Resolving the ${\varphi }_2$ ($\alpha$) ambiguity in $B\to \rho \rho$

Abstract

I propose an alternative method for measuring the $CP$ violating phase ${\varphi }_2$ ($\alpha$) without ambiguity in an extended SU(2) isospin triangle analysis, which can ultimately be achieved by exploiting interference effects between $B^0\to {\rho }^0{\rho }^0$ and $B^0\to a_1^{\pm }{\pi }^{\mp }$ in a time-dependent flavour-tagged amplitude analysis. Under certain assumptions on the effective ${\varphi }_2$ in each channel, I demonstrate with an idealised amplitude model that potential deviations in the measured ${\varphi }_2$ due to penguin contamination in $B^0\to a_1^{\pm }{\pi }^{\mp }$ are sufficiently large within current experimental uncertainties that this programme could be executed with Run 3 data at LHCb and easily at Belle II.

19 pages, 7 figures, replaced with journal version

References in corpus (4)

• Amplitude Analyses of $D^0\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ and $D^0\to K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ Decays
• Isospin analysis of charmless B-meson decays
• Improving the measurement of the CKM phase ${\varphi }_2=\alpha$ in $B\to \pi \pi$ and $B\to \rho \rho$ decays
• Controlling $\rho$ width effects for a precise value of $\alpha$ in $B\to \rho \rho$

Cited by in corpus (3)

• 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 ${\varphi }_2$ ($\alpha$)
• Rescaling the isospin triangle argument for constraining ${\varphi }_2$ ($\alpha$): consolidating Belle II and a potential path forward for LHCb