Strong Interaction Lecture Quantum Mechanics II, 2020 Feb 07 online .pdf version contains links to wikipedia and other stuff (click on underlined keywords) history of : paper by Chiara Mariotti parameters of Standard Model fundamental interaction SU(3) gauge group, acting on color gauge = (8 generators, Gell-Mann matrices) triplet of color states: action of generators on 3-component vectors, plot eigenvalues of lambda_3 and lambda_8 for eigenvectors octet of gluons (see graphic): action of generators via commutator on generators themselves ("adjoint representation"). Plot eigenvalues: octet figure. what experimental evidence -- for the ? -- for and color ?

"strong" interaction between (modern: residual interaction, similar to van der Waals, exchange of of other ) significant fraction of energy not from constituent quarks (see masses), but binding energy ("sea quarks") other evidence for strong interaction: sub-structure of the -- gyromagnetic ratio is not even close to 2 (see table here) electromagnetic form factor <> charge distribution inside the proton: not point-like (scattering amplitude not 1/q^2, but different at large q) short-lived resonances O(10^-24 sec) -- check out from list of /mesons color degrees of freedom: -- help to reduce certain anomalies (too technical) -- restore Pauli principle example: Delta resonance a " excitation" of the charges -1, 0, +1, +2 mass 1232 MeV, width 118 MeV (very wide <> decay via strong interaction) quadruplet (I = 3/2), spin 3/2 ("spin excitation of the nucleon")

(anti)symmetry of fermionic wave function: hint for color q# Delta^+2: all spins up (total +3/2), all isospins up (uuu, total isospin 3/2), make antisymmetric by writing sum epsilon_{abc} u^a u^b u^c with charge labels a, b, c = r, g, b

Exercise: construct diagram for decay within quark picture end product mostly: nucleon + pi -- separate "sea quarks" nucleons N (p, n) as isospin doublet (anti- have opposite isospin components) (only u and d quarks are assigned an isospin, number of s, c, ... quarks is a separate quantum number -- although: when discussing the weak interaction, each quark generation is an isospin doublet) two-quark composite particles = mesons overview on only from u, d: pi, rho, omega, eta table with masses and quantum numbers wikipedia overview with nonet schemes for mesons pions pi as isospin triplet, isospin 1, spin 0 masses pi^+-: 139 MeV, lifetime 2.6 10^-8 sec pi^0: 135 MeV, width ~ 8 eV, lifetime 8.5 10^-17 sec (much shorter!) charged pions are made from u d-bar or d u-bar pair decay via weak interaction into µ + neutrino_µ the pi^0 decays via em interaction (annihilation of d d-bar and u u-bar pairs) symmetry of wave function ( -, spin 0 = "pseudoscalar") nonet of mesons (pseudo-scalar or vector) pure u, d excitations of the eta (548 MeV, 10^-19 sec lifetime), neutral (isospin 0, spin 0, parity -, pseudoscalar), mixes with s s-bar with charges -1, 0, +1 spin-1 (vector), isospin 1 mass 775 MeV, width 149 MeV (10^-24 sec) decay into two pi via strong interaction , charge 0 spin-1, isospin 0 mass 783 MeV, with 8.4 MeV scalar mesons (spin 0): composition still unclear, e.g. around 400–550 MeV : example of Omega , full decuplets/ octets, SU(3) group with u, d, s as basis vectors ("light quarks") further aspects of quark physics

-- CKM flavor mixing matrix (in Higgs mechanism)

-- problem of confinement: "why no naked colored objects seen?" linear scaling of interaction potential

-- asymptotic freedom: specific scaling of renormalisation, interactions become weaker at high energies.

-- ground state of QCD: unstable vacuum, quark condensate ...? low-energy challenge of non-perturbative QCD, difficult.