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No rare-decay result has shown that the Standard Model is broken. The strongest signal discussed here is a 4σ tension in LHCb’s global analysis of the rare decay B0→K*μ+μ−. That is important evidence for follow-up, but it remains below the conventional 5σ threshold used for a particle-physics discovery, and the theoretical calculations are complex and still debated.
Why rare decays can reveal invisible particles
Many rare decays occur only through highly suppressed processes. In a b→sμ+μ− transition, for example, the decay proceeds through quantum loops rather than a simple tree-level interaction. Particles too heavy to produce directly can still appear virtually inside those loops and subtly change the decay rate or the directions in which the final particles emerge.
Physicists therefore compare measured branching fractions and angular distributions with Standard Model calculations. A persistent difference across several observables and decay modes could indicate an additional interaction, even when no new particle is produced on shell. A single discrepant bin is less persuasive because statistical fluctuations and modeling uncertainties can mimic a signal.
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The LHCb B0→K*μ+μ− tension
LHCb analyzed 8.4 fb−1 of proton-proton collisions collected in 2011, 2012 and 2016–2018. Its angular analysis examines how the two muons and the particles from the K* decay are distributed as a function of q2, the squared invariant mass of the dimuon system.
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A global fit combining the measured observables reports a 4σ tension with Standard Model predictions. An earlier result for the optimized angular observable known as P5′ showed a local 3.7σ deviation in one q2 bin. The newer global value is more informative because it uses the overall pattern rather than relying on one interval.
CERN describes the pattern as a confirmed tension with predictions, while also stressing that the calculations are highly complex and a subject of debate among theoretical physicists. Mark Smith, who presented the LHCb analysis, said the new measurements show “the same pattern of tensions with the Standard Model that we have seen before.” That persistence makes the result worth testing, but it does not identify a new particle or prove that the discrepancy has a non-Standard-Model cause.
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What is P5′?
P5′ is an angular observable built from the orientations of the decay products in B0→K*μ+μ−. Ratios of angular coefficients are designed to reduce some sensitivity to the uncertain form factors describing the hadrons. They do not eliminate theory uncertainty, however, and the prediction still depends on nonperturbative effects and other inputs. The quoted 3.7σ value is local to one q2 interval; it should not be read as a 3.7σ discovery claim.
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CMS is testing six related channels
CMS is extending the comparison beyond a single decay mode with preliminary measurements using 2022–2024 proton-proton data. The sample corresponds to 172 fb−1 collected at a centre-of-mass energy of 13.6 TeV. CMS compares differential branching fractions—rates measured across kinematic intervals—with predictions calculated using the Flavio framework.
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| Decay channel | Transition tested | CMS data and status | Quantity compared |
|---|---|---|---|
| B+→K+μ+μ− | b→sμ+μ− | 2022–2024; 172 fb−1 at 13.6 TeV; preliminary result | Differential branching fraction versus Flavio-based Standard Model predictions |
| B+→K*+μ+μ− | |||
| B0→KS0μ+μ− | |||
| B0→K*0μ+μ− | |||
| Bs→φμ+μ− | |||
| Λb→Λμ+μ− |
Using several final states matters because each has different backgrounds, detector effects and hadronic inputs. Agreement or disagreement that repeats across channels is more diagnostic than an effect confined to one decay. The CMS result is explicitly preliminary, so its uncertainties and interpretation can change as the analysis is finalized.
How strong is the evidence?
| Measurement | Data set | Reported deviation | How to interpret it |
|---|---|---|---|
| LHCb angular analysis of B0→K*μ+μ− | 8.4 fb−1, collected in 2011, 2012 and 2016–2018 | 4σ global-fit tension; earlier P5′ bin at 3.7σ local significance | Substantial tension, but below the conventional 5σ discovery standard; theory uncertainties remain important |
| CMS six-channel b→sμμ study | 172 fb−1, 2022–2024 at 13.6 TeV | No single combined significance stated in the cited preliminary result | Cross-check across six differential branching-fraction measurements |
| CMS semileptonic R(J/ψ) | Data set and collection period not stated in the cited summary | R(J/ψ)=0.71±0.17 (stat)±0.18 (syst), versus an SM prediction of 0.258±0.004; about a 2σ excess | Suggestive but not a discovery; statistical and systematic uncertainties are both sizable |
| Fermilab Muon g−2 | Muon magnetic-anomaly measurement | Precision of 0.14 parts per million | A complementary precision test of the Standard Model, not a rare B-meson decay measurement |
In particle physics, 5σ is the conventional threshold for claiming an observation because extremely small probabilities can still arise when many measurements, bins and analyses are examined. A 4σ effect is therefore a reason to collect more data and improve calculations, not a declaration that new physics has been found.
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Theoretical uncertainty is central to the verdict
The comparison is not simply “measured number versus an exact formula.” The final states contain composite hadrons, whose strong-interaction structure must be calculated or constrained with other data. Long-distance effects can alter both rates and angular distributions. Different theoretical treatments can therefore change the predicted central value and uncertainty. This is why CERN characterizes the calculations as complex and debated, and why an experimental excess must survive improved theory as well as independent measurements.
Other rare-decay and precision tests
Rare-decay searches are a broad strategy rather than a single experiment. ATLAS uses rare Higgs decays to test the Standard Model and look for signs of new physics. Fermilab’s Muon g−2 experiment takes a different route by measuring the muon’s magnetic anomaly to 0.14 parts per million and asking whether that precision result agrees with the Standard Model. These measurements probe different interactions and uncertainties, so they cannot be combined into one automatic “rare-decay anomaly.”
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What would clarify the anomaly?
- More Run 3 data: larger LHCb and CMS samples should reduce statistical uncertainty and test whether the same pattern appears in independent channels.
- Final CMS analyses: the six-channel study is preliminary; finalized calibrations, background estimates and systematic uncertainties are needed before assigning a definitive significance.
- Improved hadronic calculations: more reliable predictions can show whether the apparent gap is compatible with strong-interaction effects.
- Cross-experiment consistency: agreement among LHCb, CMS and other measurements would make an instrumental or analysis-specific explanation less likely.
- Compatible patterns elsewhere: a new interaction should affect related observables in a calculable way, not just one angular bin.
Leon Carus, presenting the results, said that clarifying the experimental picture with the LHC Run 3 data set and improving theoretical calculations should help determine the origin of the observed patterns. For now, the most accurate conclusion is that rare B-meson decays provide a promising indirect search for new phenomena, while the Standard Model remains the working theory.
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