Dalitz plot
Encyclopedia
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 decay
s may move apart.
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 mass
es 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.
R.H. Dalitz
introduced this technique in 1953 to study decays of K mesons (which at that time were still referred to as "tau-mesons"). It can be adapted to the analysis of four-body decays as well. 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.
Scatterplot
A scatter plot or scattergraph is a type of mathematical diagram using Cartesian coordinates to display values for two variables for a set of data....
often used in particle physics
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
to represent the relative frequency of various (kinematically distinct) manners in which the products of certain (otherwise similar) three-body decay
Particle decay
Particle decay is the spontaneous process of one elementary particle transforming into other elementary particles. During this process, an elementary particle becomes a different particle with less mass and an intermediate particle such as W boson in muon decay. The intermediate particle then...
s may move apart.
The kinematics
Kinematics
Kinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces that cause the motion....
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 mass
Invariant mass
The invariant mass, rest mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference related by Lorentz transformations...
es 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
Dynamics (mechanics)
In the field of physics, the study of the causes of motion and changes in motion is dynamics. In other words the study of forces and why objects are in motion. Dynamics includes the study of the effect of torques on motion...
of three-body decays.
R.H. Dalitz
Richard Dalitz
Richard Henry Dalitz was an Australian physicist known for his work in particle physics.Born Dimboola, Victoria near Melbourne, Dalitz studied physics and mathematics at Melbourne University before moving to the United Kingdom in 1946, starting his PhD research at the University of Cambridge...
introduced this technique in 1953 to study decays of K mesons (which at that time were still referred to as "tau-mesons"). It can be adapted to the analysis of four-body decays as well. 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.