Lattice calculation of the R-ratio smeared with Gaussian kernel

Abstract

The ratio $R(E)$ of the cross-sections for $e^{+}{e}^{-}\to$ hadrons and $e^{+}{e}^{-}\to \hat{I}{¼}^{+}\hat{I}{¼}^{-}$ is a valuable energy-dependent probe of the hadronic sector of the Standard Model. Moreover, the experimental measurements of $R(E)$ are the inputs of the dispersive calculations of the leading hadronic vacuum polarization contribution to the muon $g-2$ and these are in significant tension with direct lattice calculations and with the muon $g-2$ experiment. In this talk we discuss the results of our first-principles lattice study of $R(E)$. By using a recently proposed method for extracting smeared spectral densities from Euclidean lattice correlators, we have calculated $R(E)$ convoluted with Gaussian kernels of different widths $\ddot{I}ƒ$ and central energies up to $2.5$ GeV. Our theoretical results have been compared with the KNT19 [1] compilation of experimental results smeared with the same Gaussian kernels and a tension (about three standard deviations) has been observed for $\ddot{I}ƒ\sim 600$ MeV and central energies around the $\ddot{I}$-resonance peak.

Contribution to the 39th International Symposium on Lattice Field Theory (Lattice2022), 8th-13th August, 2022, Bonn, Germany