Bootstrapping the leading hadronic muon anomaly

We bootstrap the leading-order hadronic contribution to <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>a</a:mi><a:mi>μ</a:mi></a:msub></a:math> using unitarity, analytic properties, crossing symmetry and finite energy sum rules (FESR) from 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>a</c:mi><c:mi>μ</c:mi></c:msub></c:math>. 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>ρ</e:mi></e:math>-resonance peak similar to experimental hadronic cross-ratio data, providing a bootstrap prediction for <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>ρ</g:mi></g:math>-meson mass.