Dalitz Plot

  The Dalitz plot is a way to represent the entire phase space, viz. all essential kinematical variables, of any three-body final state in a scatter plot or two-dimensional histogram. Dalitz introduced it in 1953 [Dalitz53]. Let a reaction be

For a given incident energy, two of the three possible two-body effective masses of the final state fully describe the reaction. Choosing as abscissa and ordinate the squares of the effective masses (p_i = four-momentum of track i)

the third effective mass squared (m₃₅²) is constant along lines at , as

For fixed p₁ and p₂, i.e. fixed total energy, the physical region of a Dalitz plot is inside a well-defined area, and in the absence of resonances or interferences can be shown to be uniformly populated. Resonant behaviour of two of the final state particles gives rise to a band of higher density, parallel to one of the coordinate axes or along a line.

The following graph shows a Dalitz plot for the annihilation process

an example taken from the Crystal Barrel experiment, of exceptionally high statistics (here some 750000 events, from [Landua96]):

In its projection, the various f₀- and f₂-resonances are clearly visible. The plot has an inherent 6-fold symmetry, as all particles are identical.