On the determination of the relative probability of $\mathitΥ(5S) \rightarrow B_s^{(*)}\bar B^{(*)}_s$ decays
A. E. Bondar, E. K. Karkaryan, A. A. Simovonian, M. I. Vysotsky
TL;DR
This paper proposes a model-independent method to determine the fraction $f_s$ of $\Upsilon(5S)$ decays that produce $B_s^{(*)}\bar B_s^{(*)}$ by analyzing the time dependence of semileptonic decays of the produced $B\bar B$ pairs and the ratio of same-sign to opposite-sign dileptons. By deriving explicit time-dependent dilepton rates and combining them into observables, the authors show that the $B_s$-pair fraction $\epsilon_{SS}$ (and thus $f_s$) can be extracted without relying on $\Upsilon(5S)$ branching fractions, exploiting isotopic invariance and near-equality of semileptonic widths $\mathcal{B}(B^0\to\ell\nu X)\approx \mathcal{B}(B^+\to\ell\nu X)\approx \mathcal{B}(B_s\to\ell\nu X)$. They include corrections for the $B^+$ lifetime and discuss experimental feasibility, estimating a few-percent precision with Belle II data and outlining extensions to $\Upsilon(4S)$ decays for CP-violation studies. The method promises a model-independent route to normalize $B_s$ decays (e.g., $B_s\to D_s\pi^+$) and to improve the determination of rare decays such as $B_s\to\mu^+\mu^-$. Overall, it provides a practical, data-driven framework for reducing systematic uncertainties in heavy-flavor measurements at $e^+e^-$ colliders.
Abstract
Semileptonic decays of the $B \overline{B}$ pairs produced in the $\mathitΥ(5S)$ can be used to find the relative probability of $\mathitΥ(5S) \rightarrow B_s \overline{B}_s$ decays. This could be achieved by the study of time dependence of $B$-meson decays to the leptons of equal and opposite signs.