The hadronic running of the electromagnetic coupling and electroweak mixing angle

We present results for the hadronic running of the electromagnetic coupling and the weak mixing angle from simulations of lattice QCD with Nf=2+1 flavours of O(a)-improved Wilson fermions. Using two different discretisations of the vector current, we compute the quark-connected and -disconnected contributions to the hadronic vacuum polarisation (HVP) functions Π¯γγ and Π¯Zγ for spacelike squared momenta Q2≤7 GeV2.
Our results are extrapolated to the physical point using ensembles at four lattice spacings, with pion masses ranging from 130 to 420 MeV.
We observe a tension of up to 3.5 standard deviations between our lattice results for Δα(5)had(−Q2) and estimates based on the R-ratio for space-like momenta in the range Q2=3−7GeV2. To obtain an estimate for Δα(5)had(M2Z), we employ the Euclidean split technique. The implications for comparison with global electroweak fits are assessed.