Maximising the physics potential of $B^\pm\to\pi^\pm\mu^+\mu^-$ decays

We present a method that maximises the experimental sensitivity to new physics contributions in $B^\pm\to\pi^\pm\mu^+\mu^-$ decays. This method relies on performing an unbinned maximum likelihood fit to both the measured dimuon $q^2$ distribution of $B^\pm\to\pi^\pm\mu^+\mu^-$ decays, and theory calculations at spacelike $q^2$, where QCD predictions are most reliable. We exploit the known analytic properties of the decay amplitude and employ a dispersion relation to describe the non-local hadronic contributions across spacelike and timelike $q^2$ regions. The fit stability and the sensitivity to new physics couplings and new sources of $CP$-violation are studied for current and future data-taking scenarios, with the LHCb experiment as an example. The proposed method offers a precise and reliable way to search for new physics in these decays.