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Confidence in the Neutrino Mass Hierarchy

Aug 21, 2013, 1:55 PM
B326 (IHEP)



Neutrino Oscillation Physics WG1


Prof. Jarah Evslin (Institute of High Energy Physics, Chinese Academy of Sciences)


Analyses of neutrino mass hierarchy determinations at future experiments determine an expected Delta Chi^2. As the hierarchy is a discrete choice, and not a continuous degree of freedom, this Delta Chi^2 does not obey Wilks' theorem. As a consequence it does not follow a chi^2 distribution and its square root is not the number s of sigmas of confidence that can be expected. I will present a simple formula for s as a function of the expected value of Delta chi^2.


I will review Wilks' theorem, which is used to relate Delta Chi^2 to the confidence in a null hypothesis. I will then explain why Wilks' theorem does not apply to the neutrino mass hierarchy. I will show that Delta chi^2 obeys a Gaussian distribution even considering the effects of nuisance parameters. I will then use this distribution to answer 3 questions: (1) What is the probability that a fit of the data to the true hierarchy yields a lower chi^2 than a fit to the false hierarchy? (2) With what confidence does the median experiment determine the hierarchy? (3) What is the probability of determining the hierarchy with s sigmas of confidence?

Primary author

Prof. Jarah Evslin (Institute of High Energy Physics, Chinese Academy of Sciences)

Presentation materials