Outline of Topics discussed in the Lecture for Graduate Nuclear
(PHYS722/822 Fall 2018)
- Elementary objects: Quarks u,d,s,c,b,t and their antiparticles
- Quantum numbers of quarks: I, I3, S, C,... All quarks
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
- All of these "flavor" quantum numbers change sign (except I)
- 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
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
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
- Gluons can couple to each other directly (NOT like photons)
- Running Coupling Constant aS
Proportional to 1/ln(Q2/LQCD2)
where LQCD is the only scale
200 MeV) of the theory.
- Due to an interplay of dielectric screening (quark-antiquark
gluonic enhancement (wins out) of color charges at large distances
- Asymptotic Freedom at large momenta/small distances: aS
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: aS
is large, perturbation theory breaks down. Only "exact" solution is
(Lattice QCD). Can use symmetries of the Lagrangian for effective
- Consequence: Only completely colorfree objects (color
- Quarks and gluons cannot be observed in isolation. Lowest
are quark-antiquark (Mesons) and three-quark (Baryons). Potential rises
linearly with quark separation (flux tube or string model) until the
band snaps" and new mesons are created.
- Effective degrees of freedom at small energies: Constituent
quarks surrounded by a "cloud" of gluons and quark-antiquark pairs)
large mass (300-400 MeV).
QCD and the structure of Hadrons
- Describe Hadrons by the minimum number of valence quarks they
(uud for proton, udd for neutron etc.)
- Describe all other quark/antiquark pairs and gluons by the
and "effective interaction" of these "constituent quarks" (now called
- Potential has Coulomb-like short-range structure, linear
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
wave functions in space, flavor and spin seperately (J = 3/2)
- Octett baryons (proton/neutron, Sigmas, Xis, and Lambda) have
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
4 K*s, 1 omega) and two Singletts (Spin 0: eta'; Spin 1: phi). The
ones have lower mass and are called "pseudoscalars" because their
is negative; the spin-1 ones are called "vector".
- All hadrons can be excited in radial and angular momentum quantum
-> huge number of "particles".
- More information on Baryons, Mesons, and all elementary particles
and leptons) can be found at http://www-pdg.lbl.gov/,
especially at http://particleadventure.org/
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