Exploring CP violation and η–η′ mixing with the systems

Robert Fleischer; Robert Knegjens; Giulia Ricciardi

doi:10.1140/epjc/s10052-011-1798-8

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Particles and Fields

Eur. Phys. J. C (2011) 71: 1798
https://doi.org/10.1140/epjc/s10052-011-1798-8

Regular Article - Theoretical Physics

Exploring CP violation and η–η′ mixing with the $B^{0}_{s,d} \to J/\psi \eta^{(\prime)}$ systems

Robert Fleischer¹^*, Robert Knegjens¹ and Giulia Ricciardi²

¹ Nikhef, Science Park 105, 1098 XG, Amsterdam, The Netherlands
² Dipartimento di Scienze Fisiche, Università di Napoli Federico II and I.N.F.N., Sezione di Napoli, Complesso Universitario di Monte Sant’Angelo, Via Cintia, 80126, Napoli, Italy

^* e-mail: Robert.Fleischer@niknef.nl

Received: 27 October 2011
Published online: 18 November 2011

Abstract

The $B^{0}_{s,d} \to J/\psi \eta^{(\prime)}$ decays provide new terrain for exploring CP violation. After briefly discussing η–η′ mixing, we analyse the effective lifetimes and CP-violating observables of the B _s channels, which allow us to probe New-Physics effects in $B^{0}_{s}$ – $\bar{B}^{0}_{s}$ mixing. We have a critical look at these observables and show how hadronic corrections can be controlled by means of the B _d decays. Using measurements of the $B^{0}_{s,d}\to J/\psi \eta^{(\prime)}$ branching ratios by the Belle collaboration, we discuss tests of the SU(3)_F flavour symmetry of strong interactions, obtain the first constraints on the hadronic parameters entering the $B^{0}_{s,d} \to J/\psi \eta$ system, and predict the $B^{0}_{d}\to J/\psi \eta'$ branching ratio at the 5×10⁻⁶ level. Furthermore, we present strategies for the determination of the η–η′ mixing parameters from the $B^{0}_{s,d} \to J/\psi \eta^{(\prime)}$ observables. We also observe that the $B^{0}_{s,d} \to J/\psi \eta$ and $B^{0}_{s,d} \to J/\psi \eta'$ decays are—from a formal point of view—analogous to the quark–antiquark and tetraquark descriptions of the f ₀(980) in the $B^{0}_{s,d} \to J/\psi f_{0}(980)$ channels, respectively.