Precision Tests in $b\to s\ell^+\ell^-$ ($\ell=e,μ$) at FCC-ee

TL;DR

This work investigates precision tests of the rare b→sℓ^+ℓ^- transitions, motivated by tensions seen in B→K^*μ^+μ^- at LHCb and the prospective FCC-ee tera-Z program. It assesses B→K^*ℓ^+ℓ^- decays with ℓ = e, μ (and ττ) at FCC-ee, benchmarking against HL-LHC, and develops theory-improvement scenarios to evaluate how reduced uncertainties enable discovery or exclusion of New Physics. The analysis demonstrates FCC-ee’s cleanliness and the electron-channel advantage, showing that significant progress in long-distance charm contributions and NP sensitivity (via C9 and C10 in WET and SMEFT, plus Z′-type UV models) is achievable, especially with theory improvements (P2). It also highlights the synergy with EWPOs and high-pT Drell–Yan data, outlining the path to robust LFU tests and comprehensive constraints on NP scenarios, while calling for full detector simulations and inclusion of tau modes in future work.

Abstract

The rare semi-leptonic decays $B\to K^\ast \ell^+\ell^-$, with $\ell=e, μ$, are highly sensitive to new physics (NP) due to their suppression in the Standard Model (SM). Current LHCb measurements in the muon channel exhibit a significant tension with state-of-the-art SM theory predictions. The proposed tera-$Z$ run at FCC-ee provides a unique opportunity to untangle the origin of this tension by producing a very large sample of $B$-mesons in a clean $e^+e^-$ environment. We explore the expected precision of $B\to K^\ast \ell^+\ell^-$ ($\ell=e, μ$) measurements at FCC-ee, complementing existing studies with $τ^+τ^-$ in the final state, and compare with HL-LHC projections. For the case of muons in the final state, we show that HL-LHC and FCC-ee are expected to deliver a similar number of events, while the latter performs much better in the case of final state electrons. Regardless of the lepton flavour, we expect the FCC-ee environment to be much cleaner than at HL-LHC, with subleading systematics. We also find that a significant reduction in theory uncertainties on the SM predictions is required to capitalize on the advantage going from HL-LHC to FCC-ee. We demonstrate the power of such measurements at FCC-ee to extract information on the long-distance contribution to these decays, and to reveal evidence for new physics even if no deviations are seen in electroweak precision tests.

Figures (6)

• Figure 1: Extraction of $C_9^e$ and $C_9^\mu$ from the binned branching fraction. Black: current constraints; blue: HL-LHC projections; green: FCC-ee projections with $\mathrm{P}_1$ benchmark; red: FCC-ee projections with $\mathrm{P}_2$ benchmark. The gray band denotes the SM prediction, and the dashed black lines show current LHCb constraints (where the constraint on $C_9^e$ is inferred using $R_{K^\ast}$ and muon data). Bins 1, 2, and 3 refer to the $q^2$ intervals $[2.5, 4]$, $[4,6]$, and $[6,8]~\mathrm{GeV}^2$ respectively. See text for details.
• Figure 2: Projected fits to $\Delta C_9^{\mu,e}$ and $\Delta C_{10}^{\mu,e}$ from the binned branching ratio measurement of $B\to K^\ast\{ee,\mu\mu\}$, assuming future data follow current LHCb central values. All shaded regions denote $95\%$ CL.
• Figure 3: Projected fits to $\Delta C_9^{\mu,e}$ and $\Delta C_{10}^{\mu,e}$ from the binned branching ratio measurement of $B\to K^\ast\{ee,\mu\mu\}$, assuming future data have SM-like central values. All shaded regions denote $95\%$ CL.
• Figure 4: Projected improvements from current LHC results to HL-LHC and FCC-ee using the binned branching ratio of $B\to K^\ast\mu^+\mu^-$ and the branching ratio of $\bar{B}_s \to \mu^+\mu^-$, assuming future data have LHC-like (left) and SM-like (right) central values.
• Figure 5: New physics sensitivity of measurements from HL-LHC and FCC-ee for the three SMEFT scenarios described in the main text. In pink/purple we plot the reach of our selection of flavour observables at FCC-ee (the dashed black lines indicate sensitivity from HL-LHC), alongside complementary constraints from EWPO measurements at tera-$Z$ (blue) and Drell--Yan data at the HL-LHC (green). Note that in the second plot the upper limit of the green bands nearly coincides with the upper limit of the blue bands and is therefore not visible.