ORIGINS Guest Dr. Hiromasa Takaura (Kyoto University): Advancing the OPE: renormalon subtraction and applications to low-energy physics

The operator product expansion (OPE) is a crucial tool for analyzing high-energy properties of QCD. I introduce two recent works related to the OPE. The first addresses the renormalon problem, where each expansion term can be ambiguous due to divergences in both the perturbative series and the condensates. We eliminate renormalon ambiguities by replacing these condensates with unambiguous ones defined via the gradient flow. As an application, we demonstrate that this approach resolves the long-standing discrepancy between two seemingly reasonable perturbative approaches (FOPT and CIPT) for calculating the hadronic tau decay widths. The second study tackles the challenge of analyzing the low-energy behavior of physical observables in asymptotically free theories. The key idea is to bridge low-energy and high-energy behavior, with the latter being calculable via the OPE, by enlarging the convergence radius of the low-energy expansion. As a testing ground, I consider a solvable model, the O(N) nonlinear sigma model in two-dimensional spacetime, and demonstrate that low-energy limits of correlation functions can be extracted using the OPE.