PH 301

Dr. Cecilia VogelLecture 19

Review

Outline conservation laws hadrons, baryons, mesons flavor and color

quarks and leptons matter and antimatter

Conservation LawsEnergymomentum – in CM frame, p=0angular momentum (spin)lepton #, which = # leptons-#antileptons

each “generation”baryon #, which = (#quarks-#antiquarks)/3electric chargecolor charge

always neutral –don’t worry flavor is conserved, except in weak interactions

often accompanied by neutrino

PALCheck above Conservation

Lawsen p e

Lepton # Conservationlepton # is conserved

# electron leptons - # elect. antileptons = constant # mu leptons - # mu antileptons = constant # tau leptons - # tau antileptons = constant

example- e- + e

electron lepton number initial =0electron lepton number final = 1-1 = 0

conservedtau lepton number initial = 1tau lepton number final = 1

conserved

Baryonsbaryon is

any particle made of 3 quarkssuch as p and n

antibaryon made of 3 antiquarks such as p = uud

meson isany particle made of quarks and antiquark

such as + = udwhich has charge =? (add quark & antiquark charges)

pentaquark isany particle made of 4 quarks and an antiquark

Baryon # Conservation

# quarks - # antiquarks = constant

Usually OK to use# baryons - # antibaryons = constantso long as no pentaquarks involved

example: a proton can’t turn into a positroninitial baryon # = 1final baryon # = 0not conserved — won’t happen!

Momentum Conservationpi =pf

for simplicity, always consider the center of mass frame for the initial particlespi =0

then pf =0example: e+ + e- photonscan it just be one photon? NOpf=h/ is not =0, p not conservedCan it be two photons? YESyes — if have same l and move in opposite dir

pf = h/ - h/ = 0 (conserved)

Energy ConservationEi = Ef

mass is NOT conservedcan be turned to and from other forms of energy

example: e+ + e- photonsIf 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

2 2, , , ,tot i tot i tot f tot fm c K m c K

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???noangular momentum must be added as vectors

Angular Momentum Addition

angular momentum must be added as vectorsclassical ang mom vectors can add to anything

from the difference between the two ang mom’sto the sum

quantum ang mom vectors can add to anything

from the difference between the two ang mom’sto the sum

in integer steps

Angular Momentum Addition

quantum ang mom vectors can add to anything

from the difference between the two ang mom’sto the sum, in integer steps

example: e+ + e- ½ and ½ can add to zero1 and 1can also add to zeroso angular momentum can be conserved, 0=0

other examples:½ and ½ can add to 0 or 11 and 1 can add to 0, 1, or 2½ 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 = electronbut 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:en p e

Flavor ConservationFlavor is conserved

well, not reallyin

a down quark turns into an up quarkquark flavor not conserved

Flavor is conserved except in weak interactionsidentified by the appearance of neutrinos

en p e

Color ConservationColor is conserved what is color?

quarks have color chargered or green or blue

baryons have white or neutral color chargeone quark eachred + green + blue = white

Color Conservationanti quarks have color charge

antired (cyan) or antigreen (magenta) or antiblue (yellow)

mesons have white or neutral color chargeone quark color, one quark anticolore.g. blue + antiblue = blue + yellow = white

Color is conservedbecause it’s always neutral