PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model · Symmetry, groups and the quark model
Symmetry and Flavour, Ch Parity, charge conjugation and time reversal as operators, and the CPT theorem
Problem
The J/ψ is a ccˉ meson with JPC=1−−. Its hadronic decays proceed through annihilation of the ccˉ pair into gluons alone, which then convert to hadrons, and the strong interaction conserves C throughout. Take three facts from quantum chromodynamics without proof. A gluon, unlike a photon, is not by itself an eigenstate of C^, because C^ also acts on its colour; and a single gluon carries colour, so it cannot be the whole final state of a colourless meson's annihilation. The colourless state of two gluons has C=+1, as two photons do. Colourless three-gluon states with C=−1 exist.
((a)) Using C(J/ψ)=−1, decide whether the J/ψ can annihilate into two gluons.
((b)) State the minimum number of gluons through which the J/ψ can decay hadronically, and name the decay of a C=−1 state into photons that it parallels.