Electron-positron pairs can be produced from a photon of energy > twice the rest energy of the electron.
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1 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 from a photon of energy > twice the rest energy of the electron. A bound state of a positron and electron is hydrogenlike and is called positronium. Positrons are stable but can annihilate with an electron to produce two or three photons. + If electron-positron pair is in spin zero ( ) state. e e + e γ + γ 1 S + e γ + γ + γ 3 S + If electron-positron pair is in spin one ( ) state.
2 Early model for positron E = ( pc) + ( mc ) E = ± pc + mc E > mc ( ) ( ) or 2 Universe is filled with negative energy electrons. A photon of energy greater than twice the rest energy of the electron can excite a negative energy electron to positive energy states, creating an observable electron and a hole in the sea of negative energy electrons (which is a positron). E < mc Replaced by Quantum Electrodynamics (QED) developed by Richard Feynman in the late 1940s. All particles have antiparticles, same mass, opposite charge, same spin, opposite baryon number and strangeness. Anti-proton,, discovered in Anti-neutron,, discovered in p n
3 Feynman Diagrams
4 Fundamental Interactions Exchange particle for strong force is not pion as described earlier, but the gluon, which is massless. The range of the interaction and the appearance of the pion as the exchange particle is due to the fact that the nucleons are not fundamental particles, but made from quarks. Exchange particle for gravity, the graviton, has never been observed.
5 Particles that interact via the strong interaction are called hadrons (these are not fundamental particles). Hadrons with halfintegral spin are called baryons. Hadrons with integral spin are called mesons. All baryons have baryon number = 1 and all anti-baryons have a baryon number =!1. Baryon number is conserved.
6 Electromagnetic and Weak interactions have been unified into the Electroweak interaction. The photon, W +, W, and Z 0 are the gauge bosons. Particles that interact by the weak interaction but don t interact by the strong interaction are called leptons; electrons, muons, tau particles, and the neutrinos associated with each. Each of the three particles (e, :, J) has a value for its own flavor of lepton number of 1 as does the neutrino associated with it. The anti-particles have lepton numbers of!1. All three flavors of lepton number are conserved independently.
7 Does a particular reaction ever occur? Does it conserve energy, charge, angular momentum, linear momentum, baryon number and all three lepton numbers? n p + e + νe mn > mp + me + mν Energy: Charge: 0 = 0 Angular Momentum: ½ = ½! ½ + ½, so it can be conserved. Momentum: Three outgoing particles makes it possible to conserve. Baryon number: 1 = 1 L e : 0 = 1! 1 L : : 0 = 0 L J : 0 = 0 m m e µ + e + + γ Energy: Charge: 1 = 1 Angular Momentum: ½ = 1! ½, so it can be conserved. Momentum: Two outgoing particles makes it possible to conserve. Baryon number: 0 = 0 L e : 0 = 1 L : : 1 = 0 L J : 0 = 0 µ >
8 p m < m + m + µ + Energy: So energy conservation is violated. p n K Charge: 1 = 1 Angular Momentum: ½ = ½ + 0, so it can be conserved. Momentum: Two outgoing particles makes it possible to conserve. Baryon number: 1 = 1 L e : 1 = 0 L : : 0 = 0 L J : 0 = 0 This reaction will not occur because of energy and electron lepton number. K K + + p Σ + π 0 0 m + m > m + m Energy: K p Σ π Charge: 1 = 1 Angular Momentum: 0+½ = ½+0, so it can be conserved. Momentum: Two outgoing particles makes it possible to conserve. Baryon number: 1 = 1 L e : 0 = 0 L : : 0 = 0 L J : 0 = 0 This reaction does not occur because strangeness is not conserved. 0
9 Conserved Quantities Strangeness: The slowness of the process p+ π Λ 0 + K 0 Was considered strange behavior and implied that it did not occur via the strong interaction. So a new quantity conserved only in strong interactions was proposed. Particles can have integer values for strangeness. Isospin: differences in mass (that is, energy) between members of hadron charge multiplets, like the three kinds of pions or kaons, is similar to energy level splitting due to spin-orbit T T 3 interaction. So we can classify them as different isospin,, states with z-component,. Charge, isospin, baryon number and strangeness are related by q = eq = e T + B + S Y et = Hypercharge: Since both strangeness and baryon number are conserved in strong interactions, their sum is also conserved and given the name hypercharge, Y. In weak interacdtions, neither strangeness nor hypercharge must be conserved but they must S =±1, 0 Y =±1, 0 obey the selection rules: and.
10 If not for conservation of strangeness, all baryons would decay via the strong interaction in ~10!23 s.
11
12 Parity When the position coordinates are replaced by their inverses,, does the wave function stay the same,, or invert,? If it stays the same, the parity is +1 ψ ψ ψ ψ x x or even. If it inverts the parity is!1 or odd. All particles have an intrinsic parity. Parity is multiplicative, so we can determine the parity of the initial (or final) system by multiplying together the parities of all the particles. Parity is not conserved in weak interactions.
13 The Quark Model Gell-man and Ne eman independently in 1961 noticed that groupings of particles with the same intrinsic spin and parity had similar masses. These supermultiplets were suggested to be splittings of the same state. The strong interaction splits them into separate charge multiplets (sigma or pions) and the weak interaction causes the further splitting into separate charge states. Pictured is the baryon octet with the eight lightest baryons. Gell-Mann also proposed the eight lightest mesons formed the meson octet and the next ten lightest baryons formed the baryon decuplet. Gell-Mann suggested the reason for the supermultiplets was that these particles were all made from more fundamental particles, quarks.
14
15
16 The Standard Model
17 Baryons are made of three quarks. Their anti-particles are made of three anti-quarks.
18 The Baryon Octect
19 Mesons are made of one quark and one anti-quark. Some mesons will be their own antiparticles.
20 The Meson Nonet
21 Does the standard model violate Pauli exclusion principle? The ++ contains three up quarks and has a spin of 3/2. So all three quarks appear to have the same quantum numbers. Solution: invent a new quantum number called color charge! If quarks come in three flavors, then each of the three up quarks in ++ could be a different flavor and would then have different quantum numbers and not violate Pauli exclusion. Any one up quark can be blue: blueness = +1, redness = 0, greenness = 0 red: blueness = 0, redness = +1, greenness = 0 green: blueness = 0, redness = 0, greenness = +1 Anti-quarks have opposite numbers. Selection rules: Any particle made of quarks must be colorless, either due to having total charge of zero for each color, or having the same amount of blue, red, and green making it white. Baryons have three quarks, one blue, one red, and one green. Mesons have one quark and one anti-quark, both of the same color.
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23 Gluons Gluons - are the exchange boson that mediates the strong interaction between quarks - carry a color and an anti-color. Emission of a virtual gluon changes the color but not the flavor of the quark. A gluon can create two gluons that recombine, that is, a gluon loop.
24 Strong Force Potential Function quark confinement asymptotic freedom
25
26 Grand Unification Theories All particles are really different states of the same thing. All forces are manifestations of one force. Only at high enough energies or short enough distances do these symmetries become apparent. Proton Decay Neutrino Mass Magnetic Monopoles Quantum Gravity Superstrings
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