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This paper reports a new, model-independent measurement of the decay amplitudes for the process B0 → K*0(→ K+π−) μ+μ−. The K*0 is a short-lived particle reconstructed from a kaon and a pion. The study uses 8.4 inverse femtobarns of proton–proton collision data collected by the LHCb experiment at 7, 8 and 13 TeV. The researchers focus on the region where the muon pair has invariant mass squared q2 between 1.1 and 8.0 GeV2/c4, a range chosen to sit between two strong resonance peaks where the amplitudes change quickly and are harder to model reliably.
Instead of relying on a specific theoretical model for how the amplitudes change with q2, the team wrote each P-wave amplitude as a sum of four Legendre polynomials. Legendre polynomials are simple, orthogonal mathematical functions that act like independent building blocks for a curve. Using these polynomials reduces correlations between parameters and stabilizes the fit. The real and imaginary parts of the polynomial coefficients were measured directly. The analysis fits the full five-dimensional decay distribution — the Kπμμ mass, q2, and three angles that describe the directions of the decay products — with an unbinned extended maximum-likelihood fit. In total 32 real parameters describe the P-wave amplitudes in this approach; an S-wave component was included as a nuisance term and treated as uniform in q2, an approximation found to be negligible compared with the statistical uncertainty.
From the measured amplitudes the authors construct CP-averaged angular observables. These are combinations of the amplitude components that are commonly compared with theoretical predictions. Some of the measured observables show deviations from Standard Model expectations. In effective field theory language these deviations can be expressed as shifts in short-distance parameters called Wilson coefficients. In particular, the shift in the coefficient called C9 — which controls a key vector-like interaction in b→sμ+μ− transitions — differs from the Standard Model prediction at a level that depends on how the q2 range is binned. The paper reports a deviation for C9 that varies between 4.3 and 4.8 standard deviations depending on the binning choice.
This work matters because the b→sℓ+ℓ− family of decays has shown several tensions with the Standard Model in recent years, and it is important to know whether those tensions come from unknown strong-interaction (hadronic) effects or from new particles or forces. A model-independent, q2-unbinned amplitude measurement gives a direct, flexible way to test the q2 dependence of the observables. That helps separate effects that have the smooth q2 behaviour expected from new short-distance physics from hadronic contributions that vary differently with q2.
Important caveats remain. The analysis is limited to the q2 window 1.1–8.0 GeV2/c4 chosen to avoid resonance regions, so it does not cover the whole decay spectrum. The S-wave part of the Kπ system was modelled simply as uniform in q2; the authors checked this assumption and found its impact small compared with statistical errors, but it is still an approximation. Also, the reported size of the C9 deviation depends on the exact q2 binning used in global fits, so the numerical significance must be interpreted with that dependence in mind. Finally, the amplitude parameterisation requires fixing a choice of basis and sign conventions to remove mathematical symmetries; those choices are standard but should be borne in mind when comparing to other analyses.