PH 301

1
PH 301

• Dr. Cecilia Vogel
• Lecture 19

2
Review

• quarks and leptons
• matter and antimatter

Outline

• conservation laws
• hadrons, baryons, mesons
• flavor and color

3
Conservation Laws

• Energy
• momentum in CM frame, p0
• angular momentum (spin)
• lepton , which leptons-antileptons
• each generation
• baryon , which (quarks-antiquarks)/3
• electric charge
• color charge
• always neutral dont worry
• flavor is conserved, except in weak interactions
• often accompanied by neutrino

4
PALCheck above Conservation Laws
5
Lepton Conservation

• lepton is conserved
• electron leptons - elect. antileptons
  constant
• mu leptons - mu antileptons constant
• tau leptons - tau antileptons constant
• example
• t - ? e- nt ?ne
• electron lepton number initial 0
• electron lepton number final 1-1 0
• conserved
• tau lepton number initial 1
• tau lepton number final 1
• conserved

6
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 p u?d
• which has charge ? (add quark antiquark
  charges)
• pentaquark is
• any particle made of 4 quarks and an antiquark

7
Baryon Conservation

• quarks - antiquarks constant
• Usually OK to use
• baryons - antibaryons constant
• so long as no pentaquarks involved
• example a proton cant turn into a positron
• initial baryon 1
• final baryon 0
• not conserved wont happen!

8
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
• pfh/l is not 0, p not conserved
• Can it be two photons? YES
• yes if have same l and move in opposite dir
• pf h/l - h/l 0 (conserved)

9
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/l.
• l 2.4 pm

10
Angular Momentum Conservation

• Angular momentum is conserved
• must include spin
• example e e- ? g g
• spin of e is ½, spin of g is 1 (see table)
• so ½ ½ 1 1???
• no
• angular momentum must be added as vectors

11
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 moms
• to the sum
• quantum ang mom vectors can add to anything
• from the difference between the two ang moms
• to the sum
• in integer steps

12
Angular Momentum Addition

• quantum ang mom vectors can add to anything
• from the difference between the two ang moms
• to the sum, in integer steps
• example e e- ? g g
• ½ and ½ can add to zero
• 1 and 1can also add to zero
• so angular momentum can be conserved, 00
• 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

13
Electric Charge Conservation

• Electric charge is conserved
• example neutron decays into a proton
• baryon would be conserved (11)
• 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

14
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

15
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

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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 its always neutral