Particles and Deep Inelastic Scattering
|
|
- Laureen Lang
- 5 years ago
- Views:
Transcription
1 Particles and Deep Inelastic Scattering Heidi Schellman University HUGS - JLab - June 2010 June 2010 HUGS 1
2 Course Outline 1. Really basic stuff 2. How we detect particles 3. Basics of 2 2 scattering 4. Quark model of the prton 5. General models - Structure functions and QCD 6. Parton Distribution Functions June 2010 HUGS 2
3 The very very basics 1 This is a somewhat random list of the ground rules for particle physics. Particles are identical Elementary particles are identical except for kinematic properties such as their momentum, spin or position - if they have a distinguishing property they are a different kind of particle. This leads to interesting symmetries of their wave functions under exchange. Particles of spin 1/2, 3/2... (fermions) have wave functions which are anti-symmetric under exchange while those of spin 0,1,2... (bosons) have symmetric wave functions under exchange. The hypothesis that particles are identical thus leads to very strong constraints on the wave functions. One way of explaining why they are identical is to consider particles as being excitations in a field. June 2010 HUGS 3
4 Noether s Theorem: Noether s theorem (also known as Noether s first theorem) states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. Restated in physics terms a symmetry of a system implies that something is conserved and breaking that symmetry breaks the conservation law. Examples are: 1. Translational symmetry implies momentum conservation. 2. Rotational symmetry implies conservation of angular momentum. 3. Time invariance implies energy conservation. June 2010 HUGS 4
5 4. Gauge invariance - the fact that the vector potential in electromagnetism can be modified by the addition of derivatives of a scalar field Φ: A( x, t) A( x, t) + Φ( x, t) (1) φ( x, t) φ( x, t) 1 c Φ(x, t) t (2) without changing the physical fields leads to charge conservation. This can be generalized to cover the strong and weak interactions. June 2010 HUGS 5
6 The speed of light in vacuum is a constant The speed of light in vacuum is a constant, c. This leads, through a long series of arguments, to the principles of special relativity and an additional constraint, Lorentz invariance, under which quantities of different types, scalars, momentum vectors, electromagnetic tensors, transform in a well defined way under changes of reference frame. June 2010 HUGS 6
7 The uncertainty principle The uncertainty principle E t h (3) p x h (4) L φ h (5) This imposes stringent constraints on what you can observe and, if you want to measure something very small (small x) requires a higher and higher energy probe. June 2010 HUGS 7
8 The Schwarzchild radius of a black hole R 2MG c 2 (6) sets a limit on the maximum energy you can pack into a finite space. For example length scales below the Planck length of meters are probably off limits as any particle energetic enough to probe that scale is energetic enough to collapse under its own gravitation and become a black hole before it probes anything. June 2010 HUGS 8
9 Relativistic Kinematics Units The particles we study have integer charge in units of the electron charge and we use electromagnetism to accelerate them. For this reason, the electron-volt (ev), is our standard unit of energy. June 2010 HUGS 9
10 Table of common energies in electron volts kev 1000 ev X-rays MeV 10 6 ev nuclear interactions GeV 10 9 ev proton mass TeV ev modern accelerators The units of momentum are ev/c and those for mass are ev/c 2 as one would expect if E = mc 2. It is common to drop the c in the notation. If I mess up a factor of c assume it is one. June 2010 HUGS 10
11 Special Relativity Tensor notation First let me introduce tensor notation. We will often be dealing with mathematical objects which involve several Lorentz indices and we need a convenient form equivalent to 3-vectors in normal Euclidean space. In general, a vector like object can be written as x µ, the covariant form, or x µ, the contravariant form. You can convert a contravariant vector into a covariant vector by using the metric tensor g µν, which describes the geometry of your space (or time). x µ = g µν x ν ν g µν x ν June 2010 HUGS 11
12 there is an implicit sum over any index which appears once in the covariant part and once in the contra-variant part so I won t show the sum again. The metric tensor can be very simple, or very complex. Example: Normal vectors in 3-space For normal 3-space vectors x µ = (x, y, z), the metric tensor is just m ij = δ ij = (7) June 2010 HUGS 12
13 Example: Cross product and rotation in tensor notation You can define an anti-symmetric 3 dimensional tensor ɛ ijk such that ɛ 123 = ɛ 231 = ɛ 312 = 1 and ɛ 132 = ɛ 213 = ɛ 321 = 1 and the rest of the elements are zero. The cross product of two 3-vectors is then ( x y) c = x a y b ɛ abc (8) June 2010 HUGS 13
14 You can rotate a 3-vector by applying a rotation matrix R. x i = R ij x j (9) R has to be a unitary matrix like the one for rotation around the z axis. R ij = cos α sin α 0 sin α cos α (10) June 2010 HUGS 14
15 Example: Metric on the surface of a sphere If one is looking at the surface of a sphere of unit radius with coordinates (θ, φ) where θ is the polar angle, the metric tensor is: m ij = sin 2 θ (11) June 2010 HUGS 15
16 General definition of dot product The dot product between two general 1 dimensional tensors (vectors) is: (x y) = x µ y µ = g µν x µ y ν (12) The length of a vector is just x 2 = (x x) = x µ x µ = g µν x µ x ν (13) which is why g µν is called the metric - it defines the length. Note that, for the dot product to work,your vectors need to be defined at the same point, otherwise the metric on even the 2-sphere becomes pretty useless. June 2010 HUGS 16
17 Special Relativity Metrics in general relativity or in strange coordinate systems can get pretty hairy but the vectors and metric for normal space-time in the absence of large masses are much simpler. You can define a Lorentz 4-vector x µ = (ct, x, y, z) or (ct, x) which consists of the time coordinate and the x, y, z coordinates of a normal 3-vector. The coordinates are normally numbered 0-3 with 0 being the time-like coordinate and 1-3 indicating the space-like x, y and z. It is common to use the indices µ, ν, κ, ρ for the indices of Lorentz 4-vectors. June 2010 HUGS 17
18 The metric tensor in space-time with no gravity is: η µν = (14) You can see for yourself that if X µ = (ct, x, y, z) the length of X is X 2 = X µ X µ = η µν X µ X ν = c 2 t 2 x 2 y 2 z 2 = c 2 τ 2 (15) as you would expect for the proper time τ in special relativity. June 2010 HUGS 18
19 Triple product for 4-vectors The equivalent of a cross product uses a 4-dimensional tensor ɛ µνκρ in which any element with a repeated index like ɛ 1123 is zero, cyclical elements like ɛ 2301 are +1 and countercyclical elements like ɛ 0132 are 1 just as in the 3 dimensional case. x µ = ɛ µνκρ p ν q κ r ρ (16) June 2010 HUGS 19
20 Transformations on 4-vectors The simplest Lorentz transformation between two frames moving relative to each other is a boost along the z axis. All other situations can be reduced to this one by an appropriate set of rotations. From special relativity you know that if the relative velocity of the two frames is v, a position (x, y, z) at time t transforms as: ct = γ(ct + βz) x = x y = y z = γ(+βct + z) where β = v c and γ = 1 (1 β2 ) are the usual special relativity variables. June 2010 HUGS 20
21 In tensor form you would define a boost tensor Λ ν µ. Λ ν µ = γ 0 0 γβ γβ 0 0 γ (17) and do the transform as x µ = Λ ν µx ν. (18) In general you can do a transform along an arbitrary direction by doing a rotation to the frame where the motion is along the z axis, followed by the boost followed by a rotation to whatever direction you want in the new frame. June 2010 HUGS 21
22 x µ = R(1) ρ µλ ν ρr(2) κ νx κ (19) Where the R are rotation matrices with the form R ν µ = r 11 r 12 r 13 0 r 21 r 22 r 23 (20) 0 r 31 r 32 r 33 and the small r s would be the elements of the normal 3-dimensional rotation matrix. June 2010 HUGS 22
23 Note that the tensor notation keeps track of the ordering of the boosts and rotations which is important as in general 3-D rotations and boosts do not commute. R(1) ρ µr(2) ν ρ R(2) ρ µr(1) ν ρ (21) Λ ρ µr ν ρ R ρ µλ ν ρ (22) As you probably already know the 3-D rotation matrices form an algebraic group - called SO(3). So do the boosts. And the boosts and 3-D rotations combined form a larger group, the Poincaré group with Boosts and 3-D rotations as subgroups. June 2010 HUGS 23
24 Example: Muon decay in flight Fermilab used to have a 500 GeV beam of muon particles. The muon is a heavier version of the electron and has a mass of ± MeV/c 2 and decays with a 1/e lifetime of τ = ( ± ) 10 6 s into an electron, a muon neutrino and an electron anti-neutrino. This beam is aimed at a stationary hydrogen (proton + electron) target. June 2010 HUGS 24
25 Center of mass 1. What is the center of mass energy of the muon proton system if the proton is at rest and the muon has energy in the lab frame E lab? The center of mass energy is just E cm = X µ X µ where X µ is the sum of the muon and proton 4-vectors k µ and P µ k µ = (E lab, 0, 0, P µ = (Mc 2, 0, 0, 0) X µ = (E lab + Mc 2, 0, 0, E 2 lab m2 c 4 ) E 2 lab m2 c 4 ) E cm = 2E lab Mc 2 + (M 2 + m 2 )c 4 Note that if the muon beam energy E lab >> Mc 2 or mc 2, the center of mass energy is 2E lab Mc 2. June 2010 HUGS 25
26 2. What is the γ of the muon-proton center of mass system in the lab frame? We can get this from the energy in the CM which is E cm. The lab frame energy E = E lab + Mc 2 = γe cm + γβ(0) as the momentum in the cm. frame is zero. so γ = E lab + Mc 2 E cm June 2010 HUGS 26
27 3. How far does a 500 GeV muon which decays after the average lifetime τ in the center of mass travel in the laboratory? In the muon frame the muon is created at space-time position: x (1) µ = (0, 0, 0, 0) (23) and decays at the same position after a typical time τ at x (2) µ = (cτ, 0, 0, 0) (24) June 2010 HUGS 27
28 Now let s go to the emflaboratory frame where the muon has an energy of 500 GeV. γ µ = E lab mc 2 β µ = 1 1 γµ 2 The γ µ of the muon is so β µ is going to be very very close to one. June 2010 HUGS 28
29 In the laboratory frame the starting point is still at x µ (1) = (0, 0, 0, 0) but the decay point has moved. γ 0 0 γβ x (2) µ = γβ 0 0 γ x (2) µ = (γcτ, 0, 0, γβcτ) (25) The time duration between the create and decay in the lab frame is t = γτ = seconds. This is the famous time dilation effect. The distance between the creation and decay is d = γβcτ = meters. This means that despite the short lifetime of the muon, a beam of 500 GeV muons will, on average, go 3117 km before decaying. This means you can store muons in an accelerator. June 2010 HUGS 29
The ATLAS Experiment and the CERN Large Hadron Collider
The ATLAS Experiment and the CERN Large Hadron Collider HEP101-4 February 20, 2012 Al Goshaw 1 HEP 101 Today Introduction to HEP units Particles created in high energy collisions What can be measured in
More informationParticle Physics Lecture 1 : Introduction Fall 2015 Seon-Hee Seo
Particle Physics Lecture 1 : Introduction Fall 2015 Seon-Hee Seo Particle Physics Fall 2015 1 Course Overview Lecture 1: Introduction, Decay Rates and Cross Sections Lecture 2: The Dirac Equation and Spin
More informationStandard Model of Particle Physics SS 2012
Lecture: Standard Model of Particle Physics Heidelberg SS 22 Fermi Theory Standard Model of Particle Physics SS 22 2 Standard Model of Particle Physics SS 22 Fermi Theory Unified description of all kind
More informationSpecial Relativity. Chapter The geometry of space-time
Chapter 1 Special Relativity In the far-reaching theory of Special Relativity of Einstein, the homogeneity and isotropy of the 3-dimensional space are generalized to include the time dimension as well.
More informationStandard Model of Particle Physics SS 2013
Lecture: Standard Model of Particle Physics Heidelberg SS 23 Fermi Theory Standard Model of Particle Physics SS 23 2 Standard Model of Particle Physics SS 23 Weak Force Decay of strange particles Nuclear
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 informationProblem Set # 2 SOLUTIONS
Wissink P640 Subatomic Physics I Fall 007 Problem Set # SOLUTIONS 1. Easy as π! (a) Consider the decay of a charged pion, the π +, that is at rest in the laboratory frame. Most charged pions decay according
More informationStandard Model of Particle Physics SS 2013
Lecture: Standard Model of Particle Physics Heidelberg SS 013 Weak Interactions II 1 Important Experiments Wu-Experiment (1957): radioactive decay of Co60 Goldhaber-Experiment (1958): radioactive decay
More informationA Brief Introduction to Relativistic Quantum Mechanics
A Brief Introduction to Relativistic Quantum Mechanics Hsin-Chia Cheng, U.C. Davis 1 Introduction In Physics 215AB, you learned non-relativistic quantum mechanics, e.g., Schrödinger equation, E = p2 2m
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 informationParticles and Deep Inelastic Scattering
Particles and Deep Inelastic Scattering University HUGS - JLab - June 2010 June 2010 HUGS 1 k q k P P A generic scatter of a lepton off of some target. k µ and k µ are the 4-momenta of the lepton and P
More informationNeutrino Physics. Kam-Biu Luk. Tsinghua University and University of California, Berkeley and Lawrence Berkeley National Laboratory
Neutrino Physics Kam-Biu Luk Tsinghua University and University of California, Berkeley and Lawrence Berkeley National Laboratory 4-15 June, 2007 Outline Brief overview of particle physics Properties of
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 informationMassachusetts Institute of Technology Physics Department. Physics 8.20 IAP 2005 Special Relativity January 28, 2005 FINAL EXAM
Massachusetts Institute of Technology Physics Department Physics 8.20 IAP 2005 Special Relativity January 28, 2005 FINAL EXAM Instructions You have 2.5 hours for this test. Papers will be picked up promptly
More informationOutline Solutions to Particle Physics Problem Sheet 1
2010 Subatomic: Particle Physics 1 Outline Solutions to Particle Physics Problem Sheet 1 1. List all fundamental fermions in the Standard Model There are six letons and six quarks. Letons: e, ν e, µ, ν
More information1. Kinematics, cross-sections etc
1. Kinematics, cross-sections etc A study of kinematics is of great importance to any experiment on particle scattering. It is necessary to interpret your measurements, but at an earlier stage to determine
More informationLecture 3. Experimental Methods & Feynman Diagrams
Lecture 3 Experimental Methods & Feynman Diagrams Natural Units & the Planck Scale Review of Relativistic Kinematics Cross-Sections, Matrix Elements & Phase Space Decay Rates, Lifetimes & Branching Fractions
More informationExperimental Aspects of Deep-Inelastic Scattering. Kinematics, Techniques and Detectors
1 Experimental Aspects of Deep-Inelastic Scattering Kinematics, Techniques and Detectors 2 Outline DIS Structure Function Measurements DIS Kinematics DIS Collider Detectors DIS process description Dirac
More informationQuantum Field Theory Notes. Ryan D. Reece
Quantum Field Theory Notes Ryan D. Reece November 27, 2007 Chapter 1 Preliminaries 1.1 Overview of Special Relativity 1.1.1 Lorentz Boosts Searches in the later part 19th century for the coordinate transformation
More informationLecture 01. Introduction to Elementary Particle Physics
Introduction to Elementary Particle Physics Particle Astrophysics Particle physics Fundamental constituents of nature Most basic building blocks Describe all particles and interactions Shortest length
More informationLecture 9 - Applications of 4 vectors, and some examples
Lecture 9 - Applications of 4 vectors, and some examples E. Daw April 4, 211 1 Review of invariants and 4 vectors Last time we learned the formulae for the total energy and the momentum of a particle in
More informationSubatomic Physics: Particle Physics Study Guide
Subatomic Physics: Particle Physics Study Guide This is a guide of what to revise for the exam. The other material we covered in the course may appear in uestions but it will always be provided if reuired.
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 informationSECOND PUBLIC EXAMINATION. Honour School of Physics Part C: 4 Year Course. Honour School of Physics and Philosophy Part C C4: PARTICLE PHYSICS
A047W SECOND PUBLIC EXAMINATION Honour School of Physics Part C: 4 Year Course Honour School of Physics and Philosophy Part C C4: PARTICLE PHYSICS TRINITY TERM 05 Thursday, 8 June,.30 pm 5.45 pm 5 minutes
More informationGeorge Mason University. Physics 540 Spring Notes on Relativistic Kinematics. 1 Introduction 2
George Mason University Physics 540 Spring 2011 Contents Notes on Relativistic Kinematics 1 Introduction 2 2 Lorentz Transformations 2 2.1 Position-time 4-vector............................. 3 2.2 Velocity
More information1 Introduction. 1.1 The Standard Model of particle physics The fundamental particles
1 Introduction The purpose of this chapter is to provide a brief introduction to the Standard Model of particle physics. In particular, it gives an overview of the fundamental particles and the relationship
More informationQuantum Field Theory
Quantum Field Theory PHYS-P 621 Radovan Dermisek, Indiana University Notes based on: M. Srednicki, Quantum Field Theory 1 Attempts at relativistic QM based on S-1 A proper description of particle physics
More informationThe ATLAS Experiment and the CERN Large Hadron Collider
The ATLAS Experiment and the CERN Large Hadron Collider HEP101-2 April 5, 2010 A. T. Goshaw Duke University 1 HEP 101 Plan March 29: Introduction and basic HEP terminology March 30: Special LHC event:
More informationINTRODUCTION TO THE STANDARD MODEL OF PARTICLE PHYSICS
INTRODUCTION TO THE STANDARD MODEL OF PARTICLE PHYSICS Class Mechanics My office (for now): Dantziger B Room 121 My Phone: x85200 Office hours: Call ahead, or better yet, email... Even better than office
More informationMidterm Solutions. 1 1 = 0.999c (0.2)
Midterm Solutions 1. (0) The detected muon is seen km away from the beam dump. It carries a kinetic energy of 4 GeV. Here we neglect the energy loss and angular scattering of the muon for simplicity. a.
More informationSpace-Time Symmetries
Space-Time Symmetries Outline Translation and rotation Parity Charge Conjugation Positronium T violation J. Brau Physics 661, Space-Time Symmetries 1 Conservation Rules Interaction Conserved quantity strong
More informationPHY-105: Introduction to Particle and Nuclear Physics
M. Kruse, Spring 2011, Phy-105 PHY-105: Introduction to Particle and Nuclear Physics Up to 1900 indivisable atoms Early 20th century electrons, protons, neutrons Around 1945, other particles discovered.
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 informationChapter 46 Solutions
Chapter 46 Solutions 46.1 Assuming that the proton and antiproton are left nearly at rest after they are produced, the energy of the photon E, must be E = E 0 = (938.3 MeV) = 1876.6 MeV = 3.00 10 10 J
More information1 The pion bump in the gamma reay flux
1 The pion bump in the gamma reay flux Calculation of the gamma ray spectrum generated by an hadronic mechanism (that is by π decay). A pion of energy E π generated a flat spectrum between kinematical
More informationReminder about invariant mass:
Phy489 Lecture 6 Reminder about invariant mass: A system of n particles has a mass defined by M INV c = P TOT P TOT where is the total four momentum of the system P TOT = p 1 + p + p 3 +... + p n P TOT
More informationPH5211: High Energy Physics. Prafulla Kumar Behera Room: HSB-304B
PH5211: High Energy Physics Prafulla Kumar Behera E-mail:behera@iitm.ac.in Room: HSB-304B Information Class timing: Wed. 11am, Thur. 9am, Fri. 8am The course will be graded as follows: 1 st quiz (20 marks)
More informationIntroduction. Introduction to Elementary Particle Physics. Diego Bettoni Anno Accademico
Introduction Introduction to Elementary Particle Physics Diego Bettoni Anno Accademico 010-011 Course Outline 1. Introduction.. Discreet symmetries: P, C, T. 3. Isosin, strangeness, G-arity. 4. Quark Model
More informationLorentz-covariant spectrum of single-particle states and their field theory Physics 230A, Spring 2007, Hitoshi Murayama
Lorentz-covariant spectrum of single-particle states and their field theory Physics 30A, Spring 007, Hitoshi Murayama 1 Poincaré Symmetry In order to understand the number of degrees of freedom we need
More informationLorentz Transformations and Special Relativity
Lorentz Transformations and Special Relativity Required reading: Zwiebach 2.,2,6 Suggested reading: Units: French 3.7-0, 4.-5, 5. (a little less technical) Schwarz & Schwarz.2-6, 3.-4 (more mathematical)
More informationWeak interactions. Chapter 7
Chapter 7 Weak interactions As already discussed, weak interactions are responsible for many processes which involve the transformation of particles from one type to another. Weak interactions cause nuclear
More informationExperimental results on nucleon structure Lecture I. National Nuclear Physics Summer School 2013
Experimental results on nucleon structure Lecture I Barbara Badelek University of Warsaw National Nuclear Physics Summer School 2013 Stony Brook University, July 15 26, 2013 Barbara Badelek (Univ. of Warsaw
More informationFall Quarter 2010 UCSB Physics 225A & UCSD Physics 214 Homework 1
Fall Quarter 2010 UCSB Physics 225A & UCSD Physics 214 Homework 1 Problem 2 has nothing to do with what we have done in class. It introduces somewhat strange coordinates called rapidity and pseudorapidity
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 informationJoint Undergraduate Lecture Tour Higgs Physics and the Mystery of Mass. Heather Logan
1 CAP-CASCA Joint Undergraduate Lecture Tour 2009 Heather Logan With thanks to St. Mary s U., Acadia U., St. Francis Xavier U., Mount Allison U., & U. de Moncton 2 The Large Hadron Collider (LHC) is a
More informationNuclear and Particle Physics 3: Particle Physics. Lecture 1: Introduction to Particle Physics February 5th 2007
Nuclear and Particle Physics 3: Particle Physics Lecture 1: Introduction to Particle Physics February 5th 2007 Particle Physics (PP) a.k.a. High-Energy Physics (HEP) 1 Dr Victoria Martin JCMB room 4405
More informationUnits. In this lecture, natural units will be used:
Kinematics Reminder: Lorentz-transformations Four-vectors, scalar-products and the metric Phase-space integration Two-body decays Scattering The role of the beam-axis in collider experiments Units In this
More informationAPPENDIX E SPIN AND POLARIZATION
APPENDIX E SPIN AND POLARIZATION Nothing shocks me. I m a scientist. Indiana Jones You ve never seen nothing like it, no never in your life. F. Mercury Spin is a fundamental intrinsic property of elementary
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 informationSECOND PUBLIC EXAMINATION. Honour School of Physics Part C: 4 Year Course. Honour School of Physics and Philosophy Part C C4: PARTICLE PHYSICS
754 SECOND PUBLIC EXAMINATION Honour School of Physics Part C: 4 Year Course Honour School of Physics and Philosophy Part C C4: PARTICLE PHYSICS TRINITY TERM 04 Thursday, 9 June,.30 pm 5.45 pm 5 minutes
More informationElectroweak Physics. Krishna S. Kumar. University of Massachusetts, Amherst
Electroweak Physics Krishna S. Kumar University of Massachusetts, Amherst Acknowledgements: M. Grunewald, C. Horowitz, W. Marciano, C. Quigg, M. Ramsey-Musolf, www.particleadventure.org Electroweak Physics
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 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 information- ~200 times heavier than the e GeV µ travels on average. - does not interact strongly. - does emit bremsstrahlung in
Muons M. Swartz 1 Muons: everything you ve ever wanted to know The muon was first observed in cosmic ray tracks in a cloud chamber by Carl Anderson and Seth Neddermeyer in 1937. It was eventually shown
More informationAs usual, these notes are intended for use by class participants only, and are not for circulation. Week 6: Lectures 11, 12
As usual, these notes are intended for use by class participants only, and are not for circulation Week 6: Lectures, The Dirac equation and algebra March 5, 0 The Lagrange density for the Dirac equation
More informationThe Development of Particle Physics. Dr. Vitaly Kudryavtsev E45, Tel.:
The Development of Particle Physics Dr. Vitaly Kudryavtsev E45, Tel.: 0114 4531 v.kudryavtsev@sheffield.ac.uk The structure of the nucleon Electron - nucleon elastic scattering Rutherford, Mott cross-sections
More informationParticle Physics. experimental insight. Paula Eerola Division of High Energy Physics 2005 Spring Semester Based on lectures by O. Smirnova spring 2002
experimental insight e + e - W + W - µνqq Paula Eerola Division of High Energy Physics 2005 Spring Semester Based on lectures by O. Smirnova spring 2002 Lund University I. Basic concepts Particle physics
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 informationChapter 1 LORENTZ/POINCARE INVARIANCE. 1.1 The Lorentz Algebra
Chapter 1 LORENTZ/POINCARE INVARIANCE 1.1 The Lorentz Algebra The requirement of relativistic invariance on any fundamental physical system amounts to invariance under Lorentz Transformations. These transformations
More informationRelativistic Dynamics
Chapter 13 Relativistic Dynamics 13.1 Relativistic Action As stated in Section 4.4, all of dynamics is derived from the principle of least action. Thus it is our chore to find a suitable action to produce
More informationPH 253 Exam I Solutions
PH 253 Exam I Solutions. An electron and a proton are each accelerated starting from rest through a potential difference of 0.0 million volts (0 7 V). Find the momentum (in MeV/c) and kinetic energy (in
More informationDecays and Scattering. Decay Rates Cross Sections Calculating Decays Scattering Lifetime of Particles
Decays and Scattering Decay Rates Cross Sections Calculating Decays Scattering Lifetime of Particles 1 Decay Rates There are THREE experimental probes of Elementary Particle Interactions - bound states
More informationIntroduction to Neutrino Physics. TRAN Minh Tâm
Introduction to Neutrino Physics TRAN Minh Tâm LPHE/IPEP/SB/EPFL This first lecture is a phenomenological introduction to the following lessons which will go into details of the most recent experimental
More informationQuantum Numbers. F. Di Lodovico 1 EPP, SPA6306. Queen Mary University of London. Quantum Numbers. F. Di Lodovico. Quantum Numbers.
1 1 School of Physics and Astrophysics Queen Mary University of London EPP, SPA6306 Outline : Number Conservation Rules Based on the experimental observation of particle interactions a number of particle
More informationIntroduction to Modern Quantum Field Theory
Department of Mathematics University of Texas at Arlington Arlington, TX USA Febuary, 2016 Recall Einstein s famous equation, E 2 = (Mc 2 ) 2 + (c p) 2, where c is the speed of light, M is the classical
More informationGraduate Accelerator Physics. G. A. Krafft Jefferson Lab Old Dominion University Lecture 1
Graduate Accelerator Physics G. A. Krafft Jefferson Lab Old Dominion University Lecture 1 Course Outline Course Content Introduction to Accelerators and Short Historical Overview Basic Units and Definitions
More informationFUNDAMENTAL PARTICLES CLASSIFICATION! BOSONS! QUARKS! FERMIONS! Gauge Bosons! Fermions! Strange and Charm! Top and Bottom! Up and Down!
FUNDAMENTAL PARTICLES CLASSIFICATION! BOSONS! --Bosons are generally associated with radiation and are sometimes! characterized as force carrier particles.! Quarks! Fermions! Leptons! (protons, neutrons)!
More information{ } or. ( ) = 1 2 ψ n1. ( ) = ψ r2 n1,n2 (, r! 1 ), under exchange of particle label r! 1. ψ r1 n1,n2. ψ n. ψ ( x 1
Practice Modern Physics II, W08, Set 3 Question : Symmetric (Boson) and Anti-symmetric (Fermions) Wavefunction A) Consider a system of two fermions Which of the following wavefunctions can describe the
More informationLecture 8. CPT theorem and CP violation
Lecture 8 CPT theorem and CP violation We have seen that although both charge conjugation and parity are violated in weak interactions, the combination of the two CP turns left-handed antimuon onto right-handed
More informationAttempts at relativistic QM
Attempts at relativistic QM based on S-1 A proper description of particle physics should incorporate both quantum mechanics and special relativity. However historically combining quantum mechanics and
More informationGeometry and Physics. Amer Iqbal. March 4, 2010
March 4, 2010 Many uses of Mathematics in Physics The language of the physical world is mathematics. Quantitative understanding of the world around us requires the precise language of mathematics. Symmetries
More informationParticle Physics: Problem Sheet 5
2010 Subatomic: Particle Physics 1 Particle Physics: Problem Sheet 5 Weak, electroweak and LHC Physics 1. Draw a quark level Feynman diagram for the decay K + π + π 0. This is a weak decay. K + has strange
More information11 Group Theory and Standard Model
Physics 129b Lecture 18 Caltech, 03/06/18 11 Group Theory and Standard Model 11.2 Gauge Symmetry Electromagnetic field Before we present the standard model, we need to explain what a gauge symmetry is.
More informationUnits and dimensions
Particles and Fields Particles and Antiparticles Bosons and Fermions Interactions and cross sections The Standard Model Beyond the Standard Model Neutrinos and their oscillations Particle Hierarchy Everyday
More informationIX. Electroweak unification
IX. Electroweak unification The problem of divergence A theory of weak interactions only by means of W ± bosons leads to infinities e + e - γ W - W + e + W + ν e ν µ e - W - µ + µ Divergent integrals Figure
More informationWhat We Really Know About Neutrino Speeds
What We Really Know About Neutrino Speeds Brett Altschul University of South Carolina March 22, 2013 In particle physics, the standard model has been incredibly successful. If the Higgs boson discovered
More informationParticle Notes. Ryan D. Reece
Particle Notes Ryan D. Reece July 9, 2007 Chapter 1 Preliminaries 1.1 Overview of Special Relativity 1.1.1 Lorentz Boosts Searches in the later part 19th century for the coordinate transformation that
More informationWhat are the Low-Q and Large-x Boundaries of Collinear QCD Factorization Theorems?
What are the Low-Q and Large-x Boundaries of Collinear QCD Factorization Theorems? Presented by Eric Moffat Paper written in collaboration with Wally Melnitchouk, Ted Rogers, and Nobuo Sato arxiv:1702.03955
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 informationExtending the 4 4 Darbyshire Operator Using n-dimensional Dirac Matrices
International Journal of Applied Mathematics and Theoretical Physics 2015; 1(3): 19-23 Published online February 19, 2016 (http://www.sciencepublishinggroup.com/j/ijamtp) doi: 10.11648/j.ijamtp.20150103.11
More informationDEEP INELASTIC SCATTERING
DEEP INELASTIC SCATTERING Electron scattering off nucleons (Fig 7.1): 1) Elastic scattering: E = E (θ) 2) Inelastic scattering: No 1-to-1 relationship between E and θ Inelastic scattering: nucleon gets
More informationTutorial I General Relativity
Tutorial I General Relativity 1 Exercise I: The Metric Tensor To describe distances in a given space for a particular coordinate system, we need a distance recepy. The metric tensor is the translation
More informationLecture 8. September 21, General plan for construction of Standard Model theory. Choice of gauge symmetries for the Standard Model
Lecture 8 September 21, 2017 Today General plan for construction of Standard Model theory Properties of SU(n) transformations (review) Choice of gauge symmetries for the Standard Model Use of Lagrangian
More informationThe ATLAS Experiment and the CERN Large Hadron Collider
The ATLAS Experiment and the CERN Large Hadron Collider HEP101-2 January 28, 2013 Al Goshaw 1 HEP 101-2 plan Jan. 14: Introduction to CERN and ATLAS DONE Today: 1. Comments on grant opportunities 2. Overview
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 informationElementary Particles II
Elementary Particles II S Higgs: A Very Short Introduction Higgs Field, Higgs Boson, Production, Decays First Observation 1 Reminder - I Extend Abelian Higgs model to non-abelian gauge symmetry: ( x) +
More informationPhysics 231a Problem Set Number 1 Due Wednesday, October 6, 2004
Physics 231a Problem Set Number 1 Due Wednesday, October 6, 2004 Note: Some problems may be review for some of you. If the material of the problem is already well-known to you, such that doing the problem
More informationThe Standard Model (part I)
The Standard Model (part I) Speaker Jens Kunstmann Student of Physics in 5 th year at Greifswald University, Germany Location Sommerakademie der Studienstiftung, Kreisau 2002 Topics Introduction The fundamental
More information1. Introduction. Particle and Nuclear Physics. Dr. Tina Potter. Dr. Tina Potter 1. Introduction 1
1. Introduction Particle and Nuclear Physics Dr. Tina Potter Dr. Tina Potter 1. Introduction 1 In this section... Course content Practical information Matter Forces Dr. Tina Potter 1. Introduction 2 Course
More informationElementary Particle Physics Glossary. Course organiser: Dr Marcella Bona February 9, 2016
Elementary Particle Physics Glossary Course organiser: Dr Marcella Bona February 9, 2016 1 Contents 1 Terms A-C 5 1.1 Accelerator.............................. 5 1.2 Annihilation..............................
More informationLecture 6-4 momentum transfer and the kinematics of two body scattering
Lecture 6-4 momentum transfer and the kinematics of two body scattering E. Daw March 26, 2012 1 Review of Lecture 5 Last time we figured out the physical meaning of the square of the total 4 momentum in
More informationIntroduction to particle physics Lecture 7
Introduction to particle physics Lecture 7 Frank Krauss IPPP Durham U Durham, Epiphany term 2009 Outline 1 Deep-inelastic scattering and the structure of protons 2 Elastic scattering Scattering on extended
More informationThe Quark Parton Model
The Quark Parton Model Quark Model Pseudoscalar J P = 0 Mesons Vector J P = 1 Mesons Meson Masses J P = 3 /2 + Baryons J P = ½ + Baryons Resonances Resonance Detection Discovery of the ω meson Dalitz Plots
More informationEinstein Toolkit Workshop. Joshua Faber Apr
Einstein Toolkit Workshop Joshua Faber Apr 05 2012 Outline Space, time, and special relativity The metric tensor and geometry Curvature Geodesics Einstein s equations The Stress-energy tensor 3+1 formalisms
More informationChapter 32 Lecture Notes
Chapter 32 Lecture Notes Physics 2424 - Strauss Formulas: mc 2 hc/2πd 1. INTRODUCTION What are the most fundamental particles and what are the most fundamental forces that make up the universe? For a brick
More informationWeak interactions, parity, helicity
Lecture 10 Weak interactions, parity, helicity SS2011: Introduction to Nuclear and Particle Physics, Part 2 2 1 Weak decay of particles The weak interaction is also responsible for the β + -decay of atomic
More informationName : Physics 490. Practice Final (closed book; calculator, one notecard OK)
Name : Physics 490. Practice Final (closed book; calculator, one notecard OK) Problem I: (a) Give an example of experimental evidence that the partons in the nucleon (i) are fractionally charged. How can
More informationAsk class: what is the Minkowski spacetime in spherical coordinates? ds 2 = dt 2 +dr 2 +r 2 (dθ 2 +sin 2 θdφ 2 ). (1)
1 Tensor manipulations One final thing to learn about tensor manipulation is that the metric tensor is what allows you to raise and lower indices. That is, for example, v α = g αβ v β, where again we use
More informationChapter 17 The bilinear covariant fields of the Dirac electron. from my book: Understanding Relativistic Quantum Field Theory.
Chapter 17 The bilinear covariant fields of the Dirac electron from my book: Understanding Relativistic Quantum Field Theory Hans de Vries November 10, 008 Chapter Contents 17 The bilinear covariant fields
More informationPhysics 161 Homework 2 - Solutions Wednesday August 31, 2011
Physics 161 Homework 2 - s Wednesday August 31, 2011 Make sure your name is on every page, and please box your final answer. Because we will be giving partial credit, be sure to attempt all the problems,
More information