# Fitting to a high density scatter plot

I am trying to do a crude particle identification, using a Bethe Bloch tenchnique. Here is a plot I made from the data that I have

From what I've read, the standard method to identify charged particles is by measuring the ionization for a given momentum, in what is known as the Bethe-Bloch Equation

$$\langle \frac{dE}{dx}\rangle = \frac{P_1}{\beta^{P_4}}\left( P_2 - \beta^{P_4} - \log \left(P_3+\frac{1}{(\beta\gamma)^{P_5}}\right)\right)$$

So I tried to fit it and found out the parameters that are used by the detector people (ALICE, in their documentation, they write that the parameters were found using some simulation program). So these parameters become given constants. Now the entire Bethe-Bloch curves are normalized to the values of the minimum ionizing particle. In the literature, this is referred to as MIP value. So I tried a one-parameter fit for the above curve, leaving ROOT to find out the value of the normalization constant.

However, I get absurd results.

The three "fits" in the figure are supposed to be for pions, electrons and protons. However, they are not really accurate, as you can compare this to any of the standard plots released by CERN.

For instance, this is a plot from STAR experiment, which obviously has much lower multiplicity.

What are the techniques used by practitioners to find this normalization constant. I am using the same platform but the fitting routine is clearly inadequate for such magnitude of data.

PS: I do not have access to any online data or grid, etc. Most of the analysis code on the web seem to be based on somethings called ESDs and AODs and not for local standalone analysis (which is understandable but undfortunate for me)

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I think this is fine on this site, since it's not about the statistical technique itself, but about applying it to a particular physics situation. I changed the title a bit to reflect that. –  David Z Aug 11 '11 at 21:47
How sure are you that (1) the cern plot is data and not MC, (2) The cern plot is not using a generalized version of the formula (much progress had been made since Bethe-Bloch), and (3) that your detector is not going non-linear on you (the low band in dE/dx appears to have less structure that the cern plot)? I also notice that you do not have data as low in momentum as cern. Finally, which fitter did you use (ROOT supports multiple fitting methods, and the default is not always best). –  dmckee Aug 11 '11 at 22:18
@david and dmckee I had posted a plot from pp collision (which was the same, except much lower multiplicity). I have explained the removal in an email to team+physics email.. Basically, the behaviour at low momentum is the same except that the multiplicity is much much higher. I could not find free-to-distribute plots for heavy ion collisions, maybe some from STAR experiments exist, if anyone knows of any, I can post them as a comparision. –  yayu Aug 11 '11 at 22:56
@dmckee I have replaced it by a plot of the actual data, so no MC. I used the version of Bethe Bloch provided for the AOD macros. I also used the default TH1::Fit –  yayu Aug 11 '11 at 23:09
Another reason the form of the plot looks different from the released ones is that in ALICE Pb-Pb collisions, the multiplicity of pions is so much higher, that it populates the scatter plot obscuring the curves of the electron and the muon. –  yayu Aug 11 '11 at 23:58

The data set you show is a jumble of multiple contributions (and the cern fits agree, see how many times those lines intersect and how they all lie close together in the horizontal band on the right side of the plot?), and that makes for a problem.

You need some way to disentangle these bits.

The first thing I would tell a grad student to try is to separate the data-set on the basis of some other variables and fit each line to a sub-set of the data that she was confident contained mostly the particle they were interested in. This would generally be done by taking advantage of other data recorded about each hit in the plot{*}.

If no additional data was available I would suggest using geometric cuts in the $dE/dx$--$p$ plane to select the data to fit. That is fit to the parts of the plot which identifiable belong to a single particle species.

If you are ambitious you could use a track density-and-width-model to sequentially subtract the results of each fit you get in order to make the next one easier (at the cost of making the uncertainty analysis high correlated---yuck!).