Constraining electroweak penguin graph contributions in measurements of the CKM phase alpha using $B\to \pi \pi$ and $B\to \rho \rho$ decays

Abstract

The unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix has been well established by both direct and indirect measurements without any evidence of discrepancy. The CKM weak phase $\alpha$ is directly measured using an isospin analysis in $B\to \pi \pi$ and $B\to \rho \rho$ assuming that electroweak penguin contributions are ignorable. However, electroweak penguins are sensitive to NP, hence, it is important to experimentally estimate their effects. We determine the size of both electroweak penguin and isospin amplitudes, directly from $B\to \pi \pi$ and $B\to \rho \rho$ experimental data, using in addition the indirectly measured value of $\alpha$. We find that electroweak penguin contribution are indeed small and agree with SM expectations within $1\sigma$. We also find that there is a mild enhancement of the $\Delta I=\frac{1}{2}$ transition amplitude.