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.