Option J: Particle physics J1 Particles and interactions

Option J: Particle physics J1 Particles and interactions
This part of Option J has already been covered in Option D4 Particles and interactions. It is replicated here without any changes. © 2006 By Timothy K. Lund

Description and classification of particles J.1.1 State what is meant by an elementary particle. J.1.2 Identify elementary particles. J.1.3 Describe particles in terms of mass and various quantum numbers. J.1.4 Classify particles according to spin. J.1.5 State what is meant by an antiparticle. J.1.6 State the Pauli exclusion principle. © 2006 By Timothy K. Lund

Description and classification of particles State what is meant by an elementary particle. An elementary particle is one which has no internal structure. PRACTICE: At one time it was thought that atoms were elementary particles. Explain why they are not. SOLUTION: They have an internal structure: Namely protons, neutrons and electrons. © 2006 By Timothy K. Lund EXAMPLE: At one time it was thought that protons and neutrons were elementary particles Explain why they are not. SOLUTION: Protons and neutrons are each built from three elementary particles called quarks.

Description and classification of particles Identify elementary particles. There are three major divisions in the elementary particles that have been identified, to date. The force carriers are the particles that allow compatible particles to sense and react to each other’s presence through exchange of these carriers. The quarks are the heavier, tightly bound particles that make up particles like protons and neutrons. The leptons are the lighter, more loosely bound particles like electrons. © 2006 By Timothy K. Lund FYI For example, quarks interact via the strong force particles called gluons.

Description and classification of particles Identify elementary particles. The force carriers: There are four force carriers… INTERACTION 1: STRONG: Strongest of all the interactions between particles. We can give it an arbitrary value of 1 for comparison. INTERACTION 2: ELECTROMAGNETIC: This is the NEXT strongest. In comparison to the strong interac-tion, it has a relative strength of 10-2. INTERACTION 3: WEAK: This interaction has a relative strength of 10-6. INTERACTION 4: GRAVITATIONAL: This interaction has a relative strength of 1.0 © 2006 By Timothy K. Lund 0.01

Description and classification of particles Identify elementary particles. The force carriers: In 1933 Hideki Yukawa developed the theory of exchange forces. The basic idea is that all forces are due to the exchange of particles between like elementary particles. Consider two protons in space. Yukawa postulated that the protons exchange photons and repel each other because of this exchange. © 2006 By Timothy K. Lund FYI This photon exchange is the electromagnetic force.

Description and classification of particles Identify elementary particles. The force carriers: Yukawa explained that the electromag netic force was long range (in fact infinite in range) because photons "live forever" until they are absorbed. Yukawa explained that the strong force was short range (in fact only in the nuclear range) because the strong force exchange particle (the gluon) has a very short life. © 2006 By Timothy K. Lund LONG RANGE EXCHANGE PARTICLE SHORT RANGE EXCHANGE (VIRTUAL) PARTICLE

Description and classification of particles Identify elementary particles. The force carriers: The following table compares the exchange particles (force carriers) by range and mass. INTERACTION RANGE EXCHANGE PARTICLE REST MASS STRONG 10-15 m GLUON g 120 MeV / c2 Electromagnetic  PHOTON  © 2006 By Timothy K. Lund WEAK 10-18 m W+, W- and Z 80 GeV / c2 Gravitation  GRAVITON 

Description and classification of particles Identify elementary particles. The quarks: Although you have heard of protons and neutrons, both of which react to the strong force exchange particle (the gluon), you have probably not heard of most of the following particles: Particle Symbol Particle Symbol Particle Symbol © 2006 By Timothy K. Lund proton p delta 0 sigma + neutron n delta - sigma 0 lambda 0 delta ++ sigma - omega - delta + xi 0 FYI With the advent of particle research the list of new particles became endless!

Description and classification of particles Identify elementary particles. The quarks: In 1964 the particle model was looking quite complex and unsatisfying. Murray Gell-Mann proposed a model where all the strong-force particles were made up of three fundamental particles called quarks. Quark © 2006 By Timothy K. Lund Flavor Symbol Charge d u Up u + 2/3 u Down d - 1/3 Strange s - 1/3 Charm c + 2/3 proton Bottom b - 1/3 Top t + 2/3 FYI A proton is uud and a neutron is udd.

Description and classification of particles Identify elementary particles. The quarks: Each quark has an antiquark, which has the opposite charge as the corresponding quark. © 2006 By Timothy K. Lund FYI Baryons are particles made up of 3 quarks or 3 antiquarks. Mesons are particles made up of a 1 quark and 1 antiquark.

Description and classification of particles Identify elementary particles. The leptons: You are already familiar with two of the six leptons: the electron and the electron neutrino. Leptons, unlike quarks, do NOT participate in the strong interaction. THE LEPTONS © 2006 By Timothy K. Lund Charged Leptons Uncharged Leptons electron e electron neutrino e muon  muon neutrino  tau  tau neutrino  FYI Of course the leptons also have their antiparticles.

Description and classification of particles Identify elementary particles. The leptons: The leptons interact only via the electromagnetic force carrier, the photon. Leptons, unlike quarks, do not react to the gluon. Quarks react to both the gluon and the photon. © 2006 By Timothy K. Lund FYI Leptons and quarks also react to gravitons.

Description and classification of particles Identify elementary particles. The Higgs particle is another particle that physicists think exists and are in search of. This particle is the one that gives quarks and leptons their mass. To date the Higgs particle has not yet been found. © 2006 By Timothy K. Lund FYI CERN and the Large Hadron Collider were developed with the Higgs boson in mind.

The Large Hadron Collider at CERN.
© 2006 By Timothy K. Lund

Description and classification of particles Describe particles in terms of mass and various quantum numbers. QUARKS u (up) c (charm) t (top) Charge / e +2/3 Mass / mp 1/3 1.7 186 d (down) s (strange) b (bottom) -1/3 0.5 4.9 © 2006 By Timothy K. Lund LEPTONS e(electron) (muon) (tau) Charge / e -1 Mass / mp 0.0005 0.1 1.9 e (e-neutrino)  (-neutrino)  (-neutrino) 0

Description and classification of particles Describe particles in terms of mass and various quantum numbers. Quarks have a baryon number of 1/3 and antiquarks have a baryon number of -1/3. quark (q) or antiquark (q) baryon number B Quark: B = +1/3 Antiquark: B = -1/3 PRACTICE: Find the baryon number of a baryon, a meson, and an electron: SOLUTION: A baryon has three quarks (or three antiquarks): For qqq we have B = +1/3 + +1/3 + +1/3 = +1. For qqq we have B = -1/3 + -1/3 + -1/3 = -1. A meson has a quark and an antiquark: For qq we have B = +1/3 + -1/3 = 0. An electron has no quarks and thus has B = 0. © 2006 By Timothy K. Lund

Description and classification of particles Describe particles in terms of mass and various quantum numbers. Leptons have a lepton number of 1 and antileptons have a lepton number of -1. lepton or antilepton lepton number L Lepton: L = +1 Antilepton: L = -1 PRACTICE: Find the lepton number of an electron, a positron, an anti electron neutrino, and a proton: SOLUTION: An electron has a lepton number of L = +1. A positron is an antiparticle and so has L = -1. An anti electron neutrino has L = -1. A proton is not a lepton and so has L = 0. © 2006 By Timothy K. Lund

Description and classification of particles Describe particles in terms of mass and various quantum numbers. Conservation of charge. © 2006 By Timothy K. Lund Conservation of baryon number. Conservation of lepton number.

Description and classification of particles Describe particles in terms of mass and various quantum numbers. L = 0 L = 0 + 1 = 1. Conservation lepton number violated. © 2006 By Timothy K. Lund We need a particle on the right with L = -1 (an antilepton). 01n  11p + -10e + e L : 1 -1

Description and classification of particles Describe particles in terms of mass and various quantum numbers. PRACTICE: Evaluate each reaction as "possible" or "not possible“ considering B, L and Q. p  n + e+ + e B: L: Q: n  p + e- + e n + p  e+ + e POSSIBLE 1 1  -1 1  1 1  © 2006 By Timothy K. Lund POSSIBLE 1 1  1 -1  1 -1  NOT POSSIBLE 1 1  -1 -1  1 1 

Description and classification of particles Classify particles according to spin. A quark (or antiquark) may have spin up (+1/2) or spin down (-1/2). A baryon is a particle made of three quarks (or three antiquarks) and so it has a spin of A meson is a particle made of one quark and one antiquark and so it has a spin of A fermion is a particle having an odd multiple of 1/2 as a spin. A boson is a particle having an integer spin. fermion quark (q) or antiquark (q) spin Spin is +1/2 Spin down -1/2 fermion baryon spin (qqq) or (qqq)  1/2 or  3/2 © 2006 By Timothy K. Lund boson meson spin (qq)  0 or  1

Description and classification of particles State what is meant by an antiparticle. Every particle has an antiparticle which has the same mass but all of its quantum numbers are the opposite. Thus an antiproton (p) has the same mass as a proton (p), but the opposite charge (-1). Thus an antielectron (e+ or e) has the same mass as an electron but the opposite charge (+1). Angels and Demons © 2006 By Timothy K. Lund FYI When matter meets antimatter both annihilate each other to become energy! Paul Dirac

Description and classification of particles State the Pauli exclusion principle. The Pauli exclusion principle states that no two identical fermions may have exactly the same set of quantum numbers. PRACTICE: Electrons and antielectrons have a spin of 1/2. Are they fermions or bosons? SOLUTION: A fermion is a particle having an odd multiple of 1/2 as a spin. A boson has an integral spin. Thus electron and positrons are fermions (as well as quarks and baryons). Mesons are bosons. © 2006 By Timothy K. Lund FYI We first saw Pauli’s exclusion principle when we looked at the orbital structure of the elements. Recall the s, p, d and f suborbitals.

Fundamental interactions J.1.7 List the fundamental interactions. J.1.8 Describe the fundamental interactions in terms of exchange particles. J.1.9 Discuss the uncertainty principle for time-energy in the context of particle creation. DONE DONE © 2006 By Timothy K. Lund

Fundamental interactions Discuss the uncertainty principle for time-energy in the context of particle creation. Recall the Heisenberg uncertainty principle: Another way of looking at the time-energy uncertainty principle is this: “If the time interval is small enough, the uncertainty in the energy can be very large.” This is a way of saying that the conservation of energy can be violated for very short periods of time! The consequences are that particles can be randomly created out of the void as long as they annihilate each other in a very short time. Heisenberg uncertainty principle ∆x∆p  h/4 (momentum form) ∆E∆t  h/4 (energy form) © 2006 By Timothy K. Lund

Fundamental interactions Discuss the uncertainty principle for time-energy in the context of particle creation. Heisenberg uncertainty principle ∆x∆p  h/4 (momentum form) ∆E∆t  h/4 (energy form) EXAMPLE: A proton and an antiproton are created from the void as allowed by the HUP. How much time do they exist before annihilating each other? SOLUTION: A proton has a mass of 1.6710-27 kg. From E = mc2 we can calculate the energy of a proton (or an antiproton) to be ∆E = (1.6710-27)(3.00108)2 = 1.5010-10 J. Since we need both p and p, the energy doubles. ∆t = h/[4∆E] = 6.6310-34 /[4(3.0010-10)] = 1.7610-25 s. © 2006 By Timothy K. Lund

Fundamental interactions Discuss the uncertainty principle for time-energy in the context of particle creation. EXAMPLE: Stephen Hawking proposed that black holes can evaporate because of virtual particle creation. How can this work? SOLUTION: At the black hole’s boundary (the Schwarzschild radius) virtual particles are created in matter-antimatter pairs out of the void. If one of the pair happens to be gobbled up by the hole, and the other has sufficient velocity to escape from the hole, the particles will not annihilate, and the black hole will be lighter by the mass of the one particle! © 2006 By Timothy K. Lund

Feynman diagrams J.1.10 Describe what is meant by a Feynman diagram. J.1.11 Discuss how a Feynman diagram may be used to calculate probabilities for fundamental processes. J.1.12 Describe what is meant by a virtual particle. J.1.13 Apply the formula for the range R for interactions involving the exchange of a particle. J.1.14 Describe pair annihilation and pair production through Feynman diagrams. J.1.15 Predict particle processes using Feynman diagrams. © 2006 By Timothy K. Lund

Feynman diagrams Describe what is meant by a Feynman diagram. Richard Feynman developed a graphic representation of particle interac tions that could be used to predict the probabilities of the outcomes of particle collisions. A typical Feynman diagram consists of two axes: Space and Time: © 2006 By Timothy K. Lund SPACE TIME FYI Some books switch the space and time axis. The IB presentation is as shown above.

Feynman diagrams Describe what is meant by a Feynman diagram. Consider two electrons approaching one-another from the top and the bottom of the page… A purely spatial sketch of this interaction would look like this: But if we also apply a time axis, the sketch would look like this: The Time axis allows us to draw the reaction in a spread-out way to make it clearer. e- The bubble of ignorance e- e- SPACE © 2006 By Timothy K. Lund e- e- TIME e- FYI The “bubble of ignorance” is the actual place in the plot that exchange particles do their thing. Ingoing and outgoing particles are labeled.

Feynman diagrams Describe what is meant by a Feynman diagram. Particles are represented with straight arrows, as were the two electrons in the previous electron-electron interaction. Exchange particles are represented with either wavy lines (photons, W+, W- and Z0), or curly lines (gluons). Electromagnetic and weak exchange Strong exchange © 2006 By Timothy K. Lund FYI You may have noticed that the electromagnetic exchange particle and the weak exchange particles all have the same wavy symbol. Indeed, it has been found that the two forces are manifestations of a single ELECTRO-WEAK force.

Feynman diagrams Predict particle processes using Feynman diagrams. e- e- EXAMPLE: The complete Feynman diagram showing the repulsion of two electrons looks like this: Here is a diagram for one electron emitting a photon:  SPACE e- e- TIME © 2006 By Timothy K. Lund e- e- SPACE  TIME

Feynman diagrams Predict particle processes using Feynman diagrams. e+ e+ EXAMPLE: In a Feynman diagram, antimatter points backward in time. This diagram represents two positrons repelling each other: Here is a diagram for one positron emitting a photon:  SPACE e+ e+ TIME © 2006 By Timothy K. Lund e+ e+ SPACE  TIME

Feynman diagrams Describe pair annihilation and pair production through Feynman diagrams. e- EXAMPLE: Here is a photon producing an electron-positron pair. Here is an electron-positron pair annihilating to become a photon: SPACE  e+ TIME © 2006 By Timothy K. Lund e+ SPACE  e- TIME

Feynman diagrams Discuss how a Feynman diagram may be used to calculate probabilities for fundamental processes. d EXAMPLE: Here is a diagram of a down quark emitting a W particle that decays into an electron and an antineutrino: u e W- SPACE e- © 2006 By Timothy K. Lund TIME FYI One can use Feynman diagrams to map out complete processes. Using the conservation rules and the exchange particles, you can predict what kind of processes can occur.

Feynman diagrams Discuss how a Feynman diagram may be used to calculate probabilities for fundamental processes. EXAMPLE: Explain what has happened in this Feynman diagram. SOLUTION: The up quark of a proton (uud) emits a gluon. The gluon decays into a down quark and an anti-down quark. d d u u u u d g SPACE © 2006 By Timothy K. Lund d TIME FYI Quarks cannot exist by themselves. Thus the two quarks produced above will quickly annihilate.

Feynman diagrams Describe what is meant by a virtual particle. Exchange particles whose range of influence is limited are called virtual particles. Virtual particles can only exist within their range of influence. INTERACTION EXCHANGE PARTICLE RANGE REST MASS STRONG GLUON g 10-15 m 120 MeV / c2 Electromagnetic PHOTON   WEAK W+, W- and Z 10-18 m 80 GeV / c2 Gravitation GRAVITON  © 2006 By Timothy K. Lund LONG RANGE EXCHANGE PARTICLE SHORT RANGE EXCHANGE (VIRTUAL) PARTICLE

Feynman diagrams Apply the formula for the range R for inter-actions involving the exchange of a particle. We can use Heisenberg’s uncertainty principle to estimate the range R of exchange particles. We use ∆E = mc2 and the assumption that these virtual particles travel at the speed of light c… c = R/∆t (v = d/t) ∆t = R/c ∆E∆t  h/4 (HUP) ∆ER/c  h/4 (Substitution of ∆t = R/c) mc2R/c  h/4 (∆E = mc2) © 2006 By Timothy K. Lund particle range R  h/[4mc] FYI Be able to do this derivation. IBO requires it.

Feynman diagrams Apply the formula for the range R for inter-actions involving the exchange of a particle. particle range R  h/[4mc] EXAMPLE: A weak virtual exchange particle called the W+ boson has a mass of 89 protons. What is its approximate range of influence? SOLUTION: mp = 1.6710-27 kg so that R  h/[4mc] = 6.6310-34/[4(89)(1.6710-27)(3.00108)] = 1.1810-18 m. © 2006 By Timothy K. Lund FYI This is about the size of a quark.

Feynman diagrams Predict particle processes using Feynman diagrams. n p u u d d EXAMPLE: Explain what has hap pened in this Feynman diagram. SOLUTION: It is a diagram of a down quark emitting a W- particle that decays into an electron and an antineutrino: Recall that a neutron consists of an up-down-down quark combo. Recall that a proton consists of an up-up-down quark combo. This is non other than the beta decay (-)we talked about a long time ago. d u e W- SPACE e- © 2006 By Timothy K. Lund TIME n  p + e- + e

Feynman diagrams Predict particle processes using Feynman diagrams. EXAMPLE: Write the reaction (including the neutrino) for beta(+) decay. SOLUTION: Just know it! EXAMPLE: Now draw the Feynman diagram for the above + decay: p  n + e+ + e p n u u d d u d © 2006 By Timothy K. Lund e W+ SPACE FYI Why is the neutrino not an anti-neutrino as in the - decay? e+ TIME

Feynman diagrams Predict processes using Feynman diagrams. +2/3 Must be -1 -1/3 -1 © 2006 By Timothy K. Lund A virtual particle is a particle that has a very short range of influence. Look at charge… The particle must be a W-.

Feynman diagrams Predict processes using Feynman diagrams. Use R  h/[4mc]. m = (100109 eV c-2)(1.610-19 J/eV)(1c /3.00108)2 m = 1.7810-25 kg. R  (6.6310-34)/[4(1.7810-25)(3.00108)] © 2006 By Timothy K. Lund R  9.8810-19 m.

Option J: Particle physics J1 Particles and interactions

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