Speaker
Description
At low virtualities, hadronic vacuum polarization (HVP) limits the precision of key Standard Model tests, notably the muon anomalous magnetic moment and the running of the electromagnetic coupling. Chiral perturbation theory constrains its functional form in this regime and provides the framework for computing finite-volume effects in lattice QCD. In this seminar, I will present a three-loop (N³LO) calculation of HVP in two-flavor chiral perturbation theory, the only second three-loop computation in this effective theory.
Integration-by-parts reduction expresses the amplitude in terms of eleven three-loop master integrals, six of which are elliptic functions of the photon virtuality. Five of these are new, and all are related to the equal-mass three-loop sunset integral. I will explain how Tarasov's dimensional shift separates their divergences from their elliptic content. I will also show that renormalizability requires relations among master integrals that do not follow from integration by parts: Schouten relations, which hold only in fixed integer dimension. Differential equations then reduce the most complicated integrals to one-dimensional integrals over the sunset, enabling fast, high-precision evaluation for arbitrary complex virtualities. In the resulting amplitude, the elliptic part contains no free parameters and gives the leading contribution to the four-pion cut. I will conclude with prospects for phenomenology and for finite-volume corrections to lattice calculations.