Elementary Particles Physical Principles Benjamin Schumacher Physics 145

Elementary Particles: Physical Principles Benjamin Schumacher Physics 145 29 April 2002

Particles and antiparticles For every type of elementary particle, there exists a corresponding antiparticle. The antiparticle has exactly the same mass and spin as the particle, but opposite electric charge, etc. Example: The antiparticle of an electron e- is a positron e+ A few (but not all) uncharged elementary particles (such as the photon ) are their own antiparticles.

Dirac’s dilemma • 1927 - Paul Dirac develops relativistic quantum theory. (Predicts spin of the electron, etc. ) But there is a problem. . possible energy states +mc 2 0 - mc 2 Puzzle: Dirac’s equation predicts positive and negative electron energies, but we only ever see positive energies.

The Dirac “sea” • Dirac’s idea: All negative energy states are already filled. By the Pauli exclusion principle, no additional electrons can have negative energies. • The universe contains a vast invisible “sea” of negative energy electrons. +mc 2 0 - mc 2

Holes in the Dirac Sea • Suppose there is a “hole” or “bubble” in the Dirac sea of negative energy electrons. • Hole behaves like a particle with +mc 2 • positive energy (hole is a “lack of a negative energy electron”) 0 • positive charge (absence of a negative charge) - mc 2 • Anti-electron = positron • Discovered by Anderson in 1932 e+

Creation and annihilation • Pair creaton Input one or more photons (total energy at least 2 mc 2) and create both an electron and a positron. e+mc 2 0 - mc 2 e+

Creation and annihilation • Pair creaton Input one or more photons (total energy at least 2 mc 2) and create both an electron and a positron. e+mc 2 0 • Pair annihilation Electron and positron meet; electron “fills the hole” and releases energy (photons). Two photons are produced (momentum conservation). - mc 2 e+

A slightly different view. . . Basic “Feynman diagrams” diagrams g e- time e- e. Photon emitted e- g Photon absorbed

A slightly different view. . . g g g time e- e- g Compton scattering e- e+ Pair annihilation An antiparticle is a particle “going backwards in time”.

Fundamental forces • Strong nuclear (hadronic) force relative strength 1, short range, affects only hadrons • Electromagnetic force relative strength 10 -2, long range, affects charges • Weak nuclear force relative strength ~10 -13, short range, affects both hadrons and leptons • Gravitational force relative strength ~10 -43, long range, affects all particles

Two principles • The stronger the force, the quicker the process. The rate at which a process (e. g. , a particle decay) proceeds is related to the strength of the fundamental interaction responsible. • Anything that is not forbidden is compulsory. Any particle process that is not actually forbidden by some physical law (e. g. , a conservation law) has some probability of occuring. If a process that looks possible does not occur, then there must be a physical law that prevents it.

Virtual particles Forces are mediated by the exchange of virtual particles Example: Electromagnetic forces mediated by the exchange of virtual photons e- e ee- Where does the energy for the virtual particle come from? Virtual particles live “underneath” the Uncertainty Principle:

Yukawa and the meson H. Yukawa (1935) : Short range nuclear forces should be mediated by a massive particle. p, n range of force p, n R = 1. 5 fm mass of mpc 2 = 130 Me. V

“Who ordered that? ” • 1936 -- New particles ( , or “muons”) are detected in cosmic rays. Rest energy: 106 Me. V Muon is not a hadron -- cannot be Yukawa’s meson • Actual mesons (rest energies 130 -140 Me. V) discovered in 1947. • Since 1940’s -- Many, many new particles discovered. Many successful predictions of theory A few surprises!

Elementary Particles: The Particle Zoo Benjamin Schumacher Physics 145 1 May 2002

Particle Taxonomy “Field particles” Bosons (g, . . . ) All particles Leptons (e±, ±, n, . . . ) others Hadrons Mesons ( ±, 0, . . . ) Baryons (p, n, . . . )

Particle Taxonomy “Field particles” (g, . . . ) All particles Leptons Fermions (e±, ±, n, . . . ) others Hadrons Mesons ( ±, 0, . . . ) Baryons (p, n, . . . )

Field particles particle mc 2 (Ge. V) q s g photon 0 0 1 W± “vector bosons” 79. 8 ± 1 1 91. 2 0 1 gluons 0* 0 1 strong nuclear gravitons 0 0 2 gravitational Z 0 g force electromagnetic weak nuclear

Leptons particle mc 2 (Me. V) q s mean lifetime e- electron 0. 511 -1 1/2 e+ - muon 106 -1 1/2 2. 2 ms + t- tau 1780 -1 1/2 very short t+ ne e-neutrino 0 1/2 n muon nt tau zero? very small? 0 1/2 antiparticle ne stable? oscillation? n nt

Baryons s mean lifetime antiparticle +1 1/2 p 939. 6 0 1/2 930 s n 1116 0 1/2 0. 25 ns L 0 0 1/2 10 -20 s S 0 ± 1 1/2 ~ 0. 1 ns S 0 1/2 0. 3 ns X 0 -1 1/2 0. 17 ns X+ -2 3/2 0. 13 ns W+ particle mc 2 (Me. V) q p proton 938. 3 n neutron L 0 lambda S 0 S X 0 XW- sigma ~1190 xi ~1320 omega 1672

Mesons particle 0 + K 0 K+ h 0 pions kaons eta mc 2 (Me. V) q s mean lifetime antiparticle 135 0 0 ~10 -16 s 0 139. 6 +1 0 26 ns - 493. 7 0 0 peculiar K 0 497. 7 +1 0 12. 4 ns K- 549 0 0 ~10 -19 s h 0

Particle decay mechanisms • Strong (hadronic) force decays proceed very fast (~10 -23 s) -- no such “particles” listed above. • Electromagnetic decays: Involve photons! S 0 L 0 + 10 -20 s p 0 + 0. 8 × 10 -16 s h 0 + 2 × 10 -19 s fastest decay times listed • Weak force decays are much slower -- these include all other decays listed (~0. 1 ns or longer)

Conservation laws (exact) • Energy, momentum, angular momentum • Electric charge Why not p p 0 + e+ ? • Conservation of baryon number, lepton number! Baryon number +1 for baryons -1 for antibaryons 0 for all others Lepton number +1 for leptons -1 for antileptons 0 for all others

Approximate conservation laws The reaction K+ p 0 + p+ does occur, but not fast. . . even though all three particles can participate in hadronic forces! Something strange going on! Idea: There is a quantity (“strangeness”, or S ) that is conserved by strong and EM forces, but not by the weak force. (K+ has strangeness -1. ) More approximately conserved quantities: Charm, etc.

Quarks Hadrons (baryons, mesons) are composite particles, like atoms. q B u up ~340 +2/3 1/3 d down ~340 -1/3 c charmed +2/3 1/3 s strange -1/3 t top +2/3 1/3 b bottom -1/3 more massive quark mc 2 (Me. V) constituents of nucleons (p, n)

Constructing hadrons All hadrons are composed of quarks and antiquarks. 1 baryon = 3 quarks proton u u 1 meson = 1 quark + 1 antiquark pion ( +) u d d neutron u d d kaon (K-) s u