Bootstrapping leading hadronic muon anomaly

We bootstrap the leading order hadronic contribution to $a_\mu$ using unitarity, analytic properties, crossing symmetry and finite energy sum rules (FESR) from quantum chromodynamics (QCD), establishing a lower bound. Combining this lower bound with the remaining precisely calculated contributions from quantum electrodynamics and electroweak interactions, we achieve a lower bound on muon anomaly $a_\mu$. Since the FESRs have uncertainties, our bound depends on the choices of FESRs within these uncertainties. A conservative choice of the FESR gives a conservative lower bound, consistent with Standard Model (SM) data-driven prediction. We show that there are other valid choices of FESRs within the uncertainties that lead to lower bounds, which are inconsistent with SM data-driven prediction but consistent with the measured values of the muon anomaly. The bootstrapped spectral density shows a $\rho$-resonance peak similar to experimental hadronic cross-ratio data, providing a bootstrap prediction for $\rho$-meson mass.