Elementary Particles: Physical Principles Benjamin Schumacher Physics 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 Paul Dirac develops relativistic quantum theory. (Predicts spin of the electron, etc.) But there is a problem mc 2 - mc 2 possible energy states Puzzle: Dirac’s equation predicts positive and negative electron energies, but we only ever see positive energies.

- mc 2 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. 0 +mc 2 The universe contains a vast invisible “sea” of negative energy electrons.

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

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. 0 +mc 2 - mc 2 e-e-e-e- e+e+e+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. 0 +mc 2 - mc 2 e-e-e-e- e+e+e+e+ Pair annihilation Electron and positron meet; electron “fills the hole” and releases energy (photons). Two photons are produced (momentum conservation).

A slightly different view... Feynman diagrams Basic “Feynman diagrams” e-e- e-e-  e-e- e-e-  time Photon emittedPhoton absorbed

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

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 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.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- e-e- e-e- e-e-  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 mass of  R = 1.5 fmm  c 2 = 130 MeV

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

Elementary Particles: The Particle Zoo Benjamin Schumacher Physics May 2002

Particle Taxonomy All particles others “Field particles”Leptons Hadrons Mesons Baryons ( ,...) (e ±,  ± ,...) (  ±  ,...) (p, n,...) Bosons

Particle Taxonomy All particles others “Field particles”Leptons Hadrons Mesons Baryons ( ,...) (e ±,  ± ,...) (  ±  ,...) (p, n,...) Fermions

Field particles ggluons0*01strong nuclear particle mc 2 (GeV) qsforce W±W± “vector bosons” 79.8±11 weak nuclear Z0Z0  photon001electromagneticgravitons002gravitational

Leptons e-e- electron0.5111/2  e+e+ particle mc 2 (MeV) qs mean lifetime anti- particle -- muon1061/2 2.2  s ++ -- tau17801/2very short ++ e e-neutrino01/2 muon zero? very small? 1/2 tau1/2 stable? oscillation? 0 0 e    

Baryons pproton /2  particle mc 2 (MeV) qs mean lifetime nneutron /2930 s  lambda /20.25 ns  sigma~ / s ±1 1/2~ 0.1 ns   xi~ /20.3 ns 1/20.17 ns   omega /20.13 ns anti- particle p n      

Mesons particle mc 2 (MeV) qs mean lifetime anti- particle  pions ns  13500~ s   KK kaons ns KK peculiar KK KK eta  54900~ s 

Particle decay mechanisms Strong (hadronic) force decays proceed very fast (~ s) -- no such “particles” listed above. Electromagnetic decays: Involve photons!      s    0.8 × s    2 × 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) Baryon number +1 for baryons -1 for antibaryons 0 for all others Energy, momentum, angular momentum Electric charge Why not p    e + ? Lepton number +1 for leptons -1 for antileptons 0 for all others Conservation of baryon number, lepton number!

Approximate conservation laws The reaction K      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. quark mc 2 (MeV) q B uup~340+2/3 1/3 constituents of nucleons (p,n) ddown~340-1/3 1/3 ccharmed+2/3 1/3 sstrange-1/3 1/3 ttop+2/3 1/3 bbottom-1/3 1/3 more massive

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