I am currently working on an optical simulation using Geant4 (version 4.11). In my setup, I am irradiating a LYSO scintillation crystal with 511 keV gamma photons, which generates optical photons. These optical photons are subsequently detected by a silicon-based SiPM. During the simulation, I am tracking several parameters, including energy deposit, wavelength, global time, and local time.

My focus is on analyzing the global time to extract both the decay and rise times by applying a bi-exponential fit. However, I am encountering some challenges with the fitting process. Specifically, the chi-squared value of the fit is excessively large, and the second rise time appears to be shorter than the first.

I am attaching reference images that illustrate the expected data, as well as my current output for your review. Any advice or suggestions on resolving these issues would be greatly appreciated.

Thank you in advance, and I look forward to your responses.
Reference image.

I am not an expert in ROOT, but it is clear that chi-squared is most affected by the largest values. To remove the bias, one must calculate chi-squared relative to the absolute value for the point. Also, there are too many 1 sample points that do not improve the fit.

Thanks @phirippu for responding i am unable to find the solutions how i can remove one sample points that’s appearing near zero. Can you please give some suggestions about this.

The bin count at zero points to an issue of your simulation setup. There is simply not enough information to help with that. How is this fit being generated? There are endless analysis packages out there in many languages. It should be straight forward to mask the histogram to remove both the outlier at 0 or bins with counts below some threshold.
I suspect the paper also did a weighted fit. A good diagnostic would be to recreate the plot at the bottom which shows the residuals across the bins.

You also must remove the big value bias. I think you should not use ROOT for the analysis if removing one point does not seem easy. There are indeed many tools for this kind of analysis; use the one you are most familiar with. You can also ask ChatGPT if you are looking for a code example.