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I have read that a Dalitz plot is nothing but the plot of $m_{12}^2$ vs $m_{23}^2$, and that the dots correspond to "events". However, this doesn't really tell me anything. My question can boil down to exactly what phase space variable the dots represent. I am currently trying to make a Dalitz plot for the three body decay $K_{long}\to 3\pi^0$. Now, I am able to get the boundary for the Dalitz plot by plotting the constraint

$$\cos(\theta_{12})=\frac{\frac{\left({m_\ell}^2+{m_\pi}^2-{m_{23}^2}\right) \left(-2 {m_\pi}^2+{m_{12}^2}+{m_{23}^2}\right)}{2 {m_\ell}^2}+2 {m_\pi}^2-{m_{12}^2}}{\sqrt{\frac{\left({m_\ell}^2+{m_\pi}^2-{m_{23}^2}\right)^2}{4 {m_\ell}^2}-{m_\pi}^2} \sqrt{\frac{\left(-2 {m_\pi}^2+{m_{12}^2}+{m_{23}^2}\right)^2}{{m_\ell}^2}-4 {m_\pi}^2}} $$

in the $m_{12}^2$ $m_{23}^2$ plane. However, I'm in the dark as to how to populate the inner region. My goal is to be able to answer the following question. Given the constraint above, how do I, for a given ($m_{12}^2$ ,$m_{23}^2$) know whether or not that corresponds to placing a dot there or not.

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  • $\begingroup$ you need data (or an MC). Then you plot the data. $\endgroup$ – JEB Sep 21 '18 at 2:08
  • $\begingroup$ So you need to run a simulation measuring all that? You're plotting some other phase space variable like $m_{13}^2$ or something? $\endgroup$ – InertialObserver Sep 21 '18 at 2:14
  • $\begingroup$ try this cds.cern.ch/record/2014715/plots for data $\endgroup$ – anna v Sep 21 '18 at 17:36
  • $\begingroup$ Hi @InertialObserver, I had a go at answering the question, but I suspect it's an XY question and you might actually be trying to find out how to model decay amplitudes. $\endgroup$ – dukwon Sep 22 '18 at 19:44
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Dots on a Dalitz plot should be datapoints (I say "should" because many are drawn with the "SCAT" option in ROOT, which actually fills bins with a number of randomly-placed dots proportional to the bin content). These can come from real or simulated data. Even if you want to draw the functional form of the decay rate (say from the result of an amplitude fit or an amplitude calculated from theory) it's usually easier computationally to generate accept/reject toys than to calculate its value on a fine grid of coordinates.

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