Physica A: Statistical Mechanics and its Applications 506, pp. 919-928.

**ISSN/ISBN:** Not available at this time.
**DOI:** 10.1016/j.physa.2018.05.013

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**Abstract:** According to Benford's law, the most significant digit in any given dataset is not uniformly distributed, but obeys a well defined power law distribution with smaller digits appearing more often. Previously, Shao and Ma have shown that the full widths of mesons and baryons show excellent agreement with Benford's law. Among some of the other particle physics datasets, we find that the leading decimal digit in the $\tau$ lepton branching fraction does not obey the expected logarithmic behaviour expected from the Benford distribution. We quantify the deviation from Benford's law using $\chi^2$ and obtain a $\chi^2$ value of 19.8 for eight degrees of freedom, which gives a $p$-value of about 1.1%, corresponding to a 3$\sigma$ disagreement with Benford's law. Therefore, the $\tau$ lepton branching fractions are a counter-example to Benford's law.

**Bibtex:**

```
@ARTICLE{,
author = {{Dantuluri}, Aisha and {Desai}, Shantanu},
title = "{Do {\ensuremath{\tau}} lepton branching fractions obey Benford's Law?}",
journal = {Physica A Statistical Mechanics and its Applications},
year = "2018",
month = "Sep",
volume = {506},
pages = {919--928},
doi = {10.1016/j.physa.2018.05.013},
}
```

**Reference Type:** Journal Article

**Subject Area(s):** Physics