Chiral extrapolation of hadronic vacuum polarization and isospin-breaking corrections

Abstract

By far the biggest contribution to hadronic vacuum polarization (HVP) arises from the two-pion channel. Its quark-mass dependence can be evaluated by combining dispersion relations with chiral perturbation theory, providing guidance on the functional form of chiral extrapolations, or even interpolations around the physical point. In addition, the approach allows one to estimate in a controlled way the isospin-breaking (IB) corrections that arise from the pion mass difference. As an application, we present an updated estimate of phenomenological expectations for electromagnetic and strong IB corrections to the HVP contribution to the anomalous magnetic moment of the muon. In particular, we include IB effects in the K𝐾 channel, which are enhanced due to the proximity of the K𝐾 threshold and the 𝜙 resonance. The resulting estimates make it unlikely that the current tension between lattice-QCD and data-driven evaluations of the HVP contribution is caused by IB corrections.

Theory of g-2

“…been compared to a phenomenological evaluation of isospin-breaking effects in Refs. [82][83][84][85][86], which found that the lattice calculation of these contributions cannot be the source of the discrepancy. Whether radiative corrections on the experimental side could provide an explanation of the puzzle is the subject of ongoing research [87][88][89][90][91].…”

Lattice calculation of the R-ratio smeared with Gaussian kernels

“…the channel 0 + opens in QCD+QED and also close to other thresholds (see Refs. [15,16]). Nevertheless, we notice that in order to explain the observed tension at ∼ 0.8 GeV and ∼ 0.6 GeV an isospin breaking effect larger than 2% would be needed and this is hard to reconcile with the first principle lattice calculation performed in Ref.…”

Puzzles in the hadronic contributions to the muon anomalous magnetic moment

“…Puzzles in the hadronic contributions to the muon anomalous magnetic moment has been compared to a phenomenological evaluation of isospin-breaking effects in Refs. [81][82][83][84][85], which found that the lattice calculation of these contributions cannot be the source of the discrepancy. Whether radiative corrections on the experimental side could provide an explanation of the puzzle is the subject of ongoing research [86][87][88][89][90].…”