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Recent results in $b \rightarrow s\,\ell\ell$ transitions at LHCb

This paper presents recent LHCb results on rare $b \rightarrow s\ell\ell$ transitions, highlighting persistent tensions with Standard Model predictions in processes like $B^0 \rightarrow K^{*0}\mu^+\mu^-$ , offering new theoretical insights through amplitude analyses, and reporting innovative measurements of the $B^0 \rightarrow K^+\pi^-\mu^+\mu^-$ branching fraction and the first hadron collider determination of the lepton flavor universality ratio for $B^0 \rightarrow K^{*0}\ell^+\ell^-$ at high $q^2$ .

Original authors: Juan Jose Juan Castella

Published 2026-10-12

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Juan Jose Juan Castella

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The universe is built on a set of rules known as the Standard Model, a theory that successfully predicts how the smallest particles in existence behave and interact. For decades, this framework has held up under intense scrutiny, yet physicists remain convinced it is incomplete. It does not explain gravity, dark matter, or why the universe is made of matter rather than antimatter. To find the missing pieces, scientists look for cracks in the theory, searching for moments where nature behaves slightly differently than the rules predict. One of the most promising places to look is in the decay of heavy particles called B hadrons. These particles are unstable and break apart into lighter ones, but sometimes, in very rare instances, they transform in a way that is heavily suppressed by the Standard Model. Because these rare events happen so infrequently, even a tiny influence from a new, unknown force could leave a noticeable mark, making them ideal laboratories for hunting down new physics.

Researchers at the Large Hadron Collider beauty experiment, known as LHCb, have been studying these rare decays with increasing precision. Their latest work focuses on a specific type of transformation where a heavy beauty quark changes into a strange quark, emitting a pair of leptons—particles like electrons or muons—in the process. For some time, measurements of these decays have shown a persistent tension with theoretical predictions. The data suggests that the particles are behaving in a way that the current rules of physics cannot fully explain. This has sparked a debate: are these discrepancies the first signs of a new fundamental force, or do they simply mean our understanding of the complex interactions inside the atom is still incomplete? The new results from LHCb do not settle this question, but they sharpen the picture, showing that the tension remains even as the measurements become more precise, while also offering new ways to test the theory.

In one of the most detailed studies presented, the team analyzed the decay of a neutral B meson into a K-star meson and a pair of muons. This specific decay is complex because the particles involved can spin and orient themselves in different ways, creating a rich pattern of angles and masses. By examining millions of these events, the researchers mapped out the behavior of the decay across different energy ranges. They found that while most of the measured properties matched the Standard Model, two specific aspects of the pattern continued to deviate. One of these, a measurement of how the particles fly apart, and another related to the balance of forces, both showed a difference from the prediction that is statistically significant. The data sits between one and three standard deviations away from what the theory expects, a gap that has been observed by multiple experiments around the world. When the team combined these results with other measurements, the statistical tension with the Standard Model grew stronger, suggesting that if this is indeed a sign of new physics, it is likely related to a specific type of interaction that is currently missing from our equations.

To understand whether these deviations come from new particles or from a misunderstanding of how known particles interact, the researchers performed a different kind of analysis. Instead of grouping the data into energy bins, they looked at the entire spectrum of the decay at once, using a model to separate the known, long-range effects of the strong nuclear force from the short-range signals where new physics might hide. This approach allowed them to measure the strength of the underlying forces directly. The results confirmed that the real part of the force responsible for the decay is weaker than the Standard Model predicts, aligning with the earlier observations. However, when they looked for signs of a violation of charge-parity symmetry—a subtle difference between matter and antimatter—they found none. The data showed no evidence that the new physics, if it exists, behaves differently for matter and antimatter, which helps narrow down the types of theories that could explain the anomaly.

The team also applied this same rigorous analysis to a similar decay involving a positively charged B meson. Here, the results were more ambiguous. When they assumed the known forces were exactly as theory predicted, the data suggested a tension with the Standard Model. However, when they allowed other factors to vary, the tension disappeared, and the results became consistent with other measurements of this type of decay. This highlights the difficulty of the field: the signal is so subtle that the interpretation depends heavily on how the complex background interactions are modeled. The researchers also ventured into uncharted territory by measuring a decay where the final state contains a kaon and a pion with a combined mass higher than any previously studied. This region of the decay had never been measured before, and while there are no theoretical predictions for it yet, the successful measurement opens a new window for future comparisons.

Finally, the collaboration tackled the question of lepton flavor universality, a principle stating that the laws of physics should treat electrons and muons exactly the same way, differing only in their mass. The team measured the ratio of decays producing muons to those producing electrons in a high-energy region that had never been explored at a hadron collider. The result was a ratio of 1.08, with a small margin of error. This value is fully consistent with the Standard Model, which predicts that the ratio should be exactly one. This finding is significant because it shows that while some aspects of the decay show tension with the theory, the fundamental symmetry between electrons and muons holds firm in this high-energy regime. The precision of this measurement is three times better than any previous attempt, providing a solid benchmark for future studies.

The work presented here represents a major step forward in the quest to understand the fundamental nature of the universe. The persistent tensions in the data suggest that the Standard Model is not the final word, yet the lack of a clear violation of symmetry and the consistency of some measurements mean the answer is not yet in hand. The researchers emphasize that their findings are based on data collected during the first two major runs of the collider. With the machine now operating at a much higher capacity, collecting three times as much data as before, the next generation of measurements will have the power to either confirm these hints of new physics or reveal them to be a trick of the current theoretical models. Until then, the mystery of the beauty quark's rare decay remains one of the most compelling puzzles in modern physics.

Technical Summary: Recent Results in $b \to s\ell\ell$ Transitions at LHCb

Problem and Motivation
Rare decays of $B$ hadrons, specifically $b \to s\ell\ell$ transitions, serve as critical indirect probes for New Physics (NP). These processes are highly suppressed in the Standard Model (SM) via loop diagrams, making them sensitive to potential NP contributions that are not limited by collider energy scales. However, a persistent tension exists between experimental measurements and SM predictions. Notable anomalies include the $P'_5$ angular observable in $B^0 \to K^{*0}\mu^+\mu^-$ decays and branching fraction (BF) deficits in $B^+ \to K^+\ell^+\ell^-$ decays. The origin of these tensions remains debated: they may indicate genuine NP or stem from an incomplete theoretical understanding of long-distance hadronic contributions (local form factors and non-local resonance loops). This paper presents recent results from the LHCb collaboration aimed at resolving these ambiguities through higher precision measurements and novel amplitude analyses.

Methodology
The analysis utilizes the full LHCb Run 1 and Run 2 datasets, with specific configurations for different measurements: most analyses (including the $B^0 \to K^{*0}\mu^+\mu^-$ angular and amplitude studies) employ 8.4 fb $^{-1}$ excluding 2015, while the Lepton Flavour Universality (LFU) ratio measurement utilizes the full 9 fb $^{-1}$ dataset including 2015. The approach is multi-faceted:

Binned Angular Analysis: A 5-dimensional fit ( $m_{K\pi}$ , $\cos\theta_{K\pi}$ , $\cos\theta_{\mu\mu}$ , $\phi$ , and $m_{B^0}$ ) is performed in bins of dilepton mass squared ( $q^2$ ) for $B^0 \to K^{*0}\mu^+\mu^-$ . This analysis improves upon previous work by increasing the dataset size, extending the $K\pi$ mass range, and including non-zero lepton mass effects. Crucially, it provides a full treatment of $S$ -wave and $P$ -wave components and their interference.
Unbinned Amplitude Analyses: To directly extract Wilson coefficients and non-local contributions, unbinned fits are performed over the full dilepton mass spectrum for both $B^0 \to K^{*0}\mu^+\mu^-$ $B^{0} \to K^{* 0} μ^{+} μ^{-}$ and $B^+ \to K^+\mu^+\mu^-$ $B^{+} \to K^{+} μ^{+} μ^{-}$ .
- For $B^0 \to K^{*0}\mu^+\mu^-$ , the framework is extended to include CP-violating NP by allowing complex Wilson coefficients ( $C_9, C_{10}$ ). Non-local contributions are modeled via an effective coefficient $C_9^{\text{eff}} = C_9^{\text{SM}} + C_9^{\text{NP}} + Y(q^2)$ .
- For $B^+ \to K^+\mu^+\mu^-$ , the analysis tests two sets of local form factors (HPQCD and FNAL/MILC) and assumes real Wilson coefficients, measuring the sum of vector and axial-vector contributions ( $C_V, C_A$ ).
Novel Branching Fraction Measurement: The BF of $B^0 \to K^+\pi^-\mu^+\mu^-$ is measured in the high dihadron mass region ( $1000 < m_{K\pi} < 1835$ MeV/ $c^2$ ), a phase space previously unmeasured above the $K^*(892)$ resonance.
Lepton Flavour Universality (LFU) Ratio: The ratio $R_{K^*}$ is measured at high $q^2$ ( $14 < q^2 < 22$ GeV $^2/c^4$ ) for the first time at a hadron collider. This involves comparing yields of rare muon and electron modes against their respective $J/\psi$ normalization modes, correcting for efficiency differences.

Key Contributions and Results

$B^0 \to K^{*0}\mu^+\mu^-$ Angular Observables: The updated measurement confirms that tensions with SM predictions persist. The $P'_5$ observable and the forward-backward asymmetry ( $A_{FB}$ ) deviate from SM predictions by 1.5 to 2.7 $\sigma$ , particularly near the $J/\psi$ resonance. Global fits using Flavio and EOS packages indicate a tension of 3.6 $\sigma$ (Flavio) to 3.8 $\sigma$ (EOS) in the real part of the Wilson coefficient $C_9$ . The differential branching fraction also lies below SM predictions in the $1.1 < q^2 < 6.0$ GeV $^2/c^4$ region, increasing the $C_9$ tension to 4.0 $\sigma$ (Flavio) and 4.1 $\sigma$ (EOS) when included in global fits.
Unbinned $B^0 \to K^{*0}\mu^+\mu^-$ Analysis: The amplitude fit yields real parts of $C_9$ and $C_{10}$ consistent with the CP-conserving analysis, with $\text{Re}(C_9)$ deviating by 2.1 $\sigma$ from the SM. No significant evidence for CP violation (imaginary parts) is found.
Unbinned $B^+ \to K^+\mu^+\mu^-$ Analysis: Using HPQCD form factors, the fit prefers values for $C_V$ and $C_A$ higher than the SM, resulting in a 4 $\sigma$ tension. However, when other Wilson coefficients are fixed to SM values, the one-dimensional profile for $C_9$ shifts to a value lower than predicted, aligning with other $b \to s\ell\ell$ results. Results using FNAL/MILC form factors show a similar trend but with lower significance (1.6 $\sigma$ ) due to higher uncertainties.
$B^0 \to K^+\pi^-\mu^+\mu^-$ at High Mass: This constitutes the first complete determination of the decay width in the $q^2 > 15.0$ GeV $^2/c^4$ region and the first observation of this decay above the $K^*(892)$ resonance at $q^2$ above the $J/\psi$ mass. No theoretical predictions currently exist for these specific kinematic regions.
High $q^2$ $R_{K^*}$ : The measurement yields $R_{K^*} = 1.08^{+0.14}_{-0.12}(\text{stat}) \pm 0.07(\text{syst})$ . This result is fully consistent with the SM and represents a threefold improvement in precision over previous measurements by the Belle collaboration, establishing a world-leading benchmark for hadron collider measurements in this regime.

Significance and Outlook
The paper asserts that the field of rare $b \to s\ell\ell$ decays remains a fertile ground for NP discovery, with tensions corroborated by recent high-precision data. The significance of these results lies in their ability to distinguish between NP and theoretical uncertainties. By employing unbinned amplitude analyses, the collaboration aims to directly constrain non-local hadronic effects, which are a primary source of theoretical ambiguity. Furthermore, the novel measurements of branching fractions in unexplored phase spaces and the high-precision $R_{K^*}$ at high $q^2$ expand the experimental landscape. The author emphasizes that while current results are based on Run 1 and 2 data, the significantly larger dataset collected during Run 3 will provide even greater precision, which is essential for the sensitivity required to definitively resolve the nature of these anomalies.

Technical Summary: Recent Results in b→sℓℓb \to s\ell\ellb→sℓℓ Transitions at LHCb

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Technical Summary: Recent Results in $b \to s\ell\ell$ Transitions at LHCb