We present a method that maximizes the experimental sensitivity to new physics contributions in B±→π±μ+μ− decays. This method relies on performing an unbinned maximum likelihood fit to both the measured dimuon q2 distribution of B±→π±μ+μ− decays, and theory calculations at spacelike q2, where QCD predictions are most reliable. Using known properties of the decay amplitude we employ a dispersion relation to describe the nonlocal hadronic contributions across spacelike and timelike q2 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. Published by the American Physical Society 2024