A conceptual issue on the statistical determination of the neutrino velocity

TL;DR

This paper critically examines the statistical methods used to measure neutrino velocity, highlighting potential issues in data combination procedures and proposing ways to verify the accuracy of the statistical framework.

Contribution

It provides a detailed analysis of the statistical procedure for neutrino velocity measurement and suggests a consistency check to ensure the correctness of the data analysis method.

Findings

The order of summation and normalization affects the statistical inference.

A proposed consistency check can validate the PDF-composing procedure.

Highlights potential conceptual issues in neutrino velocity measurement methods.

Abstract

We discuss a conceptual issue concerning the neutrino velocity measurement, in connection with the statistical method employed by the OPERA collaboration for the inference of the neutrino time of flight. We expound the theoretical framework that underlies the delicate statistical procedure illustrating its salient aspects. In particular, we show that the order of the two operations of sum and normalization used to combine the single waveforms so as to build the global PDF is a crucial point. We also illustrate how a consistency check able to test the correctness of the PDF-composing procedure should be designed.