Shannon entropy and hadronic decays

TL;DR

This paper explores how Shannon entropy quantifies the information gained from measuring new hadronic decay branching ratios, offering a novel perspective on particle decay data analysis.

Contribution

It introduces the application of Shannon entropy to quantify information content in hadronic decay branching ratios, providing a new analytical tool for particle physics.

Findings

Shannon entropy effectively measures information gain from decay data.

Entropy analysis can compare decay channel distributions and quantum-state probabilities.

Examples demonstrate the utility of entropy in particle decay analysis.

Abstract

How much information is added to the Review of Particle Physics when a new decay branching ratio of a hadron is measured and reported? This is quantifiable by Shannon's information entropy $S(i) =-\sum_{f}BR_{(i\longrightarrow f)}\log BR_{(i\longrightarrow f)}$ that takes as input the experimental branching ratios (BR) of the decay distribution of particle i. It may be used at two levels, against the distribution of decay-channel probabilities, or against the distribution of individual quantum-state probabilities (integrating the phase space of those states provides the former). We illustrate the concept with some examples.