Electroweak effects in the extraction of the CKM angle $γ$ from $B \to D π$ decays

The angle $γ$ 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 $B \to D π$ modes and show that their impact on the determination of $γ$ could be enhanced by an accidental cancellation of poorly known hadronic matrix elements. However, we do not expect the resulting shift in $γ$ to exceed $\big|δγ^{Dπ} /γ\big| \lesssim {\mathcal O}\big(10^{-4}\big)$.

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