(PHYS722/822 Fall 2018)

- Elementary objects: Quarks u,d,s,c,b,t and their antiparticles
- Quantum numbers of quarks: I, I
_{3}, 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 = I
_{3}+ (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}(Q^{2}): Proportional to 1/ln(Q^{2}/L_{QCD}^{2}) 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).

- 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.
- 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/

(explains Delta-Nucleon mass splitting and rho-pion mass splitting)