Improving the measurement of the CKM phase ${\varphi }_2=\alpha$ in $B\to \pi \pi$ and $B\to \rho \rho$ decays

Abstract

CP-violating asymmetries in $B\to \pi \pi$ and $B\to \rho \rho$ decays can help specify the weak phase ${\varphi }_2=\alpha$ of the Cabibbo-Kobayashi-% Maskawa (CKM) matrix. We discuss the impact of improved measurements of these processes such as will be available in the near future, finding special value in better measurement of the time-dependent CP violation parameter $S_{00}$ in $B^0\to {\pi }^0{\pi }^0$ and $B^0\to {\rho }^0{\rho }^0$. Reducing the errors on $B\to \rho \rho$ measurements by a factor of two can potentially lead to an error in ${\varphi }_2=\alpha$ just above $2^{\circ }$, at which level isospin-breaking corrections must be considered.

arXiv comment14 pages, 7 figures. To be published in Physics Letters B; minor typographic corrections

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Cited by in corpus (6)

• Superfactory of bottomed hadrons Belle II
• Controlling $\rho$ width effects for a precise value of $\alpha$ in $B\to \rho \rho$
• Resolving the ${\varphi }_2$ ($\alpha$) ambiguity in $B^0\to a_1^{\pm }{\pi }^{\mp }$
• Impact of systematic and amplitude model correlations within and between systems of combined input: A case study with ${\varphi }_2$ ($\alpha$)
• Resolving the ${\varphi }_2$ ($\alpha$) ambiguity in $B\to \rho \rho$
• Rescaling the isospin triangle argument for constraining ${\varphi }_2$ ($\alpha$): consolidating Belle II and a potential path forward for LHCb