The smeared $R$-ratio in isoQCD from first-principles lattice simulations

TL;DR

This paper presents first-principles lattice QCD simulations to determine the smeared R-ratio, crucial for phenomenology and muon g-2 calculations, with improved accuracy and reduced uncertainties.

Contribution

It advances previous work by using high-statistics ETMC lattice data and Low Mode Average techniques to accurately compute the smeared R-ratio at multiple lattice spacings.

Findings

Successful determination of the smeared R-ratio with Gaussian kernels of width ~200

Use of spectral reconstruction techniques to control errors

Enhanced precision over previous studies

Abstract

The $R$-ratio is a phenomenological observable of great relevance, both in itself and in applications such as the dispersive approach to the muon anomalous magnetic moment. It can be investigated from first-principles with controlled statistical and systematic errors in lattice QCD by introducing an arbitrary smearing kernel and employing spectral reconstruction techniques, such as the well-known Hansen-Lupo-Tantalo method. Improving upon a first study published in 2023, we show preliminary results using the correlation functions produced by ETMC in $N_f = 2+1+1$ lattice simulations at four lattice spacings, different volumes and with higher statistics w.r.t. our previous study. The new correlators, thanks to the implementation of the Low Mode Average technique, allow the determination of the $R$-ratio smeared with Gaussian kernels of widths down to $\sigma \sim 200$ with phenomenologically relevant precision.