Clebsch-Gordan Coefficients

Size: px
Start display at page:

Download "Clebsch-Gordan Coefficients"

Transcription

1 Phy489 Lecture 7

2 Clebsch-Gordan Coefficients 2 j j j2 m m m 2 j= j j2 j + j j m > j m > = C jm > m = m + m Two systems with spin j and j 2 and z components m and m 2 can combine to give a system which (quantum-mechanically) is a linear combination of states having spin j from j -j 2 to j +j 2 (in integer steps) each having a z component of m = m + m 2. So if we make a measurement of the total angular momentum of a state made up of the two spin states as defined above, the square of the Clebsch-Gordan (CG) coefficient j j j2 C m m m 2 represents the probability of obtaining a measurement of J 2 = j(j+) ħ 2

3 Tables of Clebsch-Gordan Coefficients j X j 2 Table for combining spin j with spin j 2 2 j j j2 m m m 2 j= j j2 j + j j m > j m > = C jm > m = m + m J J... m m... m m 2 m m j j j2 C m m m 2

4 Problem from Last Time An electron in a hydrogen atom is in a state with orbital angular momentum number =. If the total angular momentum quantum number is j=3/2, and the z component of total angular momentum is / 2 what is the probability of finding the electron with? m s = + / 2 Need x Clebsch-Gordan Table (spin + = )

5 Clesch Gordan Coefficients from PDG Listings

6 Combine 2 spin particles as in Griffiths example 4.4 Four possible outcomes for J,M> X + + /2 + /2 + /2 - /2 - /2 + /2 /2 /2 /2 - /2 - /2 - /2 -

7 Combine 2 spin particles as in Griffiths example 4.4 X + + /2 + /2 + /2 - /2 - /2 + /2 /2 /2 /2 - /2 - /2 - / =

8 Combine 2 spin particles as in Griffiths example 4.4 X + + /2 + /2 + /2 - /2 - /2 + /2 /2 /2 /2 - /2 - /2 - / =

9 Combine 2 spin particles as in Griffiths example 4.4 X + + /2 + /2 + /2 - /2 - /2 + /2 /2 /2 /2 - /2 - /2 - / =

10 Combine 2 spin particles as in Griffiths example 4.4 X + + /2 + /2 + /2 - /2 - /2 + /2 /2 /2 /2 - /2 - /2 - / =

11 Combine 2 spin particles as in Griffiths example 4.4 X + + /2 + /2 + /2 - /2 - /2 + /2 /2 /2 /2 - /2 - /2 - /2 - =

12 Combine 2 spin particles as in Griffiths example 4.4 X + + /2 + /2 + /2 - /2 - /2 + /2 /2 /2 /2 - /2 - /2 - /2 - =

13 Combine 2 spin particles as in Griffiths example 4.4 X + + /2 + /2 + /2 - /2 - /2 + /2 /2 /2 /2 - /2 - /2 - /2 - =

14 = + /2 + /2 + /2 - /2 - /2 + /2 /2 /2 /2 - /2 - = /2 - /2 = = Can re-write this in terms of states of definite J,M

15 Spin triplet Symmetric under 2 = /2 + /2 + /2 - /2 - /2 + /2 /2 /2 /2 - /2 - /2 - /2 - = = = Spin singlet Anti -symmetric under 2

16 Spin Formalism Write spin up and spin down states as two-component spinors spin up 2 2 = spin down 2 2 = Most general state of a spin system is then (a superposition of the two): α = α + β α, β β complex Probability that measurement of S z yields ħ/2 (e.g. spin up) is α 2 Probability that measurement of S z yields -ħ/2 (e.g. spin down) is β 2

17 Spin Matrices What about measurements of S x and S y? Must also be either ± ħ/2, but with what probability? To each component of S there is associated a 2x2 matrix Pauli spin matrix] ˆ ˆ i ˆ Sx = S y = Sz = 2 2 i 2 Each has eigenvalues of ± ħ/2 [e.g. from det( S ˆ x λi) = ] Normalized eigenvectors for S x are α = a + b a,b β 2 2 complex } χ = ± 2 ± a = 2 + b = 2 ( α β ) ( α β ) Probability of measuring S x = 2 is a 2

18 Flavour Symmetries (internal symmetries) Note that the proton (p) and neutron (n) have very similar masses: m p = MeV/c 2, m n = MeV/c 2 Heisenberg: try viewing this as two different states of the same particle (the nucleon, N). α N = = α + β p = n = β Reminiscent of spin formalism. p and n are related by a rotation in an abstract space referred to as isospin space (in analogy to spin). Adopt spin formalism to deal with systems of particles with different isospin (first for isospin in analogy to spin ). For any state we can define the isospin I and the third component I 3 (as for J). We label the components as I, I 2 and I 3 to make clear that we are not talking about components in coordinate space, but in some abstract space.

19 Warning. Isospin has NOTHING to do with real spin (e.g. angular momentum). The (confusing, so perhaps inappropriate) name is historical and comes from the similarity of the mathematical formalism, to that for handling spin. A rotation in isopin space does NOT have anything to do with rotations in physical (coordinate) space.

20 p = 2 2 Isospin We have seen that strong and electromagnetic interactions conserve strangeness, charm etc. Only the charged weak interaction can change quark flavour.there are no flavour changing neutral currents (FCNC) in the Standard Model. Isospin is just a version of conservation of quark number for u, d quarks, arising from the fact that their masses are so similar. Consider proton and neutron as members of an isospin doublet (the nucleon) n = 2 2 Heisenberg s proposal: the strong interaction is invariant under rotations in isospin space. Noether s theorem then implies that isospin is conserved in all strong interactions. Other particles fall into different isospin multiplets (each with 2I + elements) For example, pions have isospin I = (so three charge states): π π π + = = = e.g. total isospin I = /2

21 Isospin Rules for isopin assignment are a little obscure, having to do with the positions particles occupy in the eightfold way multiplets discussed in Chapter. Isospin relates states with different electric charges but very similar masses. (e.g. Hadronic states differing only in their u,d quark content) K K + sd su π π η π + ud uu, dd ud K K su sd

22 Isospin at Quark Level u = d = s = Other quark flavours (c,b,t) are also isospin singlets, like the strange quark Mesons containing u,d quarks can therefore have isospin or π π π + = ud = uu, dd = ud η = uu, dd isospin triplet I = isospin singlet I = Mesons containing only one u,d quark can only have isospin = K = us + K = ds K = us K = ds form an isospin doublet form a separate isospin doublet

23 The Eightfold Way Meson Octet (u,d,s) S = K K + isospin doublet π S = π η π + isospin triplet S = - Isospin singlet K K isospin doublet Q = - Q = Q = +

24 The Eightfold Way Baryon Octet (u,d,s) S = n p isospin doublet Σ S = - S = -2 Σ Ξ Λ Isospin singlet Ξ + Σ isospin triplet isospin doublet Q = - Q = Q = +

25 Application example: pion-nucleon scattering Six elastic πn πn processes (e.g. same particles in and out of scattering) (a) π + + p π + + p (b) π + p π + p (c) π + p π + p (d) π + + n π + + n (e) π + n π + n ( f ) π + n π + n and 4 charge-exchange processes ( ) ( ) + + g π + n π + p h π + p π + n ( ) ( ) i π + n π + p j π + p π + n Pions carry I = and nucleons, I = /2 so the total isospin can be either /2 or 3/2 Since isospin is conserved (in these strong interactions) there are two distinct amplitudes: M for I = /2 and M 3 for I = 3/2!

26 Pion-Nuclon Scattering Amplitudes π + + p : 3 3 = π π π p : = p : = n : = See Perkins Introduction to High Energy Physics section on Isospin in the pion nucleon system for more detail. (Section number varies from edition to edition; it is 3.3 in the 4th edition) π π n : = n : 3 3 = ( a) π + p π + p ( f ) π + n π + n Both are pure I = 3/2 on either side of the reaction. Both proceed purely }via the I = 3/2 amplitude M 3

27 Pion-Nucleon Scattering Amplitudes 3 2 π + p : = π + n : = ( c) π + p π + p M c = 3 M M ( ) j π + p π + n M j = M M Cross-section σ for some process is proportional to M 2

28 Relative Cross-sections for πn Scattering σ a :σ c :σ j = 9 M 3 2 : M 3 + 2M 2 : 2 M 3 M 2 At E CM = 232 MeV there is a dramatic bump (increase) in the pion-nucleon scattering cross-section, do to a πn resonance ( the Δ ). Δ carries isospin 3/2, therefore: Expect the scattering at this energy to be dominated by the isospin 3/2 channel σ a :σ c :σ j = 9 :: 2 This is listed amongst the particles on the inside cover of your text Generally, experimentally, it is easiest to measure the total cross-section, so processes (c) and (j) are combined to yield: ( ) ( π + p) = σ a σ tot π + + p σ tot σ c + σ j = 3

29 Pion-proton Scattering Cross-sections π + p π p

January 31, PHY357 Lecture 8. Quark composition of hadrons. Hadron magnetic moments. Hadron masses

January 31, PHY357 Lecture 8. Quark composition of hadrons. Hadron magnetic moments. Hadron masses January 3, 08 PHY357 Lecture 8 Quark composition of hadrons Hadron magnetic moments Hadron masses January 3, 08 Quark rules for building Hadrons! Three types of stable quark configurations established!

More information

Gian Gopal Particle Attributes Quantum Numbers 1

Gian Gopal Particle Attributes Quantum Numbers 1 Particle Attributes Quantum Numbers Intro Lecture Quantum numbers (Quantised Attributes subject to conservation laws and hence related to Symmetries) listed NOT explained. Now we cover Electric Charge

More information

Particle Physics. Michaelmas Term 2009 Prof Mark Thomson. Handout 7 : Symmetries and the Quark Model. Introduction/Aims

Particle Physics. Michaelmas Term 2009 Prof Mark Thomson. Handout 7 : Symmetries and the Quark Model. Introduction/Aims Particle Physics Michaelmas Term 2009 Prof Mark Thomson Handout 7 : Symmetries and the Quark Model Prof. M.A. Thomson Michaelmas 2009 205 Introduction/Aims Symmetries play a central role in particle physics;

More information

Lecture 9 Valence Quark Model of Hadrons

Lecture 9 Valence Quark Model of Hadrons Lecture 9 Valence Quark Model of Hadrons Isospin symmetry SU(3) flavour symmetry Meson & Baryon states Hadronic wavefunctions Masses and magnetic moments Heavy quark states 1 Isospin Symmetry Strong interactions

More information

Lecture 9. Isospin The quark model

Lecture 9. Isospin The quark model Lecture 9 Isospin The quark model There is one more symmetry that applies to strong interactions. isospin or isotopic spin It was useful in formulation of the quark picture of known particles. We can consider

More information

The Quark Parton Model

The 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 information

Problem Set # 1 SOLUTIONS

Problem Set # 1 SOLUTIONS Wissink P640 Subatomic Physics I Fall 2007 Problem Set # 1 S 1. Iso-Confused! In lecture we discussed the family of π-mesons, which have spin J = 0 and isospin I = 1, i.e., they form the isospin triplet

More information

Isospin and SU(2) Symmetry

Isospin and SU(2) Symmetry Isospin and SU() Symmetry Javier M. G. Duarte Massachusetts Institute of Technology, MA 04 (Dated: April 8, 009) We describe isospin, an abstract property of elementary particles, which reveals a deep

More information

Reminder about invariant mass:

Reminder 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 information

wave functions PhD seminar- FZ Juelich, Feb 2013

wave functions PhD seminar- FZ Juelich, Feb 2013 SU(3) symmetry and Baryon wave functions Sedigheh Jowzaee PhD seminar- FZ Juelich, Feb 2013 Introduction Fundamental symmetries of our universe Symmetry to the quark model: Hadron wave functions q q Existence

More information

Isospin. K.K. Gan L5: Isospin and Parity 1

Isospin. K.K. Gan L5: Isospin and Parity 1 Isospin Isospin is a continuous symmetry invented by Heisenberg: Explain the observation that the strong interaction does not distinguish between neutron and proton. Example: the mass difference between

More information

Homework 3: Group Theory and the Quark Model Due February 16

Homework 3: Group Theory and the Quark Model Due February 16 Homework 3: Group Theory and the Quark Model Due February 16 1. Lorentz Group. From the defining requirement that a Lorentz transformation implemented by a matrix Λ leave the metric invariant: Λ µ ρη ρσ

More information

Kern- und Teilchenphysik I Lecture 13:Quarks and QCD

Kern- und Teilchenphysik I Lecture 13:Quarks and QCD Kern- und Teilchenphysik I Lecture 13:Quarks and QCD (adapted from the Handout of Prof. Mark Thomson) Prof. Nico Serra Dr. Patrick Owen, Dr. Silva Coutinho http://www.physik.uzh.ch/de/lehre/phy211/hs2016.html

More information

Lecture 8. CPT theorem and CP violation

Lecture 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 information

The Development of Particle Physics. Dr. Vitaly Kudryavtsev E45, Tel.:

The Development of Particle Physics. Dr. Vitaly Kudryavtsev E45, Tel.: The Development of Particle Physics Dr. Vitaly Kudryavtsev E45, Tel.: 0114 2224531 v.kudryavtsev@sheffield.ac.uk Previous lecture New unstable particles discovered in 40s-50s. First hyperons (particles

More information

SU(3) symmetry and Baryon wave functions

SU(3) symmetry and Baryon wave functions INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science MPD program, co-financed by the European Union within the

More information

Dr Victoria Martin, Prof Steve Playfer Spring Semester 2013

Dr Victoria Martin, Prof Steve Playfer Spring Semester 2013 Particle Physics Dr Victoria Martin, Prof Steve Playfer Spring Semester 2013 Lecture 12: Mesons and Baryons Mesons and baryons Strong isospin and strong hypercharge SU(3) flavour symmetry Heavy quark states

More information

Partners of the SU(3) hadrons

Partners of the SU(3) hadrons Partners of the SU(3) hadrons Bernard Riley 1 The hadrons of the SU(3) J P = 0 -, ½ + and 1 - multiplets are shown to have partners of the same spin or of spin difference ½. Partnerships occur between

More information

Isospin. H. A. Tanaka

Isospin. H. A. Tanaka Isospin H. A. Tanaka Announcements Problem Set due today at 5 PM Box #7 in basement of McLennan Problem set will be posted today The Nobel Prize in Physics 05 The Royal Swedish Academy of Sciences has

More information

Discrete Transformations: Parity

Discrete Transformations: Parity Phy489 Lecture 8 0 Discrete Transformations: Parity Parity operation inverts the sign of all spatial coordinates: Position vector (x, y, z) goes to (-x, -y, -z) (eg P(r) = -r ) Clearly P 2 = I (so eigenvalues

More information

Problem Set # 4 SOLUTIONS

Problem Set # 4 SOLUTIONS Wissink P40 Subatomic Physics I Fall 007 Problem Set # 4 SOLUTIONS 1. Gee! Parity is Tough! In lecture, we examined the operator that rotates a system by 180 about the -axis in isospin space. This operator,

More information

The 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

The 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 information

Physics 125 Course Notes Identical Particles Solutions to Problems F. Porter

Physics 125 Course Notes Identical Particles Solutions to Problems F. Porter Physics 5 Course Notes Identical Particles Solutions to Problems 00 F. Porter Exercises. Let us use the Pauli exclusion principle, and the combination of angular momenta, to find the possible states which

More information

Flavour physics Lecture 1

Flavour physics Lecture 1 Flavour physics Lecture 1 Jim Libby (IITM) XI th SERC school on EHEP NISER Bhubaneswar November 2017 Lecture 1 1 Outline What is flavour physics? Some theory and history CKM matrix Lecture 1 2 What is

More information

Lecture 6 Isospin. What is Isospin? Rota4ons in Isospin space Reac4on rates Quarks and Isospin Heavier quarks FK

Lecture 6 Isospin. What is Isospin? Rota4ons in Isospin space Reac4on rates Quarks and Isospin Heavier quarks FK Lecture 6 Isospin What is Isospin? Rota4ons in Isospin space Reac4on rates Quarks and Isospin Heavier quarks FK7003 33 SU() Isospin Isospin introduced based on the observa4on that: m p = 0.9383 GeV and

More information

ψ(t) = U(t) ψ(0). (6.1.1)

ψ(t) = U(t) ψ(0). (6.1.1) Chapter 6 Symmetries 6.1 Quantum dynamics The state, or ket, vector ψ of a physical system completely characterizes the system at a given instant. The corresponding bra vector ψ is the Hermitian conjugate

More information

Lecture 6 Isospin. What is Isospin? Rota4ons in Isospin space Reac4on rates Quarks and Isospin Gell- Mann- Nishijima formula FK

Lecture 6 Isospin. What is Isospin? Rota4ons in Isospin space Reac4on rates Quarks and Isospin Gell- Mann- Nishijima formula FK Lecture 6 Isospin What is Isospin? Rota4ons in Isospin space Reac4on rates Quarks and Isospin Gell- Mann- Nishijima formula FK7003 08 SU() Isospin Isospin introduced based on the observa4on that: m p =

More information

Kern- und Teilchenphysik II Lecture 1: QCD

Kern- und Teilchenphysik II Lecture 1: QCD Kern- und Teilchenphysik II Lecture 1: QCD (adapted from the Handout of Prof. Mark Thomson) Prof. Nico Serra Dr. Marcin Chrzaszcz Dr. Annapaola De Cosa (guest lecturer) www.physik.uzh.ch/de/lehre/phy213/fs2017.html

More information

Introduction to particle physics Lecture 4

Introduction to particle physics Lecture 4 Introduction to particle physics Lecture 4 Frank Krauss IPPP Durham U Durham, Epiphany term 2009 Outline 1 Mesons and Isospin 2 Strange particles 3 Resonances 4 The quark model Nuclei, nucleons, and mesons

More information

Lecture 11 Weak interactions, Cabbibo-angle. angle. SS2011: Introduction to Nuclear and Particle Physics, Part 2

Lecture 11 Weak interactions, Cabbibo-angle. angle. SS2011: Introduction to Nuclear and Particle Physics, Part 2 Lecture 11 Weak interactions, Cabbibo-angle angle SS2011: Introduction to Nuclear and Particle Physics, Part 2 1 Neutrino-lepton reactions Consider the reaction of neutrino-electron scattering: Feynman

More information

Lecture notes Particle Physics II. Quantum Chromo Dynamics. 2. SU(2) and SU(3) Symmetry. Michiel Botje Nikhef, Science Park, Amsterdam

Lecture notes Particle Physics II. Quantum Chromo Dynamics. 2. SU(2) and SU(3) Symmetry. Michiel Botje Nikhef, Science Park, Amsterdam Lecture notes Particle Physics II Quantum Chromo Dynamics 2. SU(2) and SU(3) Symmetry Michiel Botje Nikhef, Science Park, Amsterdam November 2, 23 Symmetry in (particle) physics If the Lagrangian of the

More information

Quantum Field Theory. Ling-Fong Li. (Institute) Quark Model 1 / 14

Quantum Field Theory. Ling-Fong Li. (Institute) Quark Model 1 / 14 Quantum Field Theory Ling-Fong Li (Institute) Quark Model 1 / 14 QCD Quark Model Isospin symmetry To a good approximation, nuclear force is independent of the electromagnetic charge carried by the nucleons

More information

Coupling of Angular Momenta Isospin Nucleon-Nucleon Interaction

Coupling of Angular Momenta Isospin Nucleon-Nucleon Interaction Lecture 5 Coupling of Angular Momenta Isospin Nucleon-Nucleon Interaction WS0/3: Introduction to Nuclear and Particle Physics,, Part I I. Angular Momentum Operator Rotation R(θ): in polar coordinates the

More information

Particle Physics. Lecture 11: Mesons and Baryons

Particle Physics. Lecture 11: Mesons and Baryons Particle Physics Lecture 11: Mesons and Baryons Measuring Jets Fragmentation Mesons and Baryons Isospin and hypercharge SU(3) flavour symmetry Heavy Quark states 1 From Tuesday: Summary In QCD, the coupling

More information

Quantum Numbers. F. Di Lodovico 1 EPP, SPA6306. Queen Mary University of London. Quantum Numbers. F. Di Lodovico. Quantum Numbers.

Quantum 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 information

Examination paper for FY3403 Particle physics

Examination paper for FY3403 Particle physics Department of physics Examination paper for FY3403 Particle physics Academic contact during examination: Jan Myrheim Phone: 900 75 7 Examination date: December 6, 07 Examination time: 9 3 Permitted support

More information

Physics 492 Lecture 28

Physics 492 Lecture 28 Physics 492 Lecture 28 Main points of last lecture: Feynman diagrams. Main points of today s lecture:. Nuclear forces: charge exchange pion exchange Yukawa force deuteron charge independence, isospin symmetry

More information

Quark Model. Mass and Charge Patterns in Hadrons. Spin-1/2 baryons: Nucleons: n: MeV; p: MeV

Quark Model. Mass and Charge Patterns in Hadrons. Spin-1/2 baryons: Nucleons: n: MeV; p: MeV Mass and Charge Patterns in Hadrons To tame the particle zoo, patterns in the masses and charges can be found that will help lead to an explanation of the large number of particles in terms of just a few

More information

Signs of supersymmetry

Signs of supersymmetry Signs of supersymmetry Bernard Riley 1 Particles resulting from the breaking of symmetries are arranged symmetrically about mass levels that descend in geometric progression from the Planck Mass within

More information

Isospin: An Approximate Symmetry on the Quark Level

Isospin: An Approximate Symmetry on the Quark Level Isospin: An Approximate Symmetry on the Quark Level Molly S. Peeples molly@mit.edu Cambridge, MA 0139 April 7, 004 Abstract Isospin is an approximate symmetry which treats the up and down quarks as different

More information

Spin, Isospin and Strong Interaction Dynamics

Spin, Isospin and Strong Interaction Dynamics October, 11 PROGRESS IN PHYSICS Volume 4 Spin, Isospin and Strong Interaction Dynamics Eliahu Comay Charactell Ltd. P.O. Box 3919, Tel Aviv 6139 Israel. E-mail: elicomay@post.tau.ac.il The structure of

More information

Invariance Principles and Conservation Laws

Invariance Principles and Conservation Laws Invariance Principles and Conservation Laws Outline Translation and rotation Parity Charge Conjugation Charge Conservation and Gauge Invariance Baryon and lepton conservation CPT Theorem CP violation and

More information

Hadron Physics & Quantum Chromodynamics Adnan Bashir, IFM, UMSNH, Mexico August 2013 Hermosillo Sonora

Hadron Physics & Quantum Chromodynamics Adnan Bashir, IFM, UMSNH, Mexico August 2013 Hermosillo Sonora Hadron Physics & Quantum Chromodynamics Adnan Bashir, IFM, UMSNH, Mexico August 2013 Hermosillo Sonora Hadron Physics & QCD Part 1: First Encounter With Hadrons: Introduction to Mesons & Baryons, The Quark

More information

The Standard Model (part I)

The 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 information

Notes on SU(3) and the Quark Model

Notes on SU(3) and the Quark Model Notes on SU() and the Quark Model Contents. SU() and the Quark Model. Raising and Lowering Operators: The Weight Diagram 4.. Triangular Weight Diagrams (I) 6.. Triangular Weight Diagrams (II) 8.. Hexagonal

More information

DEEP INELASTIC SCATTERING

DEEP 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 information

PHYS 420: Astrophysics & Cosmology

PHYS 420: Astrophysics & Cosmology PHYS 420: Astrophysics & Cosmology Dr Richard H. Cyburt Assistant Professor of Physics My office: 402c in the Science Building My phone: (304) 384-6006 My email: rcyburt@concord.edu My webpage: www.concord.edu/rcyburt

More information

Properties of the proton and neutron in the quark model

Properties of the proton and neutron in the quark model Properties of the proton and neutron in the quark model A good way to introduce the ideas encoded in the quark model is to understand how it simply explains properties of the ground-state baryons and mesons

More information

Nuclear 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 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 information

Lecture 3: Quarks and Symmetry in Quarks

Lecture 3: Quarks and Symmetry in Quarks Lecture 3: Quarks and Symmetry in Quarks Quarks Cross Section, Fermions & Bosons, Wave Eqs. Symmetry: Rotation, Isospin (I), Parity (P), Charge Conjugate (C), SU(3), Gauge symmetry Conservation Laws: http://faculty.physics.tamu.edu/kamon/teaching/phys627/

More information

.! " # e " + $ e. have the same spin as electron neutrinos, and is ½ integer (fermions).

.!  # e  + $ e. have the same spin as electron neutrinos, and is ½ integer (fermions). Conservation Laws For every conservation of some quantity, this is equivalent to an invariance under some transformation. Invariance under space displacement leads to (and from) conservation of linear

More information

Baryon Resonance Determination using LQCD. Robert Edwards Jefferson Lab. Baryons 2013

Baryon Resonance Determination using LQCD. Robert Edwards Jefferson Lab. Baryons 2013 Baryon Resonance Determination using LQCD Robert Edwards Jefferson Lab Baryons 2013 Where are the Missing Baryon Resonances? What are collective modes? Is there freezing of degrees of freedom? What is

More information

Nuclear Force. Spin dependent difference in neutron scattering. Compare n-p to n-n and p-p Charge independence of nuclear force.

Nuclear Force. Spin dependent difference in neutron scattering. Compare n-p to n-n and p-p Charge independence of nuclear force. Nuclear Force Spin dependent difference in neutron scattering cross sections of ortho- and para-hydrogen. Compare n-p to n-n and p-p Charge independence of nuclear force. Nuclear and Radiation Physics,

More information

PHYS 3446 Lecture #17

PHYS 3446 Lecture #17 PHY 3446 Lecture #7 Monday, Nov. 6, 26 Dr.. Elementary Particle Properties Quantum Numbers trangeness Isospin Gell-Mann-Nishijima Relations Production and Decay of Resonances Monday, Nov. 6, 26 PHY 3446,

More information

Quarks and hadrons. Chapter Quark flavor and color

Quarks and hadrons. Chapter Quark flavor and color Chapter 5 Quarks and hadrons Every atom has its ground state the lowest energy state of its electrons in the presence of the atomic nucleus as well as many excited states which can decay to the ground

More information

Part 6: Hadrons: quantum numbers and excited states

Part 6: Hadrons: quantum numbers and excited states FYSH3, fall 3 Tuomas Lappi tuomas.v.v.lappi@jyu.fi Office: FL49. No fixed reception hours. fall 3 Part 6: Hadrons: quantum numbers and excited states Introductory remarks Properties of hadrons can be understood

More information

Quantum Numbers. Elementary Particles Properties. F. Di Lodovico c 1 EPP, SPA6306. Queen Mary University of London. Quantum Numbers. F.

Quantum Numbers. Elementary Particles Properties. F. Di Lodovico c 1 EPP, SPA6306. Queen Mary University of London. Quantum Numbers. F. Elementary Properties 1 1 School of Physics and Astrophysics Queen Mary University of London EPP, SPA6306 Outline Most stable sub-atomic particles are the proton, neutron (nucleons) and electron. Study

More information

Lie Theory in Particle Physics

Lie Theory in Particle Physics Lie Theory in Particle Physics Tim Roethlisberger May 5, 8 Abstract In this report we look at the representation theory of the Lie algebra of SU(). We construct the general finite dimensional irreducible

More information

Quantum Field Theory II

Quantum Field Theory II Quantum Field Theory II Christof Wetterich April 5, 006 This is a first draft of the script to Prof. Wetterich s QFT II lecture at the university of Heidelberg in the summer semester 006. The latest version

More information

The Λ(1405) is an anti-kaon nucleon molecule. Jonathan Hall, Waseem Kamleh, Derek Leinweber, Ben Menadue, Ben Owen, Tony Thomas, Ross Young

The Λ(1405) is an anti-kaon nucleon molecule. Jonathan Hall, Waseem Kamleh, Derek Leinweber, Ben Menadue, Ben Owen, Tony Thomas, Ross Young The Λ(1405) is an anti-kaon nucleon molecule Jonathan Hall, Waseem Kamleh, Derek Leinweber, Ben Menadue, Ben Owen, Tony Thomas, Ross Young The Λ(1405) The Λ(1405) is the lowest-lying odd-parity state of

More information

Quark Model History and current status

Quark Model History and current status Quark Model History and current status Manon Bischoff Heavy-Ion Seminar 2013 October 31, 2013 Manon Bischoff Quark Model 1 Outline Introduction Motivation and historical development Group theory and the

More information

The Λ(1405) is an anti-kaon nucleon molecule. Jonathan Hall, Waseem Kamleh, Derek Leinweber, Ben Menadue, Ben Owen, Tony Thomas, Ross Young

The Λ(1405) is an anti-kaon nucleon molecule. Jonathan Hall, Waseem Kamleh, Derek Leinweber, Ben Menadue, Ben Owen, Tony Thomas, Ross Young The Λ(1405) is an anti-kaon nucleon molecule Jonathan Hall, Waseem Kamleh, Derek Leinweber, Ben Menadue, Ben Owen, Tony Thomas, Ross Young The Λ(1405) The Λ(1405) is the lowest-lying odd-parity state of

More information

The Standard Theory of Elementary Particle Physics and Beyond

The Standard Theory of Elementary Particle Physics and Beyond The Standard Theory of Elementary Particle Physics and Beyond An Introduction in (about) 20 lectures CINVESTAV, Mexico City, Mexico 10 February-2April, 2005 Luciano Maiani, Universita di Roma La Sapienza

More information

QUANTUM MECHANIC S. Symmetries

QUANTUM MECHANIC S. Symmetries Walter Greiner Berndt Müller QUANTUM MECHANIC S Symmetries 1. Symmetries in Quantum Mechanics 1 1.1 Symmetries in Classical Physics 1 1.2 Spatial Translations in Quantum Mechanics 1 9 1.3 The Unitary

More information

INTRODUCTION TO THE STANDARD MODEL OF PARTICLE PHYSICS

INTRODUCTION 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 information

Particle Physics. All science is either physics or stamp collecting and this from a 1908 Nobel laureate in Chemistry

Particle Physics. All science is either physics or stamp collecting and this from a 1908 Nobel laureate in Chemistry Particle Physics JJ Thompson discovered electrons in 1897 Rutherford discovered the atomic nucleus in 1911 and the proton in 1919 (idea of gold foil expt) All science is either physics or stamp collecting

More information

Electron-positron pairs can be produced from a photon of energy > twice the rest energy of the electron.

Electron-positron pairs can be produced from a photon of energy > twice the rest energy of the electron. Particle Physics Positron - discovered in 1932, same mass as electron, same charge but opposite sign, same spin but magnetic moment is parallel to angular momentum. Electron-positron pairs can be produced

More information

Quark model. Jan 30, 2006 Lecture 8 1

Quark model. Jan 30, 2006 Lecture 8 1 Quark model Jan 30, 2006 Lecture 8 1 Quark model of hadrons!!!! Developed long before QCD was recognized as the appropriate quantum field theory of the strong interactions Postulate that 1.! All baryons

More information

Quarks and Hadrons. Properties of hadrons Pions and nucleons Strange particles Charm and beauty Breit-Wigner distribution Exotics

Quarks and Hadrons. Properties of hadrons Pions and nucleons Strange particles Charm and beauty Breit-Wigner distribution Exotics Quarks and Hadrons Properties of hadrons Pions and nucleons Strange particles Charm and beauty Breit-Wigner distribution Exotics J. Brau Physics 661, Quarks and Hadrons 1 Quark Flavors 3 pairs Called generations

More information

Basic Physical Chemistry Lecture 2. Keisuke Goda Summer Semester 2015

Basic Physical Chemistry Lecture 2. Keisuke Goda Summer Semester 2015 Basic Physical Chemistry Lecture 2 Keisuke Goda Summer Semester 2015 Lecture schedule Since we only have three lectures, let s focus on a few important topics of quantum chemistry and structural chemistry

More information

Quarks and hadrons. Chapter 7

Quarks and hadrons. Chapter 7 Chapter 7 Quarks and hadrons Every atom has its ground state the lowest energy state of its electrons in the presence of the atomic nucleus as well as many excited states, which can decay to the ground

More information

T 1! p k. = T r! k., s k. ', x' ] = i!, s y. ', s y

T 1! p k. = T r! k., s k. ', x' ] = i!, s y. ', s y Time Reversal r k ' = r k = T r k T 1 p k ' = p k, s k ' = s k T cannot be represented by an unitary operator. Unitary opera$ons preserve algebraic rela$ons between operators, while T changes the sign

More information

Analysis of diffractive dissociation of exclusive. in the high energetic hadron beam of the COMPASS-experiment

Analysis of diffractive dissociation of exclusive. in the high energetic hadron beam of the COMPASS-experiment Analysis of diffractive dissociation of exclusive K π`π events in the high energetic hadron beam of the -experiment Prometeusz K. Jasinski on behalf of the Collaboration Institut für Kernphysik Mainz Johann-Joachim-Becher-Weg

More information

PhysicsAndMathsTutor.com 1

PhysicsAndMathsTutor.com 1 Q1. (a) The K meson has strangeness 1. State the quark composition of a meson... State the baryon number of the K meson... (iii) What is the quark composition of the K meson?.... The figure below shows

More information

PhysicsAndMathsTutor.com

PhysicsAndMathsTutor.com OR K π 0 + µ + v ( µ ) M. (a) (i) quark antiquark pair OR qq OR named quark antiquark pair 0 (iii) us (b) (i) Weak any of the following also score mark: weak interaction weak interaction force weak nuclear

More information

Part 7: Hadrons: quarks and color

Part 7: Hadrons: quarks and color FYSH3, fall Tuomas Lappi tuomas.v.v.lappi@jyu.fi Office: FL49. No fixed reception hours. kl Part 7: Hadrons: quarks and color Introductory remarks In the previous section we looked at the properties of

More information

hybrids (mesons and baryons) JLab Advanced Study Institute

hybrids (mesons and baryons) JLab Advanced Study Institute hybrids (mesons and baryons) 2000 2000 1500 1500 1000 1000 500 500 0 0 71 the resonance spectrum of QCD or, where are you hiding the scattering amplitudes? real QCD real QCD has very few stable particles

More information

1. 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 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 information

Particle Physics Outline the concepts of particle production and annihilation and apply the conservation laws to these processes.

Particle Physics Outline the concepts of particle production and annihilation and apply the conservation laws to these processes. Particle Physics 12.3.1 Outline the concept of antiparticles and give examples 12.3.2 Outline the concepts of particle production and annihilation and apply the conservation laws to these processes. Every

More information

Angular Momentum. Andreas Wacker Mathematical Physics Lund University

Angular Momentum. Andreas Wacker Mathematical Physics Lund University Angular Momentum Andreas Wacker Mathematical Physics Lund University Commutation relations of (orbital) angular momentum Angular momentum in analogy with classical case L= r p satisfies commutation relations

More information

NATIONAL OPEN UNIVERSITY OF NIGERIA

NATIONAL OPEN UNIVERSITY OF NIGERIA NATIONAL OPEN UNIVERSITY OF NIGERIA SCHOOL OF SCIENCE AND TECHNOLOGY COURSE CODE: PHY 409 COURSE TITLE: ELEMENTARY PARTICLE PHYSICS Course Title Course Developer Course Code PHY 409 ELEMENTARY PARTICLE

More information

Nucleon Spectroscopy with Multi-Particle Operators

Nucleon Spectroscopy with Multi-Particle Operators Nucleon Spectroscopy with Multi-Particle Operators Adrian L. Kiratidis Waseem Kamleh, Derek B. Leinweber CSSM, The University of Adelaide 21st of July - LHP V 2015 - Cairns, Australia 1/41 Table of content

More information

III. Particle Physics and Isospin

III. Particle Physics and Isospin . Particle Physics and sospin Up to now we have concentrated exclusively on actual, physical rotations, either of coordinates or of spin states, or both. n this chapter we will be concentrating on internal

More information

Discovery of Pions and Kaons in Cosmic Rays in 1947

Discovery of Pions and Kaons in Cosmic Rays in 1947 Discovery of Pions and Kaons in Cosmic Rays in 947 π + µ + e + (cosmic rays) Points to note: de/dx Bragg Peak Low de/dx for fast e + Constant range (~600µm) (i.e. -body decay) small angle scattering Strange

More information

SU(3) systematization of baryons. Vadim Guzey. Theory Center, Jefferson Lab

SU(3) systematization of baryons. Vadim Guzey. Theory Center, Jefferson Lab SU(3) systematization of baryons Vadim Guzey Theory Center, Jefferson Lab In collaboration with M.V. Polyakov: V. Guzey, hep-ph/05176 V. Guzey and M.V. Polyakov, hep-ph/051355 Cake seminar, Theory Group,

More information

When Perturbation Theory Fails...

When Perturbation Theory Fails... When Perturbation Theory Fails... Brian Tiburzi (University of Maryland) When Perturbation Theory Fails... SU(3) chiral perturbation theory? Charm quark in HQET, NRQCD? Extrapolations of lattice QCD data?

More information

Quarks and the Baryons

Quarks and the Baryons Quarks and the Baryons A Review of Chapter 15 of Particles and Nuclei by Povh Evan Phelps University of South Carolina Department of Physics and Astronomy phelps@physics.sc.edu March 18, 2009 Evan Phelps

More information

DISCRETE SYMMETRIES IN NUCLEAR AND PARTICLE PHYSICS. Parity PHYS NUCLEAR AND PARTICLE PHYSICS

DISCRETE 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 information

Rotations in Quantum Mechanics

Rotations in Quantum Mechanics Rotations in Quantum Mechanics We have seen that physical transformations are represented in quantum mechanics by unitary operators acting on the Hilbert space. In this section, we ll think about the specific

More information

d 3 r d 3 vf( r, v) = N (2) = CV C = n where n N/V is the total number of molecules per unit volume. Hence e βmv2 /2 d 3 rd 3 v (5)

d 3 r d 3 vf( r, v) = N (2) = CV C = n where n N/V is the total number of molecules per unit volume. Hence e βmv2 /2 d 3 rd 3 v (5) LECTURE 12 Maxwell Velocity Distribution Suppose we have a dilute gas of molecules, each with mass m. If the gas is dilute enough, we can ignore the interactions between the molecules and the energy will

More information

The scales of atomic and particle physics in relation to Planck scale

The scales of atomic and particle physics in relation to Planck scale The scales of atomic and particle physics in relation to Planck scale B F Riley 1 The scales of atomic and particle physics are shown to be related to Planck scale through multiplication by small integer

More information

Evidence for the Strong Interaction

Evidence for the Strong Interaction Evidence for the Strong Interaction Scott Wilbur Scott Wilbur Evidence for the Strong Interaction 1 Overview Continuing search inside fundamental particles Scott Wilbur Evidence for the Strong Interaction

More information

Are these states normalized? A) Yes

Are these states normalized? A) Yes QMII-. Consider two kets and their corresponding column vectors: Ψ = φ = Are these two state orthogonal? Is ψ φ = 0? A) Yes ) No Answer: A Are these states normalized? A) Yes ) No Answer: (each state has

More information

Introduction to Gauge Theories

Introduction to Gauge Theories Introduction to Gauge Theories Basics of SU(n) Classical Fields U() Gauge Invariance SU(n) Gauge Invariance The Standard Model Michel Lefebvre University of Victoria Physics and Astronomy PHYS506B, spring

More information

Hadronic Resonances in a Hadronic Picture. Daisuke Jido (Nuclear physics group)

Hadronic Resonances in a Hadronic Picture. Daisuke Jido (Nuclear physics group) Daisuke Jido (Nuclear physics group) Hadrons (particles interacting with strong interactions) are composite objects of quarks and gluons. It has been recently suggested that the structures of some hadrons

More information

PHYS 3446 Lecture #21

PHYS 3446 Lecture #21 PHYS 3446 Lecture #21 Monday, Nov. 27, 2006 Dr. 1. The Standard Model Quarks and Leptons Gauge Bosons Symmetry Breaking and the Higgs particle Higgs Search Strategy Issues in the Standard Model Neutrino

More information

Introduction to Elementary Particles

Introduction to Elementary Particles David Criffiths Introduction to Elementary Particles Second, Revised Edition WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA Preface to the First Edition IX Preface to the Second Edition XI Formulas and Constants

More information

Production cross sections of strange and charmed baryons at Belle

Production cross sections of strange and charmed baryons at Belle Production cross sections of strange and charmed baryons at Belle Gifu University E-mail: sumihama@rcnp.osaka-u.ac.jp Production cross sections of strange and charmed baryons in the e + e annihilation

More information

The 1405 MeV Lambda Resonance in Full-QCD

The 1405 MeV Lambda Resonance in Full-QCD , Waseem Kamleh, Derek B. Leinweber, and M. Selim Mahbub Special Research Centre for the Subatomic Structure of Matter School of Chemistry & Physics, University of Adelaide, SA, 5005, Australia E-mail:

More information

PHYSICS PARTICLE. An Introductory Course of. Palash B. Pal. CRC Press. Saha Institute of Nuclear Physics. Kolkata, India. Taylor &.

PHYSICS PARTICLE. An Introductory Course of. Palash B. Pal. CRC Press. Saha Institute of Nuclear Physics. Kolkata, India. Taylor &. An Introductory Course of PARTICLE PHYSICS Palash B. Pal Saha Institute of Nuclear Physics Kolkata, India W CRC Press Taylor &. Francis Croup Boca Raton London New York CRC Press is an imprint of the &

More information