# Dalitz plot analysis

I have seen a few Dalitz plots so far and tried to understand how they are useful. So one of the advantages of these plot is that the non-uniformity in the plots can tell something about the intermediate states that we cannot detect. My question is how do you extract the mass of these resonant particles from such plots? What additional information would you need?

• this wiki entry seems sufficient to me en.wikipedia.org/wiki/Dalitz_plot . The mass you extract from the mass plot, once you know the kinematic region where it is clear, you can cut and clean a resonance. – anna v Mar 14 '13 at 7:26
• no no. I know that density variations correspond to resonances but what I dont know is how the dense regions mathematically relate to the mass of the resonant particles. – venu Mar 14 '13 at 19:38
• I'm sorry I'll make that more precise by saying that I know that the more dense regions on the plot may correspond to resonances but I don't understand how to calculate the mass of the resonant particles. – venu Mar 14 '13 at 19:39
• Do you know about cuts in variables? From the link above: "For example, if particle A decays to particles 1, 2, and 3, a Dalitz plot for this decay could plot m12^2 on the x-axis and m23^2 on the y-axis." The two axis are the square of the invariant mass of the pairs of particles. The Daliz plot shows where another resonance may exist which can interfere with the fit for the mass in the projection. If you cut the second mass the fit ( a gaussian, or a breit-wigner) for the first can be clearer and unbiased. – anna v Mar 15 '13 at 3:35
• The Dalitz plot is not for resonance discovery, but for a study of the three body state: virgilio.mib.infn.it/~dini/meson2004/img2.html . – anna v Mar 15 '13 at 3:45

## 1 Answer

Let me make my comments into an answer:

A Dalitz plot is a tool for further study of resonances, not for determining their mass. Resonances are seen on the plot for the invariant mass distribution, the the square root of the measure of the four vector of the sum of the constituent particles. As with the recent discovery of the Higgs. In this plot, which is the invariant mass distribution of the sum of many particles, a number of cuts have been applied to clean up the resonance, and a fit ( red line) gives the mass.

The Dalitz plot is for the simpler situation of a decay into three particles. In this case, if there are two resonances for example, the subset of invariant mass plots of pairs will have interference from the kinematic constraints. The plot allows to study this and also gives extra information on the three body parent state, if it is also a resonance, studying the interference patterns.