A Parameterization Invariant Approach to the Statistical Estimation of the CKM Phase $\alpha$

TL;DR

This paper introduces a Bayesian method for estimating the CKM phase alpha that remains invariant under parameterization, providing a natural interpretation of the distribution and discussing the impact of excluding certain data.

Contribution

It presents a parameterization-invariant Bayesian approach to estimating the CKM phase alpha, emphasizing interpretation and the effect of data removal.

Findings

Bayesian approach is invariant to parameterization.

Distribution interpretation aligns with subjective Bayesian perspective.

Removing information about B^{00} affects the estimation process.

Abstract

In contrast to previous analyses, we demonstrate a Bayesian approach to the estimation of the CKM phase $\alpha$ that is invariant to parameterization. We also show that in addition to {\em computing} the marginal posterior in a Bayesian manner, the distribution must also be {\em interpreted} from a subjective Bayesian viewpoint. Doing so gives a very natural interpretation to the distribution. We also comment on the effect of removing information about $\mathcal{B}^{00}$.