A recent analysis has identified the cause of a factor-of-four discrepancy in the limits obtained for the $B^+ \to K^+ a$ decay from Belle II experiment data. This decay, which produces a kaon and a light, invisible particle such as the QCD axion, is crucial for the search for new physics. The difference is attributed to the choice of kinematic variable space used in the reinterpretations of $B^+ \to K^+ \nu\bar\nu$ data.

The study highlights that the resolution in the reconstructed di-neutrino invariant mass, $q^2_{\rm rec}$, is a key factor. Fine-grained binning of $q^2_{\rm rec}$ allows for resolving the narrow axion signal, whereas coarse binning dilutes it into a background-dominated range. Conversely, the inclusion of a BDT (Boosted Decision Tree) axis trained for $B^+ \to K^+ \nu\bar\nu$ adds little discriminating power for the $B^+ \to K^+ a$ decay, as this axis is largely uncorrelated with $q^2$. Numerical tests performed confirm these expectations.

The authors conclude that subleading shape systematics, omitted from the $q^2_{\rm rec}$-based approach, actually lower the $B^+ \to K^+ a$ limit, making the $q^2_{\rm rec}$-based bound conservative. A dedicated reanalysis confirms that the choice of kinematic axes alone accounts for the sensitivity difference. These results suggest that likelihoods dominated by BDT variables are of limited use for reinterpretations when the signal shape differs appreciably from the BDT's training signal. Therefore, it is advocated that experimental collaborations publish likelihood projections in physical variable spaces alongside BDT-based likelihoods, to maximize the reinterpretability of their measurements.