Resolving the ${\varphi }_2$ ($\alpha$) ambiguity in $B^0\to a_1^{\pm }{\pi }^{\mp }$

Abstract

I propose an alternative method for measuring the $CP$ violating phase ${\varphi }_2$ ($\alpha$) without ambiguity in an extended SU(3) flavour symmetry analysis, which can ultimately be achieved by exploiting interference effects between $B\to AP$ and $B\to VV$ decay channels, where $A,V,P$ indicates an axial-vector, vector and pseudo-scalar meson, respectively. Under certain assumptions on the relevant decays based on current experimental results and minimal theoretical input, I demonstrate with an idealised amplitude model that a programme to extract a single solution for ${\varphi }_2$ in the range [0,$\pi$], with the added possibility to simultaneously constrain non-factorisable SU(3)-breaking effects, could be executed to similar precision using Run 3 data at LHCb and the final Belle II sample.

arXiv comment27 pages, 8 figures

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Cited by in corpus (3)

• Impact of systematic and amplitude model correlations within and between systems of combined input: A case study with ${\varphi }_2$ ($\alpha$)
• The hadronic $\tau$ decay ${\tau }^{-}\to K_1^{-}{\nu }_{\tau }\to (K^{-}\omega ){\nu }_{\tau }\to (K^{-}{\pi }^{+}{\pi }^{-}{\pi }^0){\nu }_{\tau }$ and the axial vector mixing angle
• Rescaling the isospin triangle argument for constraining ${\varphi }_2$ ($\alpha$): consolidating Belle II and a potential path forward for LHCb