# Chi-squared plots

1. Jun 8, 2018

### kimmm

Would you please help me to understand the chi-squared plot the third plot in the bellow list.
How can I relate the cp violation ranges to the 3 and 5 sigma?
(http://inspirehep.net/record/1473193/plots)

2. Jun 8, 2018

### Orodruin

Staff Emeritus
A priori, you cannot, you need to make some assumptions on how the $\chi^2$ behaves. Essentially you need the conditions of Wilks' theorem to apply so that the $\Delta \chi^2$ is actually $\chi^2$ distributed. The aternative is deducing the distribution from a Monte Carlo simulation but that is not what is done here.

This question (whether you can use the $\chi^2$ distribution or not) was rather heatedly debated in the neutrino community 4-5 years ago. I wrote several papers on the subject, the most relevant to your question being:

Last edited: Jun 8, 2018
3. Jun 8, 2018

### Orodruin

Staff Emeritus
Also, it should be mentioned that these are sensitivity plots. They tell you the typical result you would expect from the experiment. The actual limits will later be set by the actual data, which may have up- or down-fluctuations.

4. Jun 9, 2018

### kimmm

Last edited by a moderator: Jun 10, 2018