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

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