Window contributions to the muon hadronic vacuum polarization with twisted-mass fermions

TL;DR

This paper calculates the contributions of different distance scales to the muon anomalous magnetic moment using lattice QCD with twisted-mass fermions, providing detailed insights into the hadronic vacuum polarization effects.

Contribution

It introduces a lattice calculation of position-space windows for the muon g-2, isolating specific distance scales with a smooth window function, using twisted-mass fermions and multiple lattice parameters.

Findings

Quantified short-, intermediate-, and long-distance contributions to a_mu.

Used gauge configurations with 2+1+1 dynamical quarks at multiple lattice spacings.

Provided results consistent with previous estimates and improved understanding of scale sensitivities.

Abstract

We present a lattice calculation of the Euclidean position-space windows contributing to the leading-order hadronic vacuum polarization term of the muon anomalous magnetic moment $a_\mu$. Short-, intermediate- and long-distance windows are considered in order to isolate different scales sensitive to specific integration ranges of experimental time-like data used in the R-ratio. By adopting the same smooth window function introduced by the RBC and UKQCD Collaborations with width parameter $\Delta = 0.15~\rm fm$, for the isospin-symmetric, light, quark-connected component we get $a_\mu^{\rm SD} (ud) = 48.21\,(80) \cdot 10^{-10}$ , $a_\mu^{\rm W} (ud) = 202.2\,(2.6) \cdot 10^{-10}$ and $a_\mu^{\rm LD} (ud) = 382.5\,(11.7) \cdot 10^{-10}$ in the short- (SD), intermediate- (W) and long-distance (LD) time regions, respectively, with $t_0 = 0.4~\rm fm$ and $t_1 = 1.0~\rm fm$. Our results are obtained using the gauge configurations generated by the Extended Twisted Mass Collaboration with $N_f=2+1+1$ dynamical quarks, at three values of the lattice spacing varying from 0.089 to 0.062 fm, at several lattice volumes and with pion masses in the range $M_\pi \simeq 220 - 490~\rm MeV$.