Lattice calculation of the R-ratio smeared with Gaussian kernel

TL;DR

This paper presents a lattice QCD calculation of the R-ratio, smeared with Gaussian kernels, revealing a significant tension with experimental data around the rho resonance, impacting muon g-2 calculations.

Contribution

First-principles lattice method for calculating smeared R(E) spectral densities, enabling direct comparison with experimental data and identifying notable discrepancies.

Findings

Observed a three-sigma tension with experimental R(E) around the rho peak.

Demonstrated the effectiveness of Gaussian smearing in lattice spectral density extraction.

Provided insights relevant for muon g-2 theoretical evaluations.

Abstract

The ratio $R(E)$ of the cross-sections for $e^+e^-\to$ hadrons and $e^+e^-\to \mu^+\mu^-$ 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 $\sigma$ 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 $\sigma\sim 600$ MeV and central energies around the $\rho$-resonance peak.