# Reparametrization Invariance, the controversial extraction of $\alpha$ from $B\to\pi\pi$ and New Physics

## TL;DR

This paper examines the extraction of the weak phase alpha from B→ππ decays, highlighting issues with parametrizations, and shows that proper analysis resolves discrepancies between statistical methods, even considering potential New Physics effects.

## Contribution

It clarifies the role of reparametrization invariance in alpha extraction and demonstrates the validity of results across different statistical approaches with appropriate parametrizations.

## Key findings

- No significant discrepancy between frequentist and Bayesian results.
- Exclusion of alpha values around pi/4 remains valid with New Physics.
- Inadequate parametrizations can lead to meaningless interpretations.

## Abstract

The extraction of the weak phase $\alpha$ from $B\to\pi\pi$ decays has been controversial from a statistical point of view, as the frequentist vs. bayesian confrontation shows. We analyse several relevant questions which have not deserved full attention and pervade the extraction of $\alpha$. Reparametrization Invariance proves appropriate to understand those issues. We show that some Standard Model inspired parametrizations can be senseless or inadequate if they go beyond the minimal Gronau and London assumptions: the single weak phase $\alpha$ just in the $\Delta I=3/2$ amplitudes, the isospin relations and experimental data. Beside those analyses, we extract $\alpha$ through the use of several adequate parametrizations, showing that there is no relevant discrepancy between frequentist and bayesian results. The most relevant information, in terms of $\alpha$, is the exclusion of values around $\alpha\sim \pi/4$; this result is valid in the presence of arbitrary New Physics contributions to the $\Delta I=1/2$ piece.