Part III The Standard Model Theorems Based on lectures by C. E. Thomas Notes taken by Dexter Chua Lent 2017 These notes are not endorsed by the lecturers, and I have modified them (often significantly)
More informationSUNY Stony Brook August 16, Wolfram Weise. with. Thomas Hell Simon Rössner Claudia Ratti
SUNY Stony Brook August 16, 27 PHASES of QCD POLYAKOV LOOP and QUASIPARTICLES Wolfram Weise with Thomas Hell Simon Rössner Claudia Ratti C. Ratti, M. Thaler, W. Weise: Phys. Rev. D 73 (26) 1419 C. Ratti,
More informationContents. Preface to the First Edition Preface to the Second Edition
Contents Preface to the First Edition Preface to the Second Edition Notes xiii xv xvii 1 Basic Concepts 1 1.1 History 1 1.1.1 The Origins of Nuclear Physics 1 1.1.2 The Emergence of Particle Physics: the
More informationParticle Physics I Lecture Exam Question Sheet
Particle Physics I Lecture Exam Question Sheet Five out of these 16 questions will be given to you at the beginning of the exam. (1) (a) Which are the different fundamental interactions that exist in Nature?
More informationAnomalies and discrete chiral symmetries
Anomalies and discrete chiral symmetries Michael Creutz BNL & U. Mainz Three sources of chiral symmetry breaking in QCD spontaneous breaking ψψ 0 explains lightness of pions implicit breaking of U(1) by
More informationGauge Symmetry in QED
Gauge Symmetry in QED The Lagrangian density for the free e.m. field is L em = 1 4 F µνf µν where F µν is the field strength tensor F µν = µ A ν ν A µ = Thus L em = 1 (E B ) 0 E x E y E z E x 0 B z B y
More informationOUTLINE. CHARGED LEPTONIC WEAK INTERACTION - Decay of the Muon - Decay of the Neutron - Decay of the Pion
Weak Interactions OUTLINE CHARGED LEPTONIC WEAK INTERACTION - Decay of the Muon - Decay of the Neutron - Decay of the Pion CHARGED WEAK INTERACTIONS OF QUARKS - Cabibbo-GIM Mechanism - Cabibbo-Kobayashi-Maskawa
More informationElectric Dipole Moments and the strong CP problem
Electric Dipole Moments and the strong CP problem We finally understand CP viola3on.. QCD theta term Jordy de Vries, Nikhef, Amsterdam Topical Lectures on electric dipole moments, Dec. 14-16 Introductory
More informationDark matter and IceCube neutrinos
IL NUOVO CIMENTO 38 C (2015) 31 DOI 10.1393/ncc/i2015-15031-4 Colloquia: IFAE 2014 Dark matter and IceCube neutrinos R. Biondi Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi di L Aquila,
More informationLectures on Chiral Perturbation Theory
Lectures on Chiral Perturbation Theory I. Foundations II. Lattice Applications III. Baryons IV. Convergence Brian Tiburzi RIKEN BNL Research Center Chiral Perturbation Theory I. Foundations Low-energy
More informationPARTICLE PHYSICS Major Option
PATICE PHYSICS Major Option Michaelmas Term 00 ichard Batley Handout No 8 QED Maxwell s equations are invariant under the gauge transformation A A A χ where A ( φ, A) and χ χ ( t, x) is the 4-vector potential
More informationSymmetries in Effective Field Theory
Symmetries in Effective Field Theory Sourendu Gupta SERC Main School 2014, BITS Pilani Goa, India Effective Field Theories December, 2014 Outline Outline Symmetries in EFTs Softly broken symmetries in
More informationGenesis of Electroweak. Unification
Unification Tom Kibble Imperial College London ICTP October 2014 1 Outline Development of the electroweak theory, which incorporates the idea of the Higgs boson as I saw it from my standpoint in Imperial
More informationTheory toolbox. Chapter Chiral effective field theories
Chapter 3 Theory toolbox 3.1 Chiral effective field theories The near chiral symmetry of the QCD Lagrangian and its spontaneous breaking can be exploited to construct low-energy effective theories of QCD
More information4. The Standard Model
4. The Standard Model Particle and Nuclear Physics Dr. Tina Potter Dr. Tina Potter 4. The Standard Model 1 In this section... Standard Model particle content Klein-Gordon equation Antimatter Interaction
More informationOutline. Charged Leptonic Weak Interaction. Charged Weak Interactions of Quarks. Neutral Weak Interaction. Electroweak Unification
Weak Interactions Outline Charged Leptonic Weak Interaction Decay of the Muon Decay of the Neutron Decay of the Pion Charged Weak Interactions of Quarks Cabibbo-GIM Mechanism Cabibbo-Kobayashi-Maskawa
More informationLecture III: Higgs Mechanism
ecture III: Higgs Mechanism Spontaneous Symmetry Breaking The Higgs Mechanism Mass Generation for eptons Quark Masses & Mixing III.1 Symmetry Breaking One example is the infinite ferromagnet the nearest
More informationarxiv:hep-ph/ v1 1 Feb 2005
Vector Goldstone Boson and Lorentz Invariance arxiv:hep-ph/050011v1 1 Feb 005 Ling-Fong Li Department of Physics, Carnegie Mellon University, Pittsburgh, PA 1513 January 5, 018 Abstract Spontanous symmetry
More informationOverview. The quest of Particle Physics research is to understand the fundamental particles of nature and their interactions.
Overview The quest of Particle Physics research is to understand the fundamental particles of nature and their interactions. Our understanding is about to take a giant leap.. the Large Hadron Collider
More informationHiggs mechanism and Goldstone s bosons
Remigiusz Durka Instytut Fizyki Teoretycznej Wroclaw March 15, 2008 1 / 28 Spontaneous symmetry breaking In physics spontaneous symmetry breaking takes place when a system, that is symmetric with respect
More informationPNJL Model and QCD Phase Transitions
PNJL Model and QCD Phase Transitions Hiromichi Nishimura Washington University in St. Louis INT Workshop, Feb. 25, 2010 Phase Transitions in Quantum Chromodynamics This Talk Low Temperature Lattice and
More informationHeavy quarks within electroweak multiplet
Heavy quarks within electroweak multiplet Jaime Besprosvany En colaboración: Ricardo Romero Instituto de Física Universidad Nacional Autónoma de México Instituto de Ciencias Nucleares, UNAM, 15 de marzo
More informationYou may not start to read the questions printed on the subsequent pages until instructed to do so by the Invigilator.
MATHEMATICAL TRIPOS Part III Monday 7 June, 004 1.30 to 4.30 PAPER 48 THE STANDARD MODEL Attempt THREE questions. There are four questions in total. The questions carry equal weight. You may not start
More informationThe God particle at last? Astronomy Ireland, Oct 8 th, 2012
The God particle at last? Astronomy Ireland, Oct 8 th, 2012 Cormac O Raifeartaigh Waterford Institute of Technology CERN July 4 th 2012 (ATLAS and CMS ) A new particle of mass 125 GeV I The Higgs boson
More informationEvaluation of Triangle Diagrams
Evaluation of Triangle Diagrams R. Abe, T. Fujita, N. Kanda, H. Kato, and H. Tsuda Department of Physics, Faculty of Science and Technology, Nihon University, Tokyo, Japan E-mail: csru11002@g.nihon-u.ac.jp
More informationSTANDARD MODEL and BEYOND: SUCCESSES and FAILURES of QFT. (Two lectures)
STANDARD MODEL and BEYOND: SUCCESSES and FAILURES of QFT (Two lectures) Lecture 1: Mass scales in particle physics - naturalness in QFT Lecture 2: Renormalisable or non-renormalisable effective electroweak
More informationA first trip to the world of particle physics
A first trip to the world of particle physics Itinerary Massimo Passera Padova - 13/03/2013 1 Massimo Passera Padova - 13/03/2013 2 The 4 fundamental interactions! Electromagnetic! Weak! Strong! Gravitational
More informationThe SU(3) Group SU(3) and Mesons Contents Quarks and Anti-quarks SU(3) and Baryons Masses and Symmetry Breaking Gell-Mann Okubo Mass Formulae Quark-Mo
Lecture 2 Quark Model The Eight Fold Way Adnan Bashir, IFM, UMSNH, Mexico August 2014 Culiacán Sinaloa The SU(3) Group SU(3) and Mesons Contents Quarks and Anti-quarks SU(3) and Baryons Masses and Symmetry
More informationSymmetry Groups conservation law quantum numbers Gauge symmetries local bosons mediate the interaction Group Abelian Product of Groups simple
Symmetry Groups Symmetry plays an essential role in particle theory. If a theory is invariant under transformations by a symmetry group one obtains a conservation law and quantum numbers. For example,
More informationElectroweak Theory & Neutrino Scattering
Electroweak Theory & 01.12.2005 Electroweak Theory & Contents Glashow-Weinberg-Salam-Model Electroweak Theory & Contents Glashow-Weinberg-Salam-Model Electroweak Theory & Contents Glashow-Weinberg-Salam-Model
More informationAxions Theory SLAC Summer Institute 2007
Axions Theory p. 1/? Axions Theory SLAC Summer Institute 2007 Helen Quinn Stanford Linear Accelerator Center Axions Theory p. 2/? Lectures from an Axion Workshop Strong CP Problem and Axions Roberto Peccei
More informationLecture 7 SUSY breaking
Lecture 7 SUSY breaking Outline Spontaneous SUSY breaking in the WZ-model. The goldstino. Goldstino couplings. The goldstino theorem. Reading: Terning 5.1, 5.3-5.4. Spontaneous SUSY Breaking Reminder:
More informationQuarks, Leptons and Gauge Fields Downloaded from by on 03/13/18. For personal use only.
QUARKS, LEPTONS & GAUGE FIELDS 2nd edition Kerson Huang Professor of Physics Mussuchusetts Institute qf Technology Y 8 World Scientific Singapore New Jersey London Hong Kong Publirhed by World Scientific
More informationSymmetry breaking: Pion as a Nambu-Goldstone boson
Symmetry breaking: Pion as a Nambu-Goldstone boson Stefan Kölling Universität Bonn Seminar zur theoretischen Teilchenphysik, 20.04.06 Structure 1 General theory of sponatneous symmetry breaking What it
More informationThe symmetries of QCD (and consequences)
The symmetries of QCD (and consequences) Sinéad M. Ryan Trinity College Dublin Quantum Universe Symposium, Groningen, March 2018 Understand nature in terms of fundamental building blocks The Rumsfeld
More informationElementary Particles, Flavour Physics and all that...
Elementary Particles, Flavour Physics and all that... 1 Flavour Physics The term Flavour physics was coined in 1971 by Murray Gell-Mann and his student at the time, Harald Fritzsch, at a Baskin-Robbins
More informationThe Gauge Principle Contents Quantum Electrodynamics SU(N) Gauge Theory Global Gauge Transformations Local Gauge Transformations Dynamics of Field Ten
Lecture 4 QCD as a Gauge Theory Adnan Bashir, IFM, UMSNH, Mexico August 2013 Hermosillo Sonora The Gauge Principle Contents Quantum Electrodynamics SU(N) Gauge Theory Global Gauge Transformations Local
More informationElementary particles and typical scales in high energy physics
Elementary particles and typical scales in high energy physics George Jorjadze Free University of Tbilisi Zielona Gora - 23.01.2017 GJ Elementary particles and typical scales in HEP Lecture 1 1/18 Contents
More informationThe Higgs discovery - a portal to new physics
The Higgs discovery - a portal to new physics Department of astronomy and theoretical physics, 2012-10-17 1 / 1 The Higgs discovery 2 / 1 July 4th 2012 - a historic day in many ways... 3 / 1 July 4th 2012
More informationElementary Particle Physics
Yorikiyo Nagashima Elementary Particle Physics Volume 2: Foundations of the Standard Model WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA Contents Preface XI Acknowledgments XV Color Plates XVII Part One
More informationFYS 3510 Subatomic physics with applications in astrophysics. Nuclear and Particle Physics: An Introduction
FYS 3510 Subatomic physics with applications in astrophysics Nuclear and Particle Physics: An Introduction Nuclear and Particle Physics: An Introduction, 2nd Edition Professor Brian Martin ISBN: 978-0-470-74275-4
More informationThe Origin and Status of Spontaneous Symmetry Breaking
Pontifical Academy of Sciences, Scripta Varia 119, Vatican City 2014 www.pas.va/content/dam/accademia/pdf/sv119/sv119-englert.pdf The Origin and Status of Spontaneous Symmetry Breaking FRANÇOIS ENGLERT
More informationThe Higgs amplitude mode at the two-dimensional superfluid/mott insulator transition
The Higgs amplitude mode at the two-dimensional superfluid/mott insulator transition M. Endres et al., Nature 487 (7408), p. 454-458 (2012) October 29, 2013 Table of contents 1 2 3 4 5 Table of contents
More informationSpontaneous breaking of supersymmetry
Spontaneous breaking of supersymmetry Hiroshi Suzuki Theoretical Physics Laboratory Nov. 18, 2009 @ Theoretical science colloquium in RIKEN Hiroshi Suzuki (TPL) Spontaneous breaking of supersymmetry Nov.
More informationFINAL EXAM PHYS 625 (Fall 2013), 12/10/13
FINAL EXAM PHYS 625 (Fall 2013), 12/10/13 Name: Signature: Duration: 120 minutes Show all your work for full/partial credit Quote your answers in units of MeV (or GeV) and fm, or combinations thereof No.
More informationOne-loop corrections as the origin of spontaneous chiral symmetry breaking in the massless chiral sigma model
One-loop corrections as the origin of spontaneous chiral symmetry breaking in the massless chiral sigma model a S. Tamenaga, a H. Toki, a, b A. Haga, and a Y. Ogawa a RCNP, Osaka University b Nagoya Institute
More informationAn Introduction to. Michael E. Peskin. Stanford Linear Accelerator Center. Daniel V. Schroeder. Weber State University. Advanced Book Program
An Introduction to Quantum Field Theory Michael E. Peskin Stanford Linear Accelerator Center Daniel V. Schroeder Weber State University 4B Advanced Book Program TT Addison-Wesley Publishing Company Reading,
More information2.4 Parity transformation
2.4 Parity transformation An extremely simple group is one that has only two elements: {e, P }. Obviously, P 1 = P, so P 2 = e, with e represented by the unit n n matrix in an n- dimensional representation.
More informationContents. 1.1 Prerequisites and textbooks Physical phenomena and theoretical tools The path integrals... 9
Preface v Chapter 1 Introduction 1 1.1 Prerequisites and textbooks......................... 1 1.2 Physical phenomena and theoretical tools................. 5 1.3 The path integrals..............................
More informationThe God particle at last? Science Week, Nov 15 th, 2012
The God particle at last? Science Week, Nov 15 th, 2012 Cormac O Raifeartaigh Waterford Institute of Technology CERN July 4 th 2012 (ATLAS and CMS ) A new particle of mass 125 GeV Why is the Higgs particle
More informationLe Modèle Standard et ses extensions
Particules Élémentaires, Gravitation et Cosmologie Année 2007-08 08 Le Modèle Standard et ses extensions Cours III: 15 février f 2008 Weak Interactions: from Fermi s s model to a gauge theory 15 fevrier
More informationVersatility of the Abelian Higgs Model
Versatility of the Abelian Higgs Model Ernest Ma Physics and Astronomy Department University of California Riverside, CA 92521, USA Versatility of the Abelian Higgs Model (2013) back to start 1 Contents
More informationThe 1/N expansion method in quantum field theory
III d International School Symmetry in Integrable Systems and Nuclear Physics Tsakhkadzor, Armenia, 3-13 July 2013 The 1/N expansion method in quantum field theory Hagop Sazdjian IPN, Université Paris-Sud,
More informationTwo Fundamental Principles of Nature s Interactions
Two Fundamental Principles of Nature s Interactions Tian Ma, Shouhong Wang Supported in part by NSF, ONR and Chinese NSF http://www.indiana.edu/ fluid I. Gravity and Principle of Interaction Dynamics PID)
More informationThe Standard Model and Beyond
Paul Langacker The Standard Model and Beyond CRC PRESS Boca Raton Ann Arbor London Tokyo Contents Preface xi 1 Notation and Conventions 1 1.1 Problems............................. 5 2 Review of Perturbative
More informationAharonov-Bohm Effect and Unification of Elementary Particles. Yutaka Hosotani, Osaka University Warsaw, May 2006
Aharonov-Bohm Effect and Unification of Elementary Particles Yutaka Hosotani, Osaka University Warsaw, May 26 - Part 1 - Aharonov-Bohm effect Aharonov-Bohm Effect! B)! Fµν = (E, vs empty or vacuum!= Fµν
More informationDISCRETE SYMMETRIES IN NUCLEAR AND PARTICLE PHYSICS. Parity PHYS NUCLEAR AND PARTICLE PHYSICS
PHYS 30121 NUCLEAR AND PARTICLE PHYSICS DISCRETE SYMMETRIES IN NUCLEAR AND PARTICLE PHYSICS Discrete symmetries are ones that do not depend on any continuous parameter. The classic example is reflection
More informationMany-Body Problems and Quantum Field Theory
Philippe A. Martin Francois Rothen Many-Body Problems and Quantum Field Theory An Introduction Translated by Steven Goldfarb, Andrew Jordan and Samuel Leach Second Edition With 102 Figures, 7 Tables and
More informationElectroweak physics and the LHC an introduction to the Standard Model
Electroweak physics and the LHC an introduction to the Standard Model Paolo Gambino INFN Torino LHC School Martignano 12-18 June 2006 Outline Prologue on weak interactions Express review of gauge theories
More informationBirth of electroweak theory from an Imperial perspective
Birth of electroweak theory from an Imperial perspective Tom Kibble King s College London 2 Oct 2012 Electroweak theory Oct 2012 1 Outline Story of spontaneous symmetry breaking in gauge theories and electro-weak
More information