Understanding Chi-Squared Plots & CP Violation Ranges

[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)

 

[Orodruin]

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:

• Quantifying the sensitivity of oscillation experiments to the neutrino mass ordering, Blennow et al., JHEP 1403 (2014) 028, https://inspirehep.net/record/1263770
  
• Reassessing the sensitivity to leptonic CP violation, Blennow, Coloma, Fernandez-Martinez, JHEP 1503 (2015) 005, https://inspirehep.net/record/1306284

 

[Orodruin]

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.

 

[kimmm]

• Quantifying the sensitivity of oscillation experiments to the neutrino mass ordering, Blennow et al., JHEP 1403 (2014) 028, https://inspirehep.net/record/1263770
  
• Reassessing the sensitivity to leptonic CP violation, Blennow, Coloma, Fernandez-Martinez, JHEP 1503 (2015) 005, https://inspirehep.net/record/1306284

Thank you so much for the references.