Bootstrapping leading hadronic muon anomaly

We bootstrap the leading order hadronic contribution to muon
anomalous magnetic moment. The leading hadronic contribution comes from
the hadronic vacuum polarization function (HVP). We explore the bootstrap
constraints, namely unitarity, analyticity, crossing symmetry and finite
energy sum rules (FESR) from quantum chromodynamics (QCD). The unitarity
appears as a positive semi-definite condition among the pion partial
waves, form factor and spectral density function of HVP, which establishes
a lower bound on leading order hadronic contribution to muon anomalous
magnetic moment. We also impose chiral symmetry breaking to improve the
bound slightly. By combining the lower bound with the remaining
extensively calculated contributions, we achieve a bound on anomalous
magnetic moment $a_mu^text{bootstrap-min}=11659176.3^{+3}_{-3}times
10^{-10}$ and standard model prediction saturates this bound within the
error bars. We also present a possible improvement that is saturated by
both lattice computation and measured value within the error bars.