Bootstrapping leading hadronic muon anomaly

TL;DR

This paper develops a method to estimate the muon anomalous magnetic moment contribution from hadronic effects using fundamental QCD principles, providing bounds that align with or challenge Standard Model predictions.

Contribution

It introduces a bootstrap approach based on unitarity, analytic properties, and sum rules to bound the hadronic contribution to muon g-2, incorporating uncertainties in FESRs.

Findings

The lower bounds are consistent with SM predictions.

Alternative FESR choices yield bounds conflicting with SM but matching experimental data.

The spectral density prediction aligns with the observed $ ho$-resonance peak.

Abstract

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.