Flavour Anomalies: A comparative analysis using a machine learning algorithm

We present an analysis on flavour anomalies in semileptonic rare $B$-meson decays using an effective field theory approach and assuming that new physics affects only one generation in the interaction basis and non-universal mixing effects are generated by the rotation to the mass basis. A global fit to experimental data is performed, focusing on LFU ratios $R_{D^{()}}$ and $R_{J/ψ}$ and branching ratios that exhibit tensions with Standard Model predictions on $B \rightarrow K^{()} ν\barν$ decays. In our analysis, we use a Machine Learning Montecarlo algorithm, a framework that emulates the highly non-Gaussian structure of the likelihood landscape with minimal training cost. This method enables the generation of high-resolution confidence regions and detailed correlation analyses. By comparing three different scenarios, we show that the one that introduces only mixing between the second and third quark generations and no mixing in the lepton sector, as well as independent coefficients for the singlet and triplet four fermion effective operators, provides the best fit to the experimental data. A comparison with previous results is performed. We highlight the key strengths of the Machine Learning framework in our analysis.

💡 Research Summary

The paper presents a comprehensive study of the long‑standing flavour anomalies observed in semileptonic B‑meson decays, focusing on the lepton‑flavour‑universality (LFU) ratios R_D, R_{D*}, R_{J/ψ} and the rare processes B→K^{(*)}νν that exhibit tensions with Standard Model (SM) predictions. The authors adopt an effective‑field‑theory (EFT) framework, assuming that new physics (NP) couples to only one generation in the interaction basis and that non‑universal mixing effects arise solely from the rotation to the mass basis. Within this setup they consider the dimension‑six SMEFT operators O_{ℓq}^{(1)} (singlet) and O_{ℓq}^{(3)} (triplet), whose Wilson coefficients are denoted C₁ and C₃, respectively.

A global fit is performed using an extensive data set (≈600 observables) that includes the latest measurements from Belle II, LHCb and CMS, as well as a broad set of electroweak, Higgs and flavour observables implemented via the smelli 2.3.3 package. To cope with the highly non‑Gaussian likelihood landscape, the authors develop a “Machine Learning Monte‑Carlo” (ML‑MC) algorithm. The method trains a surrogate model (Gaussian‑process‑like or neural‑network) on a modest number of likelihood evaluations and then samples the surrogate to generate high‑resolution confidence regions (1σ–4σ) and detailed correlation maps at a fraction of the computational cost of traditional Markov‑Chain Monte‑Carlo (MCMC) techniques.

Three benchmark scenarios are examined:

• Scenario I – both singlet and triplet coefficients are set equal (C₁ = C₃) and the flavour‑mixing matrices λ_ℓ and λ_q are fully general (parameterised by complex numbers α, β).
• Scenario II – C₁ = C₃ is retained but the lepton mixing matrix λ_ℓ is forced to be diagonal (no lepton‑sector mixing), while λ_q remains general.
• Scenario III – the most general case: C₁ and C₃ are allowed to differ, λ_q is restricted to mixing only between the second and third quark generations, and λ_ℓ is diagonal.

The fit results show a clear hierarchy of performance: Scenario III yields the largest reduction in χ² (Δχ² ≈ 6–7 relative to the SM), the smallest p‑value (≈ 4 × 10⁻⁸), and the most significant improvement in the pull (≈ 6 σ). The best‑fit values in this scenario are roughly C₁ ≈ −0.11 ± 0.03, C₃ ≈ −0.12 ± 0.03, with the quark‑mixing parameters α_q ≈ 0.78 and β_q ≈ 1.22. Importantly, allowing C₁ ≠ C₃ enables the simultaneous description of the excess in B→K^{()}νν branching ratios and the LFU violations in R_D^{()} and R_{J/ψ}, something that is not achievable when C₁ = C₃. The analysis also identifies two degenerate minima in the (C_{33}^L, C_{33}^R) plane for the νν channel, both compatible with the measured B→K νν and B→K* νν rates, illustrating the necessity of both left‑ and right‑handed NP contributions.

The ML‑MC framework proves its strength by reproducing the intricate, non‑Gaussian confidence contours with far fewer likelihood evaluations than a conventional MCMC, offering clear visualisation of parameter correlations (e.g., between C_{VL} and C_T, or between C_{33}^L and C_{33}^R). This efficiency makes it possible to explore high‑dimensional parameter spaces that would otherwise be prohibitive.

In conclusion, the paper demonstrates that the latest experimental landscape—where the previously noted b→sℓ⁺ℓ⁻ anomalies have largely disappeared but tensions remain in b→cτν and b→sνν transitions—favours a NP flavour structure characterised by (i) mixing only between the second and third quark generations, (ii) no mixing in the lepton sector, and (iii) independent singlet and triplet Wilson coefficients. The authors argue that this configuration provides the most natural and statistically robust explanation of the data. Moreover, the successful application of the ML‑MC algorithm suggests a powerful new tool for future global fits in flavour physics and beyond, capable of handling complex likelihoods with minimal computational overhead.