Particle Physics, Ch Hadrons: baryons, mesons and their quark content
Problem
A charm quark c and a charm antiquark cˉ combine to form a meson. The spin-1 state is the J/ψ (mass 3096.9MeV/c2) and the spin-0 state is the ηc (mass 2983.9MeV/c2). Two spin-arrow diagrams are proposed for the pair:
((a)) Diagram A: the two arrows are drawn pointing in the same direction (both up). State which total spin this arrangement belongs to, and name the charmonium state.
((b)) Diagram B: the two arrows are drawn pointing in opposite directions (one up, one down). Using the count of the four two-label arrangements among total spin 0 and total spin 1, explain why this picture alone cannot tell you whether the meson is the J/ψ or the ηc, and say what measurement would decide.