Probing the energy-smeared R-ratio on the lattice

TL;DR

This study uses lattice QCD to compute a smeared version of the R-ratio between electron-positron annihilation into hadrons and muons, enabling precision tests of the Standard Model and revealing a tension with experimental data.

Contribution

It demonstrates the feasibility of extracting smeared spectral densities from lattice QCD to analyze the R-ratio with Gaussian energy smearing, advancing theoretical methods.

Findings

Observed a three-standard-deviation tension with experimental R-ratio data.

Showed that lattice QCD can accurately study the R-ratio in Gaussian energy bins.

Highlighted the potential impact of neglected QED and isospin-breaking corrections.

Abstract

We present a first-principles lattice QCD investigation of the $R$-ratio between the $e^+e^-$ cross-section into hadrons and that into muons. By using the method of Ref.[1], that allows to extract smeared spectral densities from Euclidean correlators, we compute the $R$-ratio convoluted with Gaussian smearing kernels of widths of about $600$ MeV and central energies from $220$ MeV up to $2.5$ GeV. Our theoretical results are compared with the corresponding quantities obtained by smearing the KNT19 compilation [2] of $R$-ratio experimental measurements with the same kernels and, by centring the Gaussians in the region around the $\rho$-resonance peak, a tension of about three standard deviations is observed. From the phenomenological perspective, we have not included yet in our calculation QED and strong isospin-breaking corrections and this might affect the observed tension. From the methodological perspective, our calculation demonstrates that it is possible to study the $R$-ratio in Gaussian energy bins on the lattice at the level of accuracy required in order to perform precision tests of the Standard Model.