PH 301 Dr. Cecilia Vogel Lecture 19

Review Outline  conservation laws  hadrons, baryons, mesons  flavor and color  quarks and leptons  matter and antimatter

Conservation Laws  Energy  momentum – in CM frame, p=0  angular momentum (spin)  lepton #, which = # leptons-#antileptons  each “generation”  baryon #, which = (#quarks-#antiquarks)/3  electric charge  color charge  always neutral –don’t worry  flavor is conserved, except in weak interactions  often accompanied by neutrino

PAL Check above Conservation Law s

Lepton # Conservation  lepton # is conserved  # electron leptons - # elect. antileptons = constant  # mu leptons - # mu antileptons = constant  # tau leptons - # tau antileptons = constant  example   -  e - +    e  electron lepton number initial =0  electron lepton number final = 1-1 = 0  conserved  tau lepton number initial = 1  tau lepton number final = 1  conserved

Baryons  baryon is  any particle made of 3 quarks  such as p and n  antibaryon made of 3 antiquarks  such as  p =  u  u  d  meson is  any particle made of quarks and antiquark  such as  + = u  d  which has charge =? (add quark & antiquark charges)  pentaquark is  any particle made of 4 quarks and an antiquark

Baryon # Conservation  # quarks - # antiquarks = constant  Usually OK to use  # baryons - # antibaryons = constant  so long as no pentaquarks involved  example: a proton can’t turn into a positron  initial baryon # = 1  final baryon # = 0  not conserved — won’t happen!

Momentum Conservation  pi =pf  for simplicity, always consider the center of mass frame for the initial particles  pi =0  then pf =0  example: e + + e -  photons  can it just be one photon? NO  pf=h/ is not =0, p not conserved  Can it be two photons? YES  yes — if have same l and move in opposite dir  pf = h/ - h/ = 0 (conserved)

Energy Conservation  Ei = Ef   mass is NOT conserved  can be turned to and from other forms of energy  example: e + + e -  photons  If e- and e+ are approx at rest when they annihilate, what are the wavelengths of the photons?  Ei = (0.511MeV)+(0.511MeV)  Ef = 2hc/.  = 2.4 pm

Angular Momentum Conservation  Angular momentum is conserved  must include spin  example: e + + e -    spin of e is ½, spin of  is 1 (see table)  so ½ + ½ = 1 + 1???  no  angular momentum must be added as vectors

Angular Momentum Addition  angular momentum must be added as vectors  classical ang mom vectors can add to anything  from the difference between the two ang mom’s  to the sum  quantum ang mom vectors can add to anything  from the difference between the two ang mom’s  to the sum  in integer steps

Angular Momentum Addition  quantum ang mom vectors can add to anything  from the difference between the two ang mom’s  to the sum, in integer steps  example: e + + e -    ½ and ½ can add to zero  1 and 1can also add to zero  so angular momentum can be conserved, 0=0  other examples:  ½ and ½ can add to 0 or 1  1 and 1 can add to 0, 1, or 2  ½ and 1 can add to ½ or 3/2

Electric Charge Conservation  Electric charge is conserved  example: neutron decays into a proton  baryon # would be conserved (1=1)  but charge would not be conserved (0≠1)  so another particle produced = electron  but now electron lepton # not conserved (0≠1)  what can we add that will fix lepton #  without messing up baryon # or charge?  answer: an uncharged antilepton  All conserved in this:

Flavor Conservation  Flavor is conserved  well, not really  in  a down quark turns into an up quark  quark flavor not conserved  Flavor is conserved  except in weak interactions  identified by the appearance of neutrinos

Color Conservation  Color is conserved  what is color?  quarks have color charge  red or green or blue  baryons have white or neutral color charge  one quark each  red + green + blue = white

Color Conservation  anti quarks have color charge  antired (cyan) or antigreen (magenta) or antiblue (yellow)  mesons have white or neutral color charge  one quark color, one quark anticolor  e.g. blue + antiblue = blue + yellow = white  Color is conserved  because it’s always neutral