Dalitz plot

File:Dalitz plot.svg 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.|306x306px]]

File:Dalitz plot of D meson decay to two kaons and a pion.png experiment at CERN.{{cite journal

|author=The LHCb collaboration.

|year=2019

|title=Measurement of the branching fractions of the decays D+ → K−K+K+, D+ → π−π+K+ and D+s → π−K+K+

|journal=Journal of High Energy Physics

|volume=2019 |issue=176

|doi=10.1007/JHEP03(2019)176

|hdl=2445/162294

|hdl-access=free

}} Clear resonances $K^\{*0\}$ (vertical region of enhancement) and $\backslash phi$ (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.|306x306px]]

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.{{cite journal

|author=R. H. Dalitz

|year=1953

|title=On the analysis of τ-meson data and the nature of the τ-meson

|journal=Philosophical Magazine

|volume=44 |issue=357

|pages=1068–1080

|doi=10.1080/14786441008520365

}}{{cite journal

|author=R. H. Dalitz

|year=1954

|title=Decay of τ mesons of known charge

|journal=Physical Review

|volume=94 |pages=1046–1051

|doi=10.1103/PhysRev.94.1046

|bibcode = 1954PhRv...94.1046D

|issue=4 }}

The phase-space of a decay of a pseudoscalar into three spin-0 particles 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.

Dalitz plots play a central role in the discovery of new particles in current high-energy physics experiments, including Higgs boson research,{{cite news | first=Frank | last=Close | url=https://www.theguardian.com/obituaries/story/0,3604,1693226,00.html | title=Richard Dalitz: Physicist who mapped the behaviour of exotic particles and argued for the reality of quarks | publisher=The Guardian | date=24 January 2006}} and are tools in exploratory efforts that might open avenues beyond the Standard Model.P. Pakhlov and T. Uglov, Flavor physics at Super B-factories era, J. Phys.: Conf. Ser. 675, 022009 (2016).

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"{{cite journal

|author=E. Fabri

|year=1954

|title=A study of τ-meson decay

|journal=Nuovo Cimento

|volume=11 |pages=479–491

|doi=10.1007/BF02781042

|issue=5

|bibcode=1954NCim...11..479F

|s2cid=120859580

}}). It can be adapted to the analysis of four-body decays as well.{{cite journal

|author= M. Schulz

|year=2007

|title=Four-particle Dalitz plots to visualize atomic break-up processes

|journal=Journal of Physics B

|volume=40 |pages=3091–3099

|doi=10.1088/0953-4075/40/15/009

|bibcode = 2007JPhB...40.3091S

|issue= 15 |display-authors=etal}} 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.