Impact of correlations between $$a_{\mu }$$ and $$\alpha _\text {QED}$$ on the EW fit

We study the potential impact on the electroweak (EW) fits due to the tensions between the current determinations of the hadronic vacuum polarisation (HVP) contributions to the anomalous magnetic moment of the muon ($$a_{\mu }$$ a μ ), based on either phenomenological dispersion integrals using measured hadronic spectra or on Lattice QCD calculations. The impact of the current tension between the experimental measurement of $$a_{\mu }$$ a μ and the total theoretical prediction based on the phenomenological calculations of the HVP is also studied. The correlations between the uncertainties of the theoretical predictions of $$a_{\mu }$$ a μ and of the running of $$\alpha _\mathrm{QED}$$ α QED are taken into account in the studies. We conclude that the impact on the EW fit can be large in improbable scenarios involving global shifts of the full HVP contribution, while it is much smaller if the shift is restricted to a lower mass range and/or if the shift in $$\alpha _\text {QED}$$ α QED is obtained from that in $$a_{\mu }$$ a μ through appropriate use of the correlations. Indeed, the latter scenarios only imply at most a 2.6/16 increase in the $$\chi ^2/\text {n.d.f.} $$ χ 2 / n.d.f. of the EW fits and relatively small changes for the resulting fit parameter values.

Lattice calculation of the hadronic leading order contribution to the muon g − 2

The persistent discrepancy of about 3.5 standard deviations between the experimental measurement and the Standard Model prediction for the muon anomalous magnetic moment, aµ, is one of the most promising hints for the possible existence of new physics. Here we report on our lattice QCD calculation of the hadronic vacuum polarisation contribution $ a_\mu ^{{\rm{hvp}}} $, based on gauge ensembles with Nf = 2 + 1 flavours of O(a) improved Wilson quarks. We address the conceptual and numerical challenges that one encounters along the way to a sub-percent determination of the hadronic vacuum polarisation contribution. The current status of lattice calculations of $ a_\mu ^{{\rm{hvp}}} $ is presented by performing a detailed comparison with the results from other groups.

Maxwell's Equations, Stokes' Theorem, and the Conservation of Charge

A careful examination of the fundamentals of electromagnetic theory shows that due to the underlying mathematical assumptions required for Stokes' Theorem, global charge conservation cannot be guaranteed in topologically non-trivial spacetimes. However, in order to break the charge conservation mechanism we must also allow the electromagnetic excitation fields D, H to possess a gauge freedom, just as the electromagnetic scalar and vector potentials $\varphi$ and A do. This has implications for the treatment of electromagnetism in spacetimes where black holes both form and then evaporate, as well as extending the possibilities for treating vacuum polarisation. Using this gauge freedom of D, H we also propose an alternative to the accepted notion that a charge passing through a wormhole necessarily leads to an additional (effective) charge on the wormhole's mouth.

Update on the hadronic vacuum polarisation contributions to muon g − 2 and α(mZ2)

An update of the hadronic vacuum polarisation contributions to the muon magnetic anomaly and to the running of the electromagnetic couplings constant at the Z-boson mass is presented. Newest e+e−→ hadrons cross-section data mainly from the BABAR and VEPP-2000 experiments have been included. For the muon (g−2)/2, the lowest-order hadronic contribution is evaluated to be (693.1 ± 3.4) · 10−10, improving the precision of our previous evaluation by 21%. The full Standard Model prediction differs by 3.5 σ from the experimental value. The five-quark hadronic contribution to $ \alpha (\mathop m\nolimits_z^2 ) $ is evaluated to be (276.0 ± 0.9) · 10−4.