# Application of binned maximum likelihood fitting

I am doing a data analysis in HEP (first time) about the Higgs boson mass. I have two set of data: MC simulation data and experimental data. For the simulation data, because the number of events in each bin is large, I can perform a Gaussian fit, and it's ok. But for the experimental data (about 500 events), due to the small number of events in each bin, the use of Gaussian is not really suitable. Actually, the mass spectrum includes both signal and background, but I'm just care about the mass interval (115,135) which contains a signal peak corresponding to Higgs mass (125 GeV). How can I perform the binned maximum likelihood fit for this interval to measure the Higgs mass and check the goodness of fit? Could anyone explain how to do it? Thank you so much.

• I'd love to help, but you have to put more effort in formulating the question. What is the goal of your "data analysis"? What is in the "sample" you are talking about? Also note that here we answer question about physics -- not software frameworks (not even if it is ROOT). So, please, focus more on the physics problem at hand. – Kostya Mar 5 '17 at 18:49
• I've edited the post. Could you help me @Kostya? – Lê Dũng Mar 5 '17 at 19:33
• Is there a special reason why do you prefer to perform a Gaussian fit? It is because the law of large numbers? Did you ever try to consider non-parametric estimation? – user56224 Mar 5 '17 at 20:34
• If you don't get a good answer here, you may want to try asking the statistical aspect over at Cross Validated – Kyle Kanos Mar 5 '17 at 23:12

## 1 Answer

I presume you want to fit the Higgs mass bump.

The Higgs measured mass bump shape is a Gaussian due to the process of measurement: the propagation of errors of the momenta of the particles, due to detector error measurements, for each individual Higgs.

If one ran a Montecarlo with the theoretical width of the standard model Higgs the bump would still get the order of GeV width that the measurements (page 14) give, so only upper limits to the predicted standard model width of 4 MeV can be given.

Thus the observed width is not the inherent width, so you can use a Gaussian or a Poisson if there are really very few events under the bump.

.Also there will be background events under the Higgs bump which you have to take into account as you fit, by subtracting them ?.

For the true width see an estimate https://arxiv.org/abs/1203.3456