Dalitz plot

The Dalitz plot is a two-dimensional plot often used in particle physics to represent the relative frequency of various (kinematically distinct) manners in which the products of certain (otherwise similar) three-body decays may move apart.

[2][3] The phase-space of a decay of a pseudoscalar into three spin-0 particles can be completely described using two variables.

If there are no angular correlations between the decay products then the distribution of these variables is flat.

In this case, the Dalitz plot will show a non-uniform distribution, with a peak around the mass of the resonant decay.

In this way, the Dalitz plot provides an excellent tool for studying the dynamics of three-body decays.

Dalitz plots play a central role in the discovery of new particles in current high-energy physics experiments, including Higgs boson research,[4] and are tools in exploratory efforts that might open avenues beyond the Standard Model.

[5] R.H. Dalitz introduced this technique in 1953[2][3] to study decays of K mesons (which at that time were still referred to as "tau-mesons"[6]).

[7] A specific form of a four-particle Dalitz plot (for non-relativistic kinematics), which is based on a tetrahedral coordinate system, was first applied to study the few-body dynamics in atomic four-body fragmentation processes.

Modeling of the common representation of the Dalitz plot can be complicated due to its nontrivial shape.

One can however introduce such kinematic variables so that Dalitz plot gets a rectangular (or squared) shape:[8]

This technique is commonly called "Square Dalitz plot" (SDP).

Dalitz plot for a three-body decay of a spin-0 particle of the mass into three spin-0 particles of masses , , . The grey area depicts the allowed kinematic region. The blue line shows a possible position of accumulation of events in case a spin-0 resonance is present as an intermediate state in this three-body decay, which then decays to particles 1 and 2. The orange line shows the position of accumulation of events in case another spin-0 resonance is present, decaying to particles 1 and 3.
Dalitz plot for the decay in data of the LHCb experiment at CERN . [ 1 ] Clear resonances (vertical region of enhancement) and (horizontal enhancement) can be seen. Distribution of events around resonant regions is not uniform due to spin 1 of the resonances, and interference between the resonant and non-resonant processes.