Elementary Particles: Physical Principles

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

2. 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.

3. +mc2 possible energy states 0 - mc2 Dirac’s dilemma • 1927 - Paul Dirac develops relativistic quantum theory. (Predicts spin of the electron, etc.) But there is a problem.... Puzzle: Dirac’s equation predicts positive and negative electron energies, but we only ever see positive energies.

4. +mc2 0 - mc2 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.

5. +mc2 0 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 • positive energy (hole is a “lack of a negative energy electron”) • positive charge (absence of a negative charge) • Anti-electron = positron - mc2 e+ • Discovered by Anderson in 1932

6. +mc2 0 Creation and annihilation • Pair creaton • Input one or more photons (total energy at least 2 mc2) and create both an electron and a positron. e- - mc2 e+

7. +mc2 0 Creation and annihilation • Pair creaton • Input one or more photons (total energy at least 2 mc2) and create both an electron and a positron. e- • Pair annihilation • Electron and positron meet; electron “fills the hole” and releases energy (photons). • Two photons are produced (momentum conservation). - mc2 e+

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

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

10. 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

11. 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.

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

13. p,n p,n p range of force mass of p p,n R = 1.5 fm mpc2 = 130 MeV p,n Yukawa and the meson H. Yukawa (1935) : Short range nuclear forces should be mediated by a massive particle.

14. “Who ordered that?” • 1936 -- 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 130-140 MeV) discovered in 1947. • Since 1940’s -- Many, many new particles discovered. • Many successful predictions of theory • A few surprises!

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

16. Bosons “Field particles” Leptons others Mesons Hadrons Baryons Particle Taxonomy (g, ...) All particles (e±, m±, n, ...) (p±, p0, ...) (p, n, ...)

17. “Field particles” Fermions Leptons others Mesons Hadrons Baryons Particle Taxonomy (g, ...) All particles (e±, m±, n, ...) (p±, p0, ...) (p, n, ...)

18. g photon 0 0 1 electromagnetic W± 79.8 ±1 1 “vector bosons” weak nuclear Z0 91.2 0 1 g gluons 0* 0 1 strong nuclear gravitons 0 0 2 gravitational Field particles mc2 (GeV) particle q s force

19. m- muon 106 -1 1/2 2.2 ms m+ t- tau 1780 -1 1/2 very short t+ ne e-neutrino 0 1/2 ne zero? very small? stable? oscillation? nm muon 0 1/2 nm nt tau 0 1/2 nt Leptons mean lifetime anti-particle mc2 (MeV) particle q s e- electron 0.511 -1 1/2  e+

20. anti-particle p proton 938.3 1/2  p +1 n neutron 939.6 1/2 930 s n 0 L0 lambda 1116 1/2 0.25 ns L0 0 S0 1/2 10-20 s S0 0 sigma ~1190 S 1/2 ~ 0.1 ns S ±1 X0 1/2 0.3 ns X0 0 xi ~1320 X- 1/2 0.17 ns X+ -1 W- omega 1672 3/2 0.13 ns W+ -2 Baryons mean lifetime mc2 (MeV) particle q s

21. p0 135 0 0 ~10-16 s p0 pions p+ 139.6 +1 0 26 ns p- K0 493.7 0 0 peculiar K0 kaons K+ 497.7 +1 0 12.4 ns K- h0 eta 549 0 0 ~10-19 s h0 Mesons mean lifetime anti-particle mc2 (MeV) particle q s

22. S0 L0 + g 10-20 s fastest decay times listed p0 g + g 0.8 ×10-16 s h0 g + g 2 ×10-19 s Particle decay mechanisms • Strong (hadronic) force decays proceed very fast (~10-23 s) -- no such “particles” listed above. • Electromagnetic decays: Involve photons! • Weak force decays are much slower -- these include all other decays listed (~0.1 ns or longer)

23. Conservation laws (exact) • Energy, momentum, angular momentum • Electric charge Why not p p0 + 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

24. Approximate conservation laws The reaction K+ p0 + 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.

25. mc2 (MeV) B quark q 1/3 u up ~340 +2/3 constituents of nucleons (p,n) d down ~340 -1/3 1/3 c charmed +2/3 1/3 s strange -1/3 1/3 t top +2/3 1/3 b bottom -1/3 1/3 Quarks Hadrons (baryons, mesons) are composite particles, like atoms. more massive

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