A bound state is a system of interacting particles held together so that its total energy is lower than that of the free constituents, and hence cannot dissociate without an input of energy. In QCD the physical spectrum consists entirely of color-singlet bound states of quarks and gluons — a consequence of confinement.
The observed strongly-interacting bound states (hadrons) fall into families defined by their color-singlet content:
- Mesons — quark–antiquark, \(\bar q_a q^a\), e.g. the pion \(\pi\), the kaon \(K\), the \(\rho\). Integer spin, hence bosons.
- Baryons — three quarks, \(\epsilon^{abc}q_a q_b q_c\), e.g. the proton \(uud\), neutron \(udd\), \(\Omega^-=sss\), \(\Delta^{++}=uuu\). Half-integer spin, hence fermions.
- Exotics — tetraquarks, pentaquarks, glueballs and hybrids, all still color singlets.
Unlike the Coulomb bound states of QED (atoms), quark bound states arise from a potential that rises with separation. A useful phenomenological form for the static quark–antiquark potential is the "Cornell" potential
with a short-distance Coulomb-like term and a long-distance linear term of string tension \(\sigma\approx (440\ \text{MeV})^2\). The linear term makes it impossible to isolate a single quark: pulling the pair apart eventually creates a new \(\bar q q\) pair from the vacuum rather than freeing a color charge.
Most of a hadron's mass is not the sum of current-quark masses but binding/field energy: the proton mass (\(\approx 938\) MeV) vastly exceeds \(2m_u+m_d\approx 9\) MeV. Computing this spectrum from first principles is a central goal of lattice QCD, which evaluates hadron correlators on gauge configurations to extract bound-state masses.