Option 212: UNIT 2 Elementary Particles

Option 212: UNIT 2 Elementary Particles
Department of Physics and Astronomy Option 212: UNIT 2 Elementary Particles SCHEDULE 7-Feb pm Dr Matt Burleigh Intro lecture 11-Feb am Prof Peter Maksym Problem solving (15-Feb pm Problem Workshop) 18-Feb am Dr Matt Burleigh Follow-up

UNIT 2: OUTLINE SYLLABUS:
1st Lecture Introduction Hadrons and Leptons Spin & Anti-Particles The conservation laws: Lepton Number Baryon number Strangeness 2nd Lecture Problem solving Check a decay for violation of conservation laws Quarks Properties of a particle given quark combination 3rd Lecture Follow-up Fundamental forces and field particles The standard model

Recommended Books Chapter 41, PA Tipler Quarks Leptons and The Big Bang, J Allday The Cosmic Onion, F Close

Web Sites Brief introduction to Particle Physics Introductions to Particle Physics CERN web site 212 Option - Lecture notes in MS Powerpoint

Elementary Particle Physics Cosmic Rays
INTRODUCTION to Elementary Particle Physics Cosmic Rays Fundamental building blocks of which all matter is composed: Elementary Particles Pre-1930s it was thought there were just four elementary particles electron proton neutron photon 1932 positron or anti-electron discovered, followed by many other particles (muon, pion etc) We will discover that the electron and photon are indeed fundamental, elementary particles, but protons and neutrons are made of even smaller elementary particles called quarks

CLASSIFICATON OF PARTICLES
An elementary particle is a point particle without structure that is not constructed from more elementary entities With the advent of particle accelerator in the 1950’s many new elementary particles were discovered. The question arose whether perhaps there were too many to all be elementary. This has led to the need for classification of particles.

FUNDAMENTAL INTERACTIONS AND THE CLASSIFICATION OF PARTICLES
Fundamental interactions Participating particles gravitation electromagnetic strong nuclear force weak nuclear force all particles with mass those carrying charge Hadrons (and quarks) Leptons (and quarks)

HADRONS Hadrons interact through strong forces. There are two classes, mesons and baryons. Mesons have zero or integral spin (0 or 1) with masses that lie between the electron and the proton. Baryons have half integral spin (1/2 or 3/2) and have masses that are always greater than or equal to that of the proton. Hadrons are not elementary particles. As we will see later, they are made of quarks

Leptons interact through weak inter-
actions, but not via the strong force. Leptons were originally named because they were “Light-particles”, but we now know the Tau is twice as heavy as a proton Neutrinos were originally thought to be massless, but they probably have a small mass Read more in Tipler p. 1336 All leptons have spin of 1/2. There are six kinds of lepton: electron e-, muon m-, and tau t -, and 3 neutrinos ne, nm, nt Note that each distinct neutrino is associated with one of the other leptons

Beta Decay and the discovery of the neutrino (Tipler p.1314)
32He + e- × 31H 32He + e- + ne √ - In Beta decay a neutron decays into a proton plus an electron If decay energy shared by proton and emitted electron, energy of electron would be unique But observed electrons have a range of energies – must be a third particle involved: the neutrino Third particle must have no charge or mass, as they are accounted for by the He nucleus and electron.

A particle has an intrinsic spin angular momentum
Spin ½ particles: Electrons, protons, neutrons and neutrinos all have an intrinsic spin characterised by the quantum number s = 1/2 Particles with half-integer spin (1/2, 3/2, 5/2, …) are called Fermions They obey the Pauli exclusion principle Particles with integer spin (s = 0, 1, 2, …. ), e.g. mesons, are called Bosons They do not need to obey the Pauli exclusion principle, and any number can occupy the same quantum state

Matter & Antimatter Every particle has an antiparticle partner
Read Tipler P.1339 to find out how Dirac predicted the existence of anti-particles in 1927 e- - electron e+ - positron p - proton p - antiproton Here are some examples n - neutron n - neutrino n - antineutron - antineutrino

Antimatter For each particle there is an associated antiparticle
Anti-particles always created in particle-anti particle pairs s s g -> e- + e+ e- e+ E2 x 511 keV Electron Pair Production

Antimatter * Antiparticle has the same mass and magnitude of spin as the particle * Antiparticle has the opposite charge to the particle The positron is stable but has a short-term existence because our Universe has a large supply of electrons The fate of a positron is annihilation Electron Pair Annihilation e- + e+ ->2 s moc2 s = 1/2 e- e+ Each photon gets eg = mec2 pg = mec s

Some Fundamental Particles
Symbol Rest energy MeV Charge Spin Antiparticle Mass less boson  1  photon Leptons Neutrino Electron Muon  e  0.511 105.7 -1 1/2  e  Meson Pion  o 140 135 +1  o Baryons Proton neutron 1/2 p- p+ no 938.3 939.6 +1 - n

Can a conceivable reaction or decay occur?
The Conservation Laws Can a conceivable reaction or decay occur? Conservation of energy The total rest mass of the decay products must be less than the initial rest mass of the particle before decay Conservation of linear momentum When an electron and a positron at rest annihilate, two photons must be emitted Angular momentum must be conserved in a decay or reaction Net electric charge before must equal net charge after a decay or reaction

The Conservation Laws Can a conceivable reaction or decay occur? Conservation of Baryon number We assign Baryon Number B=+1 to all Baryons, B=-1 to all anti-Baryons, and B=0 to all other particles Baryon number must be conserved in a reaction Conservation of Lepton number Lepton number must be conserved in a reaction BUT…..

The Conservation Laws Can a conceivable reaction or decay occur? Conservation of Lepton number contd: …..because the neutrino associated with an electron is different to a neutrino associated with a muon, we assign separate Lepton numbers Le, Lm and Lt to the particles e.g. for e and ne, Le=+1, for their anti-particles Le=-1, and for all other leptons and other particles Le=0 Conservation of Strangeness There are other conservation laws which are not universal, e.g. strange particles have a property called strangeness which must be conserved in a decay or reaction

Some Fundamental Particles
Symbol Rest energy MeV B Le Antiparticle Neutrino Electron Muon Tau Pion Kaon Proton Neutron Lambda Sigma  e  - 0.511 105.7 1784  o 140 135  p+ no L    938.3 939.6 1115.6 1189.4 1192.5 1197.3 e   L L S  photon Leptons Photon    + Hadrons Mesons K+ Ko 493.7 497.7 +1 K- Baryons p- n  Category See also Tipler Table 41-1 Page 1337 For strangeness, examine Figure 41-3 Page 1344 _ _ _ _ _ _

Checking Baryon Numbers
a) p+ + n p+ + n 2p+ + p + n p+ + p + p _ _ _ Answer: a) B = 1+1 on left hand side B = 2 on right hand side too! Allowed reaction! b) B = 2 on left hand side B = -1 on right hand side Forbidden reaction

Checking Lepton Numbers
a) µ- b) π+ e- + ne + n µ+ + n + ne _ Answer: a) Before decay Le = 0 and Lm = +1 After decay Le = 0 and Lm = +1 Allowed reaction! b) Before decay Lm = 0 and Le = 0 After decay Lm = 0 and Le = 1 Forbidden reaction!

Is Strangeness Conserved?
b) π- + p K+ +   -+  Answer: a) Initial state has S = 0 Final state has S = = 0 Allowed reaction! b) Initial state has S = 0 Final state has S = -1 Forbidden reaction!

(a) n -> p+ + p- + m+ + m- (b) p0 -> e+ + e- + g
Conservation Laws Test the following decays for violation of the conservation of electric charge, baryon number and lepton number. (a) n -> p+ + p- + m+ + m- (b) p0 -> e+ + e- + g

Conservation Laws Solution
Method: Use Table 41-1 and the conservation laws for Baryon number and Lepton number (a) n -> p+ + p- + m+ + m- Total charge on both sides = 0 : conserved Baryon number changes from +1 to 0: violated Lm = 0 on both sides : conserved Process not allowed (b) p0 -> e+ + e- + g Baryon number on both sides = 0 : conserved Le = 0 on both sides: conserved Process is allowed

Quarks - The Smallest Building Blocks of Matter
Gell–Mann & Zweig 1963

Three Different Types of QUARKS
π+ Meson There are three elementary quarks (flavors) That make up the fundamental particles: Up u Down d Strange s u d p Baryon Name Spin Charge Baryon Strangeness Up u / / / Down d / / / Strange s 1/ / / Anti-quarks maintain spin, but change sign of S and B!

Different types of quarks contd.
Mesons – quark + anti-quark ( q q ) Baryons – three quarks ( q q q ) Anti-baryons – three anti-quarks ( q q q) By 1967 it was realised that new kinds of quarks were required to explain discrepancies between the model and experiment Charm (c) Bottom (b) – discovered 1977 Top (t) – discovered 1995

Quark combinations Find the baryon number, charge & strangeness of the following quark combinations and identify the hadron: (a) uud (b) udd (c) uus (d) dds

Quark combinations Solution
Method: for each quark combination determine the baryon number B, the charge q and the strangeness S; then use Tipler Table 41-2 to find a match. (a) uud B = 1/3 + 1/3 + 1/3 = 1 q = 2/3 + 2/3 – 1/3 = 1 S = 0 It is a proton (b) udd q = 2/3 – 1 /3 – 1/ 3 = 0 It is a neutron (c) uus Ditto, B=1, q=1, S= -1 and it is a S+ (d) dds Ditto, B=1, q=-1, S= -1 and it is a S-

Quark spin The angular momentum vector of a spin ½ quark can have one of two settings up or down So a meson can have its two quark spins parallel with each other or anti-parallel: Spin Spin 0

Quark spin contd. Baryons e.g. uud: Spin 3/2 Spin 1/2
The spin ½ particle is a proton, spin 3/2 particle is a D+ Note that is also spin ½ (parallel, parallel, anti-parallel)

The Baryon Octet - Eight Spin 1/2 Baryons
EIGHT FOLD WAY PATTERNS S = 0 S = -1 S = -2 Q = +1 Q = 0 Q = -1   n    p  (ddu) (uud) The Baryon Octet - Eight Spin 1/2 Baryons

State which of the following decays or reactions violates one or more of the conservation laws, and give the law(s) violated in each case: (a) p -> n + e+ + ne (b) n -> p + p- (c) e+ + e- -> g (d) p + p -> g + g (e) ne + p -> n + e+ (a) mp < mn : energy conservation is violated. Also Le=0 on lhs, but Le=-2 on rhs (b) mn < mp + mp : energy conservation is violated (c) Momentum conservation is violated: in pair annihilation, two photons (g rays) must be emitted to conserve momentum (d) Allowed (e) Le=-1 on both sides, but mp < mn so energy conservation violated

Consider the following decay chain
X0 -> L0 + p0 L0 -> p + p- p0 -> g + g p- -> m- + nm m- -> e- + ne + nm (a) write the overall decay reaction for X0 to the final decay products (b) are the final decay products stable? (c) Check the overall decay reaction for the conservation of electric charge, baryon number, and lepton number (d) Check the overall decay reaction for conservation of strangeness. Is the reaction possible via the weak or strong interactions?

(a) X0 -> p + 2g + nm + e- + ne + nm
(b) Use Table The proton is stable for 1031 years. In contrast, the neutron is only stable for 930secs. Answer: yes, stable. (c) Charge conservation: 0 -> p + e- = 0: conserved. Baryon number 1 -> 1: conserved. Lepton number Le: 0 -> e- + ne = 1 + (-1) = 0: conserved. Lm: 0 -> = 0. (d) See Tipler p Strangeness must be conserved if reaction occurs via strong interaction. Here S=-2 on lhs and S=0 on rhs. But if DS=+/-1, then can occur via weak interaction. In first two parts of reaction, DS=1 (L0 has S=-1) so is allowed via weak interaction.

(a) Leptons consist of three quarks
True or false? (a) Leptons consist of three quarks (b) Mesons consist of a quark and an anti-quark (c) The six flavors of quark are up, down, charmed, strange, left and right (d) Neutrons have no charm (a) False: leptons are fundamental particles e.g e- (c) False: there is no left and right quark, but there are top and bottom quarks (d) True: neutrons are made of udd quarks (b) True

Quark confinement No isolated quark has ever been observed
Believed impossible to obtain an isolated quark If the PE between quarks increases with separation distance, an infinite amount of energy may be required to separate them When a large amount of energy is added to a quark system, like a nucleon, a quark-antiquark pair is created Original quarks remain confined in the original system Because quarks always confined, their mass cannot be accurately known

Quark color Consider the W- particle, which consists of three strange quarks Remember that quarks have spin ½ The W- has spin 3/2, so its three strange quarks must be arranged thus: But Pauli exclusion principle forbids these identical (same flavor, same mag of spin, same direction of spin) quarks occupying identical quantum states The only way for this to work is if each quark possesses a further property, color: Quarks in a baryon always have these three colours, such that when combined they are “color-less” ( qr , qy , qb ) In a meson, a red quark and its “anti-red” quark attract to form the particle

Field Particles In addition to the six fundamental leptons (e-, m-, t-, ne, nm, nt) and six quarks, there are field particles associated with the fundamental forces (weak, strong, gravity and electro-magnetic) For example, the photon mediates the electro-magnetic interaction, in which particles are given the property “charge” The theory governing electro-magnetic interactions at the quantum level is called Quantum Electrodynamics (QED) Similarly, gravity is mediated by the graviton The “charge” in gravity is mass The graviton has not been observed

Field Particles The weak force, which is experienced by quarks and leptons, is carried by the W+, W-, and Z0 particles These have been observed and are massive (~100 GeV/c2) The “charge” they mediate is flavor The strong force, which is experienced by quarks and hadrons, is carried by a particle called a gluon The gluon has not been observed The “charge” is color The field theory for strong interactions (analagous to QED) is called Quantum Chromodynamics (QCD)

Electroweak theory The electromagnetic and weak interactions are considered to be two manifestations of a more fundamental electroweak interaction At very high energies, >100GeV the electroweak interaction would be mediated (or carried) by four particles: W+, W-, W0, and B0 The W0 and B0 cannot be observed directly But at ordinary energies they combine to form either the Z0 or the massless photon In order to work, electroweak theory requires the existence of a particle called the Higgs Boson The Higgs Boson is expected have a rest mass > 1TeV/c2 Head-on collisions between protons at energies ~20TeV are required to produce a Higgs Boson (if they exist) Such energies will only be achieved by the next generation of particle accelerators (eg Large Hadron Collider at CERN)

The Standard Model The combination of the quark model, electroweak theory and QCD is called the Standard Model In this model, the fundamental particles are the leptons, the quarks and the force carriers (photon, W+, W-, Z0, and gluons) All matter is made up of leptons or quarks Leptons can only exist as isolated particles Hadrons (baryons and mesons) are composite particles made of quarks For every particle there is an anti-particle Leptons and Baryons obey conservation laws Every force in nature is due to one of four basic interactions: Stong, electromagnetic, weak and gravitational A particle experiences one of these basic interactions if it carries a charge associated with that interaction

Properties of the basic interactions
Gravity Weak Electro-magnetic Strong Acts on Mass Flavor Electric charge Color Particles participating All Quarks, leptons Electrically charged Quarks, Hadrons Mediating particle Graviton W+, W-, Z0 Photon Gluon

Grand Unified Theories (GUTs)
In a GUT, leptons and quarks are considered to be two aspects of a single class of particle Under certain conditions a quark could change into a lepton and vice-versa Particle quantum numbers are not conserved These conditions are thought to have existed in the very early Universe A fraction of a second after the Big Bang In this period a slight excess of quarks over anti-quarks existed, which is why there is more matter than anti-matter in out Universe today One of the predictions of GUTs is that the proton will decay after 1031 years In order to observe one decay, a large number of protons must be observed Such experiments are being attempted

Crib sheet (or what you need to know to pass the exam)
The zoo of particles and their properties Leptons (e-, m-, p-, ne , nm, np) Hadrons (baryons and mesons) Their anti-particles The conservation laws and how to apply them (energy, momentum, baryon number, lepton numbers, strangeness) Quarks and their properties Flavors: up, down, strange, charm, top ,bottom How to combine quarks to form baryons and mesons Quark spin and color The eight-fold way patterns Fundamental forces and field particles The standard model And from special relativity, its important to understand the concepts of rest mass and energy, and the equations of conservation of relativistic energy and momentum

Circular Accelerator Requires LEP: Large Electron Positron Collider
large magnetic field; B large radius; R charged particles; q

Example 1 Maximum Energy
A cyclotron has magnet poles with radius 0.50 m and a magnetic field with magnitude 1.50 T. Find the maximum particle energy if this cyclotron is used to accelerate protons. For protons q = 1.6x10-19 C and mp = 1.67x10-27 kg. SOLUTION

Forces acting on charged particles moving in a circular accelerator
Cyclotron 1. Particles moving in constant magnetic field: F = qvxB 2. Particles moving in a circular orbit: F = mv2/r 3. Particles have an angular frequency :

Wilson Cloud Chamber DELPHI Drift Chamber - CERN DETECTORS Cloud Chamber Charged particles move through a super saturated gas; a mixture of evaporated liquid and non-condensing gas. A constant magnetic field is applied perpendicular to the path of the charged particles Condensation starts around ions formed by passing charged particles and the resulting droplets are photographed

PIONS Example 3 Determine the magnitude of the momentum and the speed of a proton at a point where the observed radius of curvature of the path in a cloud chamber is r=2.67 m and the magnitude of the magnetic field is B=0.14T. Solution p = mv = qrB = 5.98x10-20 kgm/s v = p/m = 3.58 x 107 m/s

PROBLEMS For each of the following decay reactions give all possible electric charges of each particle and the energy Q released in the decay. a) π µ +  b) π g + g c) µ e- + n + n Which of the following processes are absolutely forbidden and why? p e+ + g n p + e- + ne π + π n + p n p + e+ + ne πo + n π + p n + n πo+ π+ + π- π+ + n π- + p

PROBLEMS Two body decay: A ---> B + C Show that in a frame of reference in which A is at rest the kinetic energy of particle B is given by:  In the case of scattering of pions by protons calculate the momentum pπ and the kinetic energy Tπ of the pion in the laboratory frame as a function of Etotal the total energy of the pion-proton system in the centre of mass frame. 5. Calculate the threshold for the production of an e-+e+ pair production by a photon in the presence of an initially stationary e-.

SOLUTIONS a) nµ and nµ have zero charge. Q = Mπc2 - Mµc2 = 33.9 MeV; assuming that neutrinos have have zero rest energy For initial stationary pion pn = -pµ = p Eµ + E = Mπc2 c(p2+Mµc2)1/2 + cp = Mπc2 p = c(Mπ2 - Mµ2)/(2Mπ) Eµ=c2(M2π+Mµ2)/(2Mπ) Tµ=Eµ-Mµc2 = c2(Mπ-Mµ)2/(2Mπ) = 4.12 MeV b) g has no charge Q = 135 MeV

SOLUTIONS c) µ+ ---> e+ + ne + nµ µ- ---> e- + e + nµ Neutrinos have charge zero. Q = MeV a) Forbidden. It does not conserve the baryon number. b) Allowed c) Forbidden. It does not conserve charge. d) Forbidden. It does not conserve charge. e) Forbidden. It does not conserve the baryon number. f) Allowed. g) Forbidden. Does not conserve charge.

SOLUTIONS Energy is conserved ===> EA,total = EB,total + EC,total Momentum is conserved ===> pA = 0 pB = -pC Total energy E for a particle is: E = ((pc)2 + mc2)1/2 (1) EC = EA - EB (2) (pBc)2 = (pCc)2; EB2 -MB2c4 = EC2 -MC2c4 Eq. 2 gives E2B - M2Bc4 = E2A -2EAEB+E2B - M2Cc4 EB = ((MAc2)2 + (MBc2)2 - (MCc2)2 )/(2MAc2) TB = EB -MBc2 =

SOLUTIONS ECM = Wc2 where W is the invariant mass of the pion-proton system. E2CM = c2(p2+m 2c2) where ECM is the total energy and p the momentum in an arbitrary reference frame. In the laboratory reference frame: EL = mπc2 + mpc2 + Tπ; where Tπ is the kinetic energy of the pion. p = pπ = ( (Tπ + mπc2)2 - mπ2c4)1/2 / c =[ Tπ (Tπ +2mπc2) ]1/2/c Tπ = [m2 -(mp+mπ)2 ]c2/(2mp) = (m+mp+mπ)(m-(mp+mπ))c2/(2mp) pπ = [{m2 -(mp + mπ)2 }{m2 - (mp + mπ)2}]1/2

continuing mπc2 = GeV mpc2 = GeV Therefore, Tπ = (E )(E )/ [GeV] Pπ = [Tπ(t )]1/2 For E = Pπ = 0.74 GeV and Tπ = 0.61 GeV For E = 2.64 GeV Pπ = 3.26 GeV and Tπ = 3.12 GeV

SOLUTIONS In the centre of mass system: Mass is invariant Net momentum = 0 pc = 0 Pair production at threshold leads to a final state which consists of two electrons and one positron at rest with total energy Ecentre = 3mcc2 In laboratory frame: Elab = hn + mec2 plab = hn/c Therefore, for the invariable mass we get : E2total - (cp)2

SOLUTIONS 5. continuing (3mec2)2 = (hn+mec2)2 - (plabc)2 (3mec2)2 = hn hn mec2 + me2c4 - hn (3mec2)2 = me2c4 + hn mec2 and hn = 4 mec2

COLLIDERS & Centre of Mass Frame
CM: No net momentum W2c4 = (EL + mtc2)2-(pLc)2 = mb2c4 + mt2c4 + 2mtc2EL The invariant mass: W 1) W2c4 = E2total - p2Lc2 2) Wc2 = ECM mb = mbombard. mt = mtarget EL = [(mbc2)2 + pL2c2]1/2 Et = mtc2 Laboratory Frame Available Energy

Example 2 Available Energy Threshold energy for pion, π, production: A proton with Kinetic Energy T collides with a proton at rest, producing a pion (πo, rest Energy = 135 Mev). What minimum value of T is recorded? Total available energy must be at least Solution ECM = (2mp + mπ)c2 For the energy at CM this gives ECM2 = (2mpc2)2 + (mπc2)2 + 2 mπc2(2mpc2) = 4.044x106 (MeV)2 ECM2 = 2(mpc2)2 + 2Etotal,pmpc2 Etotal, p = mpc2 + mπc2 (2+mπ/(2mp)) = ( ) MeV Incident protons Tk ≥ 280 Mev

Beta Decay 31H 32He + e- + n 31H 32He + e- √ WHAT IS THE PROBLEM HERE?

ATOMIC SUBSTRUCTURE 10-18 m

Example 8, Chap.41, page 1333 in Tipler
State if one of the following decays or processes violate one or more of the conservation laws and if so identify the law/laws violated. a) p+ n e+ + e- p + p- ne + p n + e+ + v-e p+ + p- g g + g n + e+ Answer: a) Violating energy conservation b) Violating energy conservation c) Violating momentum conservation d) Allowed e) Allowed

Option 212: UNIT 2 Elementary Particles

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