Electroweak effects in the extraction of the CKM angle $\gamma$ from $B \to D \pi$ decays

TL;DR

This paper calculates second-order electroweak corrections to $B o D \pi$ decays, showing their minimal impact on the precise determination of the CKM angle $\gamma$, with potential effects enhanced by hadronic uncertainties.

Contribution

It provides the first detailed calculation of electroweak effects in $B o D \pi$ decays relevant for $\gamma$ extraction, highlighting their negligible size.

Findings

Electroweak corrections are very small, less than 10^{-4} in $\gamma$ shift.

Potential enhancement due to hadronic matrix element cancellations.

Supports the robustness of $\gamma$ determination from tree-level decays.

Abstract

The angle $\gamma$ of the standard CKM unitarity triangle can be determined from tree-level $B$-meson decays essentially without hadronic uncertainties. We calculate the second-order electroweak corrections for the $B \to D \pi$ modes and show that their impact on the determination of $\gamma$ could be enhanced by an accidental cancellation of poorly known hadronic matrix elements. However, we do not expect the resulting shift in $\gamma$ to exceed $\big|\delta \gamma^{D\pi} /\gamma \big| \lesssim {\mathcal O}\big(10^{-4}\big)$.