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
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2. When/where discovered
Nobel Prize?
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
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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”
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4. Pi-mu coupling
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5. 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
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6. ISOSPIN
Assume the strong force is ~identical between baryons (p,n,N*) and between three pions
Introduce concept of Isospin with (p,n) forming an isopsin doublet I=1/2 and pions in an isopsin triplet I=1, and quarks (u,d) in a I=1/2 doublet
Isospin isn’t spin but has the same group algebra SU(2) as spin and so same quantum numbers and addition rules
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7. Baryons and Mesons
3 quark combinations (like uud) are called baryons. Historically first understood for u,d,s quarks
“plotted” in isospin 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
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8. Baryons and Mesons
Use group theory to understand: what states are allowed “mixing” (how decay) state changes (step-up/down) magnetic moments of
as masses are so different this only partially works – broken
SU(2) Isospin –very good (u/d quark same mass) SU(3) for s-quark – good with caveats SU(4) with c-quark – not so good
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9. Baryons
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10. Baryon Wave Functions
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:
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11. Baryon Wave Functions
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 (4*9*6=216 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)
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12. Meson Wave Functions
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
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13. 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
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14. Hadrons, Partons and Jets
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 or pdf)
PDFs mostly measured in experiments using nu,e,mu,p etc. Some theoretical modeling
Even at highest energy collisions, quarks still pointlike particles (no structure) as distances of F (G. Blazey et al)
single quark produces other gluons and quarks  jet. Have similar fragmentation function
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15. Fragmentation functions
u,d,s p c
fraction of energy which quark (or gluon) has for either particle or jet b
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16. 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
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17. 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.
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18. Hadrons and QCD 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
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19. quark-gluon coupling 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
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20. Group Theory
W/Z bosons and gluons carry weak charge and color charge (respectively)Bosons couple to Bosons
SU(2) and SU(3) which have 3 and 8 “base” vectors can be used to represent weak and strong forces. The base vectors are the W+,W-,Z and the 8 gluons. Exact (non-broken) symmetry
The group algebra tells us about boson interaction. So for W/Z use
SU(2) used for 3D rotations angular momentum (orbital and spin) isospin (hadrons – broken) weak interactions  weak “isospin”
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21. Group Theory – SU(3)
3x3 unitary matrices with det=1. 2n2-n2-1=8 parameters. Have group algebra
and representation of generators
and 3 color states
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22. 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
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23. More Pions p p -> d pi+ Total I ½ ½ 0 1 1 Iz ½ ½ 0 1 1
Useful to think of pions as I=1 isospin triplet and p,n is I=1/2 doublet (from quark plots)
Look at reactions:
p p -> d pi Total
I ½ ½
Iz ½ ½
p n -> d pi Total
I ½ ½ or 1
Iz ½ - ½
in the past we combined 2 spin ½ states to form S=0 or 1
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24. More Pions
Reverse this and say eigentstate |p,n> is combination of I=1 and I=0
reactions:
then take the “dot product” between |p,n> and |d,pi0> brings in a 1/sqrt(2) (the Clebsch-Gordon coefficient)
Square to get A/B cross section ratio of 1/2
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