We present a lattice determination of the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, aHVPμ, in the so-called short and intermediate time-distance windows, aSDμ and aWμ, defined by the RBC/UKQCD Collaboration.
We employ a subset of the gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with Nf=2+1+1 flavors of Wilson-clover twisted-mass quarks, which are close to the physical point for the masses of all the dynamical flavors. The simulations are carried out at three values of the lattice spacing ranging from ≃0.057 to ≃0.080 fm with linear lattice sizes up to L≃7.6~fm.
For the short distance window we obtain aSDμ(ETMC)=69.33(29)⋅10−10, which is consistent with the recent dispersive value aSDμ(e+e−)=68.4(5)⋅10−10 within ≃1.6σ.
In the case of the intermediate window we get the value aWμ(ETMC)=235.0(1.1)⋅10−10, which is consistent with the result aWμ(BMW)=236.7(1.4)⋅10−10 by the BMW collaboration as well as with the recent determination by the CLS/Mainz group of aWμ(CLS)=237.30(1.46)⋅10−10 at the ∼1.0−1.3σ level. However, it is larger than the dispersive result aWμ(e+e−)=229.4(1.4)⋅10−10 by ≃3.1σ. The tension increases to ≃4.2σ if we average our ETMC result with the BMW and the CLS/Mainz ones.
C. Alexandrou, "Lattice calculation of the short and intermediate time-distance hadronic vacuum polarization contributions to the muon magnetic moment using twisted-mass fermions" arXiv:2206.15084 (June 30, 2022) (82 pages).Our accurate lattice results in the short and intermediate windows hint at possible deviations of the e+e− cross section data with respect to Standard Model (SM) predictions distributed somewhere in the low (and possibly intermediate) energy regions, but not in the high energy region.
Euclidean time windows in the integral representation of the hadronic vacuum polarization contribution to the muon g−2 serve to test the consistency of lattice calculations and may help in tracing the origins of a potential tension between lattice and data-driven evaluations.
In this paper, we present results for the intermediate time window observable computed using O(a) improved Wilson fermions at six values of the lattice spacings below 0.1 fm and pion masses down to the physical value. Using two different sets of improvement coefficients in the definitions of the local and conserved vector currents, we perform a detailed scaling study which results in a fully controlled extrapolation to the continuum limit without any additional treatment of the data, except for the inclusion of finite-volume corrections. To determine the latter, we use a combination of the method of Hansen and Patella and the Meyer-Lellouch-Lüscher procedure employing the Gounaris-Sakurai parameterization for the pion form factor. We correct our results for isospin-breaking effects via the perturbative expansion of QCD+QED around the isosymmetric theory.
Marco Cè, et al., "Window observable for the hadronic vacuum polarization contribution to the muon g−2 from lattice QCD" arXiv:2206.06582 (June 14, 2022) (report number MITP-22-038, CERN-TH-2022-098).Our result at the physical point is awinμ=(237.30 ± 0.79 stat ± 1.22 syst) × 10−10, where the systematic error includes an estimate of the uncertainty due to the quenched charm quark in our calculation. Our result displays a tension of 3.8σ with a recent evaluation of a^win(μ) based on the data-driven method.
Lattice QCD had not played a prominent part in the consensus paper because at that time the technique’s predictions were not sufficiently precise. State-of-the-art mathematical techniques and sheer supercomputing power subsequently helped the BMW team to give their lattice-QCD simulations enough of a boost to make the grade. Since then, at least eight teams of physicists around the world have been racing to validate or improve on the BMW prediction. They have started by focusing on a limited range of the particle energies that BMW simulated.
Two preliminary results from this energy ‘window’ were posted on the arXiv preprint repository in April 2022: one by Christopher Aubin at Fordham University in New York City, and his collaborators4, and the other by Gen Wang at the University of Aix-Marseille in France5. Earlier this month, two more groups — one led by Hartmut Wittig at Johannes Gutenberg University in Mainz, Germany, the other by Silvano Simula at the National Institute for Nuclear Physics in Rome — announced their own window results at a muon conference in Los Angeles, California. Simula’s group is writing a preprint, and Wittig’s group submitted its preprint on 14 June6. All four calculations validated BMW’s own window results, even though their lattice techniques vary. “Very different ways of approaching the problem are getting a very similar result,” says Aubin.
“As time goes by, the different groups are converging on a result that agrees with BMW’s, at least in the intermediate window,” says Davide Giusti, a physicist at the University of Regensburg, Germany, who is a former member of Simula’s collaboration, and who now works with another lattice-QCD group led by his Regensburg colleague Christoph Lehner.
QED = 116 584 718.931 ± 0.104
EW = 153.6 ± 0.1
QCD = HVP+HLbL = 6937 ± 44
The QED and EW components are both profoundly easier to calculate, and are much more precisely determinable, than the QCD component, and are undisputed.HVP = 6845 ± 40HLbL = 92 ± 18