# Dalitz plot

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## Dalitz plot

Pictorial representation in high-energy nuclear physics for data on the distribution of certain three-particle configurations. Many elementary-particle decay processes and high-energy nuclear reactions lead to final states consisting of three particles (which may be denoted by *a*, *b*, *c*, with mass values *m*_{a}, *m*_{b}, *m*_{c}). Well-known examples are provided by the *K*-meson decay processes, Eqs. (1) and (2), and by the *K*- and -meson reactions with hydrogen, Eqs. (3) and (4).

*E*(measured in the barycentric frame), these final states have a continuous distribution of configurations, each specified by the way this energy

*E*is shared among the three particles. (The barycentric frame is the reference frame in which the observer finds zero for the vector sum of the momenta of all the particles of the system considered.)

*See*Elementary particle

If the three particles have kinetic energies *T*_{a}, *T*_{b}, and *T*_{c} (in the barycentric frame), Eq.

*F*within an equilateral triangle

*LMN*of side 2

*Q*/3, such that the perpendiculars

*FA*,

*FB*, and

*FC*to its sides are equal in magnitude to the kinetic energies

*T*

_{a},

*T*

_{b}, and

*T*

_{c}. The most important property of this representation is that the area occupied within this triangle by any set of configurations is directly proportional to their volume in phase space.

Not all points *F* within the triangle *LMN* correspond to configurations realizable physically, since the *a*, *b*, *c* energies must be consistent with zero total momentum for the three-particle system. With nonrelativistic kinematics and with equal masses *m* for *a*, *b*, *c*, the only allowed configurations are those corresponding to points *F* lying within the circle inscribed within the triangle, shown as (i) in the illustration. More generally, with relativistic kinematics, the limiting boundary is distorted as illustrated by the boundary curve (ii), drawn for the ω → 3π decay process, where the final masses are equal.