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 Standard Model: paper by Chiara Mariotti parameters of Standard Model
fundamental interaction
SU(3) gauge group, acting on color
gauge bosons = gluons (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 strong interaction?
-- for quarks and color charge?
"strong" interaction between nucleons
(modern: residual interaction, similar to van der Waals, exchange of pions of other mesons)
significant fraction of energy not from constituent quarks (see quark masses),
but binding energy ("sea quarks") other evidence for strong interaction:
sub-structure of the proton
-- 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 baryons/mesons
color degrees of freedom:
-- help to reduce certain anomalies (too technical) -- restore Pauli principle
example: Delta resonance
a "spin excitation" of the nucleon charges -1, 0, +1, +2
mass 1232 MeV, width 118 MeV (very wide <> decay via strong interaction)
isospin 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-particles 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 (parity -, spin 0 = "pseudoscalar") nonet of mesons (pseudo-scalar or vector)
pure u, d excitations of the pion
eta meson (548 MeV, 10^-19 sec lifetime), neutral (isospin 0, spin 0, parity -,
pseudoscalar), mixes with s s-bar rho meson 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
omega meson, 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
strange quark: example of Omega baryon, 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.
