An exploration of $B_s \to J/\psi s\bar{s}$

TL;DR

This paper explores methods to measure the $B_s$ mixing phase $\,phi_s$ using alternative decay modes, aiming to distinguish small New Physics effects from hadronic uncertainties and improve parameter constraints.

Contribution

It proposes new decay channels and techniques for extracting $\,phi_s$ and estimating mixing angles, enhancing the precision of $B_s$ mixing studies.

Findings

Potential of $B_s o J/\psi \, ext{eta}^{(\prime)}$ and $B_s o J/\psi f_0(980)$ decays for $\,phi_s$ extraction.

Branching ratios can estimate $\,eta$--$\,eta'$ mixing angles.

Effective lifetime measurements can constrain $\,phi_s$ and $\,\, ext{ extbackslash}Delta ext{ extbackslash}Gamma_s$.

Abstract

Measurements of the $B_s^0$--$\bar{B}_s^0$ mixing phase $\phi_s$ appear to be converging towards the SM prediction, suggesting that contributions from New Physics (NP), if present, are small. This poses the question of whether smallish NP in $\phi_s$ can be distinguished from the hadronic uncertainties present in the interfering $B_s$ decay mode. In this paper we discuss the potential of extracting $\phi_s$ from the decay modes $B_s\to J/\psi \eta^{(\prime)}$ and $B_s\to J/\psi f_0(980)$ and how their respective hadronic uncertainties can be controlled. In addition, we demonstrate how the branching ratios of the former decays can be used to estimate the $\eta$--$\eta'$ mixing angles. Finally, we point out that effective lifetime measurements of decay modes such as the $B_s\to J/\psi f_0(980)$ can be used to constrain both $\phi_s$ and the $B_s$ decay width difference $\Delta\Gamma_s$, complementary to the usual time-dependent tagged analysis.