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Prospects for measuring $C P$ violation in $B_{s}^{0} \to ϕ μ^{+} μ^{-}$ via a time-dependent angular analysis

Sebastian Schmitt , Amr Elmarassy , Michele Atzeni , and Eluned Smith

Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

Phys. Rev. D 113, 036001 – Published 2 February, 2026

DOI: https://doi.org/10.1103/4wpp-rrxk

Abstract

This work investigates the prospects for performing a time-dependent angular analysis of $B_{s}^{0} \to ϕ μ^{+} μ^{-}$ decays at hadron colliders, and introduces new optimized angular observables associated with $B_{s}^{0}$ -mixing in the decay rate. The time-dependent normalized decay rate and corresponding probability density function is presented both for when the flavor of the $B_{s}^{0}$ meson at production is tagged and when it is untagged. The normalized angular terms linked to $B_{s}^{0}$ -mixing in the tagged (untagged) case are denoted $Z_{i}$ ( $H_{i}$ ), and their optimized counterparts as $Q_{i}$ ( $M_{i}$ ). The expected sensitivities of these observables at the end of Run 3, Run 4, and Run 5 of the LHC are determined using pseudoexperiments generated with a decay-time resolution, background level, and signal yield similar to those reported by the LHCb Collaboration. It is found that all observables can be extracted with Run 3 statistics, and that the $H_{i}$ and $Z_{i}$ observables have similar sensitivity, despite the former being suppressed by mixing terms. Moreover, the angular observables only accessible via flavor tagging, such as the equivalent of $P_{5}^{'}$ in the $B_{s}^{0}$ system, are found to exhibit sensitivities comparable to current measurements in $B^{0} \to K^{* 0} μ^{+} μ^{-}$ decays once Run 5 datasets are available. Fits to the observables to extract the Wilson coefficients show a significant increase in precision when either the observables accessible via time-dependent analysis, or flavor tagging, are included. A marked increase in sensitivity to $C P$ -violating short-distance effects is observed for a subset of the new optimized $M_{i}$ and $Q_{i}$ observables.

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References (70)

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Phys. Rev. D 113, 036001– Published 2 February, 2026

Vol. 113, Iss. 3 — 1 February 2026

Received 21 October 2025
Accepted 23 December 2025

DOI: https://doi.org/10.1103/4wpp-rrxk

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Prospects for measuring $C P$ violation in $B_{s}^{0} \to ϕ μ^{+} μ^{-}$ via a time-dependent angular analysis

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Prospects for measuring CP violation in Bs0→ϕμ+μ− via a time-dependent angular analysis

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Prospects for measuring $C P$ violation in $B_{s}^{0} \to ϕ μ^{+} μ^{-}$ via a time-dependent angular analysis