# Understanding Chi-Squared Plots & CP Violation Ranges

• kimmm
In summary, the conversation discusses the use of chi-squared plots in relation to CP violation ranges. It is mentioned that Wilks' theorem must be applied for the chi-squared distribution to be valid, or alternatively, a Monte Carlo simulation can be used. This topic was debated in the neutrino community a few years ago, and the speaker has written several relevant papers on the subject. It is also noted that these plots show sensitivity and not actual limits, which will be determined by future data. References are provided for further reading.

#### 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)

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:

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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.

Orodruin said:
Thank you so much for the references.

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## 1. What is a Chi-Squared plot?

A Chi-Squared plot is a graphical representation of the Chi-Squared statistic, which is used to determine the difference between an observed data set and an expected data set. It helps to assess the goodness of fit between a theoretical model and actual data.

## 2. How is the Chi-Squared plot used in particle physics?

In particle physics, the Chi-Squared plot is used to analyze data from particle collisions and compare it to theoretical predictions. It helps to identify any discrepancies between the observed data and the expected data, which can indicate the presence of new particles or interactions.

## 3. What is CP violation and how is it related to Chi-Squared plots?

CP violation refers to the violation of the combined symmetry of charge conjugation (C) and parity (P) in particle interactions. It is related to Chi-Squared plots because the presence of CP violation can be detected by analyzing the Chi-Squared plot and looking for deviations from the expected data.

## 4. What do the ranges in a CP violation plot represent?

The ranges in a CP violation plot represent the possible values of the CP violation parameter, which is a measure of the strength of CP violation in a particular particle interaction. These ranges can be determined by analyzing the Chi-Squared plot and finding the best fit for the observed data.

## 5. How are Chi-Squared plots and CP violation ranges used to validate the Standard Model?

The Standard Model of particle physics is a theoretical framework that describes the fundamental particles and forces in the universe. Chi-Squared plots and CP violation ranges are used to analyze data from particle interactions and compare it to the predictions of the Standard Model. If the observed data agrees with the model, it provides validation for the Standard Model. However, if there are significant deviations from the expected data, it could indicate the need for a new model or theory.