1. P461 - particles I1 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. P461 - particles I2 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 (callel 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”

3. P461 - particles I3 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  states spin 3/2 Charges = uuu(2) uud(1) udd(0) ddd(-1) N,  decay by strong interaction N -> p/n +  with lifetimes of 10 -23 sec (pion is quark-antiquark meson)

4. P461 - particles I4 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 triplit 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

5. P461 - particles I5 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 (deculplet) for spion 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 0f 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. P461 - particles I6 Baryon Wave Functions Antisymmetric as 3 s=1/2 quarks 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:

7. P461 - particles I7 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 -> 1 8 more terms. And then multiply by 6 color terms from S=3/2 page 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

8. P461 - particles I8 Hadron + Quark masses Mass of hadron = mass of constituent quarks plus binding energy Bare quark masses: u = 1-5 MeV d = 3-9 MeV s = 75-170 MeV c = 1.15 – 1.35 GeV b = 4.0–4.4 GeV t = 169-179 GeV Top quark decay so quickly it never binds into a hadron. No binding energy correction and so best determined mass value (though < 200 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

9. P461 - particles I9 Hadrons, Partons and Jets The quarks and gluons which make up a hadron are called partons Proton consists of: 3 valence quarks (about 40% of momentum) gluons (about 50% opf the momentum) “sea” quark-antiquark pairs The sea quarks are constanly 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 0f 0.002 F (G. Blazey et al)