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.

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

References in corpus (6)

• Big-Bang Nucleosynthesis
• Current status of the Standard Model CKM fit and constraints on $\Delta F=2$ New Physics
• Measurement of CP Asymmetries and Branching Fractions in Charmless Two-Body B-Meson Decays to Pions and Kaons
• Measurement of CP Asymmetry in a Time-Dependent Dalitz Analysis of B^0 \to (ρπ)^0 and a Constraint on the Quark Mixing Matrix Angle ϕ_2
• A precise determination of $\alpha$ using $B^0\to {\rho }^{+}{\rho }^{-}$ and $B^{+}\to K^{\ast 0}{\rho }^{+}$
• CP violation in beauty decays

Cited by in corpus (4)

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