Outline of Topics discussed in the Lecture for Graduate Nuclear Physics 
(PHYS722/822 Fall 2018)

QCD

• Elementary objects: Quarks u,d,s,c,b,t and their antiparticles
• Quantum numbers of quarks: I, I₃, S, C,... All quarks have baryon number A=1/3 and charge Q = 2/3 (u,c,t) or -1/3 (d,s,b)
• General formula for charge (for ALL hadrons): Q = I₃ + (A+S+C+...)/2
• All of these "flavor" quantum numbers change sign (except I) for antiquarks
• Additional quantum number: Color charge (r,g,b for quarks; "y,m,c" = yellow, magenta, cyan for antiquarks)
• Necessary to account for Fermi statistics of Delta⁺⁺
• Necessary to account for 3 times higher production cross section for quarks than for muons in e⁺e^- annihilation
• Is absolutely conserved (like electric charge)
• Is the source of the strong interaction
• Quantum Chromo Dynamics (QCD): interaction between quarks and gluons due to color charge
• Eight gluons, each carrying a color (r,g,b) AND an anti-color (y,m,c). Interact with quarks by changing their color. Example: a blue quark (b) can absorb a green-antiblue (gy)  gluon to become a green quark (g).
• Gluons are massless, electrically neutral gauge bosons with spin 1 (just like photons)
• Gluons can couple to each other directly (NOT like photons) =>
• Running Coupling Constant a_S (Q²): Proportional to 1/ln(Q²/L_QCD²) where L_QCD is the only scale (about 200 MeV) of the theory.
• Due to an interplay of dielectric screening (quark-antiquark pairs) and gluonic enhancement (wins out) of color charges at large distances
• Asymptotic Freedom at large momenta/small distances: a_S is small (0.116 at the mass of the Z boson), perturbation theory works, DIS and many other "hard processes" can be quantitatively explained
• Confinement at small momenta/large distances: a_S is large, perturbation theory breaks down. Only "exact" solution is numerical (Lattice QCD). Can use symmetries of the Lagrangian for effective theories (Chiral symmetry).
• Consequence: Only completely colorfree objects (color singletts) can exist in Nature
• Quarks and gluons cannot be observed in isolation. Lowest possible states are quark-antiquark (Mesons) and three-quark (Baryons). Potential rises linearly with quark separation (flux tube or string model) until the "rubber band snaps" and new mesons are created.
• Effective degrees of freedom at small energies: Constituent quarks (=valence quarks surrounded by a "cloud" of gluons and quark-antiquark pairs) with large mass (300-400 MeV).

QCD and the structure of Hadrons

• Describe Hadrons by the minimum number of valence quarks they must contain (uud for proton, udd for neutron etc.)
• Describe all other quark/antiquark pairs and gluons by the "effective mass" and "effective interaction" of these "constituent quarks" (now called U, D, S,...)
• Potential has Coulomb-like short-range structure, linear confinement form at large distance, and a strong spin-spin ("chromomagnetic") force that wants to anti-align quark spins.

(explains Delta-Nucleon mass splitting and rho-pion mass splitting)
• Decuplett baryons (Deltas, Sigma*s, Xi*s and Omega) have completely symmetric wave functions in space, flavor and spin seperately (J = 3/2)
• Octett baryons (proton/neutron, Sigmas, Xis, and Lambda) have mixed symmetry in spin and flavor; see my HUGS writeup and our text books
• Mesons come in two Octetts (Spin 0: 3 pions, 4 kaons, 1eta; Spin 1: 3 rhos, 4 K*s, 1 omega) and two Singletts (Spin 0: eta'; Spin 1: phi). The spin-0 ones have lower mass and are called "pseudoscalars" because their parity is negative; the spin-1 ones are called "vector".
• All hadrons can be excited in radial and angular momentum quantum numbers -> huge number of "particles".
• More information on Baryons, Mesons, and all elementary particles (quarks and leptons) can be found at http://www-pdg.lbl.gov/, especially at http://particleadventure.org/