An introduction to the quark model

Few-charge systems History of the quark model Mesons Baryons Multiquarks and other exotics Outlook
Permutation symmetry for (qqQ)
For instance Ξ − = (ssd) or Λ = (uds) in the limit where SU(2) is
exact
Ψ = ψ(x, y) ψs ψi ψc ,
should be antisymmetric (A), given that ψc is A,
For instance Λ ground state has I = 0 (A), and Sqq = 0 (A), while
ψ(x, y) is symmetric (S) in x,
For instance, ψ(x, y) ∝ exp[−a x 2 − b y 2 ] in HO.
First orbital excitation of Λ? Keep I = 0. If ψ(x, y) is excited in y,
i.e., ℓy = 1, then keep Sqq = 0, thus Sqqs = 1/2 and two
possibilities
J = 1/2
J = 3/2
with the possibility of spin-orbit splitting among them
Other orbital excitation of Λ? Yes, with ψ(x, y) now odd in x, and
thus Sqq = 1, and various recoupling for Sqqs and J.
JMR Quark Model