Four-flavour leading-order hadronic contribution to the muon anomalous magnetic moment

Abstract

We present a four-flavour lattice calculation of the leading-order hadronic vacuum polarisation contribution to the anomalous magnetic moment of the muon, a hvp µ , arising from quark-connected Feynman graphs. It is based on ensembles featuring N f = 2+1+1 dynamical twisted mass fermions generated by the European Twisted Mass Collaboration (ETMC). Several light quark masses are used in order to yield a controlled extrapolation to the physical pion mass. We employ three lattice spacings to examine lattice artefacts and several different volumes to check for finite-size effects. Incorporating the complete first two generations of quarks allows for a direct comparison with phenomenological determinations of a hvp µ . Our final result including an estimate of the systematic uncertainty a hvp µ = 6.74(21)(18) · 10 −8 shows a good overall agreement with these computations.

Hadronic vacuum polarization contribution to aμ from full lattice QCD

“…This agrees well with the only earlier u/d/s/c lattice QCD result, 674(28) × 10 −10 [13], but has errors from the lattice calculation reduced by a factor of four. It also agrees with earlier non-lattice results using experimental data, ranging from (×10 10 ): 694.9(4.3) [5] to 681.9(3.2) [7].…”

“…As discussed in [13], most of the light-quark mass dependence of a µ can be removed by rescaling the vacuum polarization with appropriate powers of m latt ρ /m expt ρ . Here we show that rescaled results from large masses are consistent with the corrected results from physical masses, giving us confidence in both types of result.…”

The hadronic vacuum polarization contribution to the muon g − 2 from lattice QCD

“…This concerns both a hvp µ , studied in [28][29][30][31][32][33][34][35][36][37][38][39][40], as well as a hlbl µ [41][42][43][44][45][46][47][48][49]. Lattice calculations of a hvp µ proceed by evaluating a convolution integral over Euclidean momenta Q 2 [28,50].…”

“…We add that our results are in good agreement with those of refs. [33,39] which were performed for N f = 2+1+1 flavours.…”

Finite-volume electromagnetic corrections to the masses of mesons, baryons, and nuclei

“…As upcoming experiments, Fermilab E989 and J-PARC E34, plan to reduce the experimental uncertainty down to 0.14 ppm, theoretical calculations of non-perturbative hadronic contributions must be refined in the short term. LQCD is expected to contribute to improving the theoretical prediction of the standard model, and several recent efforts have been directed at obtaining the hadronic vacuum-polarization and hadronic light-by-light contributions to the muon g − 2 [68][69][70][71][72][73][74][75][76][77][78]. Theoretical challenges facing these calculations have been identified and will be addressed during the next few years.…”