Simultaneous fit of several datasets with common parameters

ROOT
1

Dear experts,

I am trying to fit the dE/dx of four types of particles using an approximated Bethe-Bloch curve (defined in this paper Eq. (J.1) ).

Screenshot from 2023-10-25 11-02-15
Screenshot from 2023-10-25 11-02-15993×180 7.72 KB

Therefore, I have one specific parameter for each dataset (the particle’s mass, embedded in beta in the expression above) and five common parameters.

Screenshot from 2023-10-25 10-46-14
Screenshot from 2023-10-25 10-46-141475×895 51.6 KB

Fitting them independently is trivial; you can see the result in the attached plot.

However, I cannot find how to make a constrained fit that takes into account the fact that the datasets share 5 out of 6 parameters.

I found this tutorial, but it appears to me that this is not exactly the same situation.

Any hint or pieces of advice is welcome! Thank you.
Tristan

2

Hi @Tristan!

Fitting them independently is trivial; you can see the result in the attached plot.

That’s great already! Can you maybe share the script that produces this plot, so that we can better understand the problem, see how it is different from the tutorial you linked, and then give targeted advice.

Cheers,
Jonas

3

Hi Jonas,

Thanks for your quick answer. I tried to scrape down my code to make a minimal working environment.
I can also provide ROOT files to make it run using them if needed. But the overall structure is here.

MWE_MultipleFit.cxx (14.0 KB)

Cheers,
Tristan