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# .

The Dalitz plot is a scatterplot 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.[1][2]

The kinematics of a three-body decay can be completely described using two variables. In a traditional Dalitz plot, the axes of the plot are the squares of the invariant masses of two pairs of the decay products. (For example, if particle A decays to particles 1, 2, and 3, a Dalitz plot for this decay could plot m212 on the x-axis and m223 on the y-axis.) If there are no angular correlations between the decay products then the distribution of these variables is flat. However symmetries may impose certain restrictions on the distribution. Furthermore, three-body decays are often dominated by resonant processes, in which the particle decays into two decay products, with one of those decay products immediately decaying into two additional decay products. 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 and they are one of the tools applied in the search for the Higgs boson.[3]

R.H. Dalitz introduced this technique in 1953[1][2] to study decays of K mesons (which at that time were still referred to as "tau-mesons"[4]). It can be adapted to the analysis of four-body decays as well.[5] 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.
References

^ a b R. H. Dalitz (1953). "On the analysis of τ-meson data and the nature of the τ-meson". Philosophical Magazine 44: 1068. doi:10.1080/14786441008520365.
^ a b R. H. Dalitz (1954). "Decay of τ mesons of known charge". Physical Review 95 (4): 1046. Bibcode 1954PhRv...94.1046D. doi:10.1103/PhysRev.94.1046.
^ A. Kasmi, Search for the Standard Model Higgs Boson in final states with photons or taus at the Tevatron, PoS (EPS-HEP 2011) 237
^ E. Fabri (1954). "A study of τ-meson decay". Nuovo Cimento 11 (5): 479. doi:10.1007/BF02781042.
^ M. Schulz et al. (2007). "Four-particle Dalitz plots to visualize atomic break-up processes". Journal of Physics B 40 (15): 3091. Bibcode 2007JPhB...40.3091S. doi:10.1088/0953-4075/40/15/009.