The Dalitz plot in decay is observed to have essentially zero event density along the…
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 ω(782) Dalitz plot in ω→π+π−π0 decay is observed to have essentially zero event density along the entire kinematic boundary and a strong central peak. A hypothetical narrow resonance Y(1405), also decaying to π+π−π0, is instead found to have a roughly uniform Dalitz-plot density everywhere, including right up to the boundary, with only a small 10% linear variation across the plot.
((a)) Using the amplitude built from the momenta p+ and p− of the charged pions in the three-pion rest frame for a JP=1− parent, explain in one or two sentences why the ω plot must vanish on the boundary.
((b)) Which JP is consistent with the near-flat Y(1405) plot? Justify by naming the amplitude structure that would produce it.
((c)) State the one previously met three-pion decay whose measured Dalitz plot shares this plot's population right up to the boundary, and say how the two plots differ.