1. all fundamental with no underlying structure
Leptons+quarks spin ½ while photon, W, Z, gluons spin 1
No QM theory for gravity
Higher generations have larger mass

2. When/where discovered
Nobel Prize?
When/where discovered
g Mostly Europe Roentgen (sort of)1901
W/Z CERN Rubbia/vanderMeer1984
gluon DESY NO
electron Europe Thomson 1906
muon Harvard No
tau SLAC Perl 1995
ne US Reines/Cowan
nm BNL Schwartz/Lederman/Steinberger 1988
nt FNAL NO
u,d SLAC s Friedman/Kendall/Taylor
s mostly US s NO
c SLAC/BNL Richter/Ting
b FNAL NO (Lederman)
t FNAL NO
muon – Street+Stevenson had “evidence” but Piccione often gets credit in the 1940s as measured lifetime

3. Couplings and Charges
All charged particles interact electromagnetically
All particles except gamma and gluon interact weakly (have nonzero “weak” charge) (partially semantics on photon as mixing defined in this way) A WWZ vertex exists
Only quarks and gluons interact strongly; have non-zero “strong” charge (called color). This has been tested by:
magnetic moment electron and muon
H energy levels (Lamb shift)
“muonic” atoms. Substitute muon for electron
pi-mu atoms
EM charge just electric charge q
Weak charge – “weak” isospin in i=1/2 doublets used for charged (W) and have I3-Aq for neutral current (Z)
Strong charge – color charge triplet “red” “green” “blue”

4. Strong Force and Hadrons
p + p -> p + N*
N* are excited states of proton or neutron (all of which are baryons)
P = uud n = udd (bound by gluons) where u = up quark (charge 2/3) and d = down quark (charge -1/3)
About 20 N states spin ½ mass 938 – 2700 MeV
About 20 D states spin 3/2
Charges = uuu(2) uud(1) udd(0) ddd(-1)
N,D decay by strong interaction N  p/n + p with lifetimes of sec (pion is quark-antiquark meson). Identify by looking at the invariant mass and other kinematic distributions

5. Baryons and Mesons
3 quark combinations (like uud) are called baryons. Historically first understood for u,d,s quarks
“plotted” in isospin (not spin, but puts p/n into an isospin pair)vs strangeness. Have a group of 8 for spin ½ (octet) and 10 (decuplet) for spin 3/2. Fermions and so need antisymmetric wavefunction (and have some duplication of quark flavor like p = uud)
Gell-Mann tried to explain using SU(3) but badly broken (seen in different masses) but did point out underlying quarks
Mesons are quark-antiquark combinations and so spin 0 or 1. Bosons and need symmetric wavefunction (“simpler” as not duplicating quark flavor)
Spin 0 (or spin 1) come in a group of 8 (octet) and a group of 1 (singlet). Again SU(3) sort of explains if there are 3 quarks but badly broken as seen in both the mass variations and the mixing between the singlet and octet

6. Baryons D0
also

7. Baryon Wave Functions. Mostly skip
Totally Antisymmetric as 3 s=1/2 quarks - Fermions
S=3/2. spin part must be symmetric (all “aligned”). There are some states which are quark symmetric (uuu,ddd,sss). As all members of the same multiplet have the same symmetries  quark and spin are both symmetric
to be antisymmetric, obey Pauli exclusion, need a new quantum number “color” which comes in 3 (at least) indices. Color wavefunctions:

8. Baryon Wave Functions. Mostly skip
S=1/2. color part is like S=3/2. So spin*quark flavor = symmetric. Adding 3 spin = ½ to give S=1/2 produces “mixed” spin symmetry.
First combine two quarks giving symmetric 1<->2
Add on third quark to get first term
Cycle 1  2  3  more terms. And then multiply by 6 color terms from S=3/2 page (12*6=72 terms)
Why no charge 2 or charge -1particles like the proton or neutron exist  the need for an antisymmetric wavefunction makes the proton the lightest baryon (which is a good thing for us)

9. Meson Wave Functions mostly skip
quark antiquark combinations. Governed by SU(2) (spin) and strangenessSU(3) (SU(4)) for c-quark). But broken symmetries
pions have no s quarks. The h’s (or the w+f) mix to find real particles  break SU(3)
meson mass Decay
p , no s
h little s
h’ mostly s
r no s
w little s
f % KK, 15% ppp

10. Hadron + Quark masses
Mass of hadron = mass of constituent quarks plus binding energy. As gluons have F=kx, increase in energy with separationpositive “binding” energy
Bare quark masses: u = 1-5 MeV d = 3- 9 MeV s = MeV c = 1.15 – 1.35 GeV b = 4.0–4.4 GeV t = GeV
Top quark decay so quickly it never binds into a hadron. No binding energy correction and so best determined mass value (though < 300 t quark decays observed)
Other quark masses determined from measured hadron masses and binding energy model pion = “2 u/d quarks” = 135 Mev proton = “3 u/d quarks” = 940 MeV kaon = “1 s and 1 u/d” = 500 MeV Omega = “3 s quarks” = 1672 MeV
High energy p-p interactions really q-q (or quark-gluon or gluon- gluon). “partons” emerge but then hadronize. Called “jets” whose energy and momentum are mostly original quark or gluon

11. Hadrons, Partons and Jets. Mostly skip
The quarks and gluons which make up a hadron are called partons (Feynman, Field, Bjorken)
Proton consists of: valence quarks (about 40% of momentum) gluons (about 50% opf the momentum) “sea” quark-antiquark pairs
The sea quarks are constantly being made/annihilated from gluons and can include heavier quarks (s,c,b) with probability mass- dependent
X = p/p(total) is the momentum fraction and each type of particle has a probability to have a given X (parton distribution function)
single quark produces other gluons and quarks  jet. Have similar fragmentation function

12. Lepton and Baryon Conservation
Strong and EM conserve particle type. Weak can change but always leptonlepton or quarkquark
So number of quarks (#quarks-#antiquarks) conserved. Sometimes called baryon conservation B.
Number of each type (e,mu,tau) conserved L conservation
Can always create particle-antiparticle pair
But universe breaks B,L conservation as there is more matter than antimatter
At small time after big bang #baryons = #antibaryons = #leptons = #antileptons (modulo spin/color/etc) = ~#photons (as can convert to particle-antiparticle pairs)
Now baryon/photon ratio 10-10

13. Hadron production + Decay
Allowed production channels are simply quark counting
Can make/destroy quark-antiquark pairs with the total “flavor” (upness = #up-#antiup, downness, etc) staying the same
All decays allowed by mass conservation occur quickly (<10-21 sec) with a few decaying by EM with lifetimes of ~10-16 sec) Those forbidden are long-lived and decay weakly and do not conserve flavor.

14. Hadrons and QCD. Partially skip
Hadrons are made from quarks bound together by gluons
EM force QuantumElectroDynamics QED strong is QuantumChromoDynamics QCD
Strong force “color” is equivalent to electric charge except three different (identical) charges red-green-blue. Each type of quark has electric charge (2/3 up -1/3 down, etc) and either r g b (or antired, antiblue, antigreen) color charge
Unlike charge=0 photon, gluons can have color charge. 8 such charges (like blue-antigreen) combos, 2 are colorless. Gluon exchange usually color exchange. Can have gluon-gluon interaction

15. quark-gluon coupling. Mostly skip
why q-qbar and qqq combinations are stable
8 gluons each with color and anticolor. All “orthogonal”. 2 are colorless gluons
coupling gluon-quark = +c coupling gluon-antiquark = -c r b
vertex 1 +c r
vertex 2 +c b
vertex 2 -c

16. Pions Use as strong interaction example Produce in strong interactions
Measure pion spin. Mirror reactions have same matrix element but different phase space/kinematics term. “easy” part of phase space is just the 2s+1 spin degeneracy term
Find S=0 for pions

17. EM Decay of Hadrons
If a photon is involved in a decay (either final state or virtual) then the decay is at least partially electromagnetic
Can’t have u-ubar quark go to a single photon as have to conserve energy and momentum (and angular momentum)
Rate is less than a strong decay as have coupling of 1/137 compared to strong of about 0.2. Also have 2 vertices in pi decay and so (1/137)2
EM decays always proceed if allowed but usually only small contribution if strong also allowed u g g
ubar

18. c-cbar and b-bbar Mesons
Similar to u-ubar, d-dbar, and s-sbar
“excited” states similar to atoms 1S, 2S, 3S…1P, 2P…photon emitted in transitions. Mass spectrum can be modeled by QCD
If mass > 2*meson mass can decay strongly
But if mass <2*meson decays EM. “easiest” way is through virtual photons (suppressed for pions due to spin) c g m+ m-
cbar

19. c-cbar and b-bbar Meson EM-Decays: SKIP
Can be any particle-antiparticle pair whose pass is less than psi or upsilon: electron-positron, u-ubar, d-dbar, s-sbar
rate into each channel depends on charge2(EM coupling) and mass (phase space)
Some of the decays into hadrons proceed through virtual photon and some through a virtual (colorless) gluon) c g
cbar

20. Electromagnetic production of Hadrons
Same matrix element as decay. Electron-positron pair make a virtual photon which then “decays” to quark-antiquark pairs. (or mu+-mu-, etc)
electron-positron pair has a given invariant mass which the virtual photon acquires. Any quark-antiquark pair lighter than this can be produced
The q-qbar pair can acquire other quark pairs from the available energy to make hadrons. Any combination which conserves quark counting, energy and angular momentum OK e+ g q
qbar e-

21. Weak Decays
If no strong or EM decays are allowed, hadrons decay weakly (except for stable proton)
Exactly the same as lepton decays. Exactly the same as beta decays
Charge current Weak interactions proceed be exchange of W+ or W-. Couples to 2 members of weak doublets (provided enough energy) U d u d W e n

22. Decays of Leptons
Transition leptonneutrino emits virtual W which then “decays” to all kinematically available doublet pairs
For taus, mass=1800 MeV and W can decay into e+n, m+n, and u+d (s by mixing). 3 colors for quarks and so rate ~3 times higher. W e

23. Weak Decays of Hadrons
Can have “beta” decay with same number of quarks in final state (semileptonic)
or quark-antiquark combine (leptonic)
or can have purely hadronic decays
Rates will be different: 2-body vs 3-body phase space; different spin factors. Note s quark goes to up: mixing, more later W e

24. Top Quark Decay Simplest weak decay (and hadronic).
M(top)>>Mw (175 GeV vs 81 GeV) and so W is real (not virtual) and there is no suppression of different final states due to phase space
the t quark decays before it becomes a hadron. The outgoing b/c/s/u/d quarks are seen as jets t b W c u

25. Top Quark Decay Very small rate of ts or td
the quark states have a color factor of 3 t b W

26. How to Discover the Top Quark skip
make sure it wasn’t discovered before you start collecting data (CDF run top mass too heavy)
build detector with good detection of electrons, muons, jets, “missing energy”, and some B-ID (D0 Run I bm)
have detector work from Day 1. D0 Run I: 3 inner detectors severe problems, muon detector some problems but good enough. U-LA cal perfect
collect enough data with right kinematics so statistically can’t be background. mostly W+>2 jets
Total: 17 events in data collected from with estimated background of 3.8 events

27. The First Top Quark Event
muon
electron

28. u dbar Decay Rates: Pions Look at pion branching fractions (BF)
The Beta decay is the easiest. ~Same as neutron beta decay u
dbar

29. Pi Decay to e-nu vs mu-nu
Depends on phase space and spin factors
in pion rest frame pion has S=0
2 spin=1/2 combine to give S=0. Nominally can either be both right- handed or both left-handed
But parity violated in weak interactions. If m=0  all S=1/2 particles are LH and all S=1/2 antiparticles are RH
neutrino mass = 0  LH
electron and muon mass not = 0 and so can have some “wrong” helicity. Antiparticles which are LH. But easier for muon as heavier mass L+ nu

30. Polarization of Spin 1/2 Particles. Mostly skip
Obtain through Dirac equation and polarization operators. Polarization defined
the degree of polarization then depends on velocity. The fraction in the “right” and “wrong” helicity states are:
fraction “wrong” = 0 if m=0 and v=c
for a given energy, electron has higher velocity than muon and so less likely to have “wrong” helicity

31. Pion Decay Kinematics. Skip
2 Body decay. Conserve energy and momentum
can then calculate the velocity of the electron or muon
look at the fraction in the “wrong” helicity to get relative spin suppression of decay to electrons

32. Muon Decay. Partially skip
Almost 100% of the time muons decay by (have gamma few percent)
Q(muon decay) > Q(pionmuon decay) but there is significant spin suppression and so muon’s lifetime ~100 longer than pions
spin 1/2 muon  1/2 mostly LH (e) plus /2 all LH( nu) plus 1/2 all RH (antinu)
3 body phase space and some areas of Dalitz plot suppressed as S=3/2
electron tends to follow muon direction and “remember” the muon polarization. Dirac equation plus a spin rotation matrix can give the angular distribution of the electron relative to the muon direction/polarization