Data-driven analyses and model-independent fits for present $b\to s \ell \ell$ results

TL;DR

The study critically evaluates present $B$-meson anomalies in exclusive $b\to s \ell\ell$ decays within the QCD factorisation framework, examining the sensitivity to local form factors and the dubious largest low-$q^2$ bin. It advances model-independent, data-driven analyses and updates global fits with CMS and LHCb data, while parametrising non-factorisable power corrections as placeholders to explore potential hadronic versus NP origins. The results show NP indications (notably in $\delta C_9$) that depend strongly on form-factor choices and the inclusion of the largest low-$q^2$ bins, with NP significance ranging from ~2–7$\sigma$ under various assumptions; however, allowing larger power corrections reduces these significances substantially. Via bin-by-bin, helicity-dependent, and Wilks- test approaches, the paper finds no decisive statistical preference for NP over hadronic explanations given current data, underscoring the need for improved theory of hadronic effects and higher-precision future data to resolve the tensions. Overall, the work emphasizes the critical role of form-factor systematics and hadronic uncertainties in interpreting $b\to s \ell\ell$ anomalies and outlines a clear path for future experimental and theoretical progress.

Abstract

We present a critical assessment of the present $B$ anomalies in the exclusive $b \to s \ell\ell$ mode based on the QCD factorisation (QCDf) approach. In particular, we analyse the impact of different local form factor calculations and of the largest bin in the low-$q^2$ region. We also present a model-independent analysis of the new results of the LHCb and CMS experiments on the $B \to K^* μ^+μ^-$ angular observables. In addition, we update the global fit by including all $b \to s$ observables incorporating the new data from CMS and LHCb. In these analyses, we use 10% or higher guesstimates of the non-factorisable power corrections as additional uncertainties, serving as a placeholder for robust estimates of these contributions. Updating earlier results, we also analyse the combined LHCb and CMS data on the $B \to K^* μ^+μ^-$ angular observables using data-driven approaches to find indications whether these tensions between the QCDf predictions and the present data are due to underestimated subleading hadronic contributions or due to new physics effects.

Figures (12)

• Figure 1: $B^0 \to K^{*0}\mu^+\mu^-$ angular observables with SM predictions using GRvDV23 form factors and assuming 10% power corrections. The data points correspond to the CMS measurement CMS:2024atz and the LHCb results from 2020 LHCb:2020lmf and 2025 LHCb:2025update.
• Figure 2: The $1$ and $2\sigma$ confidence level (C.L.) of the $\{C_9, C_{10}\}$ fit to angular $B\to K^*\mu^+\mu^-$ observables (without $[6,8]$ and $[6.,8.68]$ GeV$^2$ bins), using the measurements from CMS CMS:2024atz and separately, two different LHCb results. The left panel uses the earlier LHCb 2020 data LHCb:2020lmf, while the right panel uses the updated LHCb 2025 result LHCb:2025update. The fits lead to Pull$_\text{SM}$ of $2.0\sigma$ for CMS and 2.3 and 5.1$\sigma$ for LHCb 2020 and 2025 data, respectively.
• Figure 3: The $1\sigma$ and $2\sigma$ C.L. regions for the $\{C_9, C_{10}\}$ fit to angular observables in $B \to K^* \mu^+ \mu^-$, when a fit to the LHCb measurements LHCb:2020lmf with and without CMS data CMS:2024atz (excluding the $q^2 \in [6, 8.68]~\text{GeV}^2$ bins in both cases) is made, with Pull$_\text{SM}$ of $5.1$ and $4.9\sigma$, respectively.
• Figure 4: The $1\sigma$ and $2\sigma$ confidence level regions for the $\{C_9, C_{10}\}$ fit to angular observables in $B \to K^* \mu^+ \mu^-$, when in the combined LHCb and CMS fit two different sets of form factors: GRvDV23-FF (orange region) and BSZ15-FF (purple contours) are used, resulting in Pull$_\text{SM}$ of $4.9$ and $6.1\sigma$, respectively.
• Figure 5: The $1$ and $2\sigma$ C.L. of the $\{C_9, C_{10}\}$ fit to angular $B\to K^*\mu^+\mu^-$ observables, using the $P_i^{(\prime)}$ and $S_i$ measurements from LHCb LHCb:2020lmf, excluding the $[6,8]$ GeV$^2$ bins, resulting in Pull$_\text{SM}$ of $5.1$ and $4.8\sigma$, respectively.