Probing the energy-smeared R-ratio on the lattice

Understand

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.