I will review the dispersive and data-driven calculations of the hadronic contributions to the Muon g-2, with emphasis on the hadronic vacuum polarization. I will discuss in detail the comparison with the lattice evaluation both of the total and of the intermediate window quantity, and the implications of the present discrepancy. I will conclude with an outlook on future developments.

I will give an overview of the RBC/UKQCD g-2 program including both the hadronic light-by-light as well as the hadronic vacuum polarization contribution.

The Muon g-2 Experiment at Fermi National Accelerator Laboratory was designed to measure the anomalous magnetic moment of the muon, $𝑎_𝜇$, with a target precision of 140 parts-per-billion (ppb); a four-fold improvement over the former measurement at Brookhaven National Laboratory. The experiment was motivated by the ~3.5 standard deviation between the BNL result and the Standard Model...

During the last 15 years the "Radio MontecarLow (“Radiative Corrections and Monte Carlo Generators for Low Energies”) Working Group, see www.lnf.infn.it/wg/sighad/, has been providing valuable support to the development of radiative corrections and Monte Carlo generators for low energy $e^+e^-$ data and tau-lepton decays. Its operation which started in 2006 proceeded until the last few years...

In this talk I will review the calculation of the short and intermediate window for g-2, based on our recent simulations performed int the Twisted Mass regularization of QCD, with physical pion mass and three different lattice spacings. Our results highlights that the tension with experimental measurement is concentrated in the intermediate energy region.

The muon anomalous magnetic moment is currently one of the most intriguing measurements, as it marks a 4.2 𝜎 deviation from the reference prediction of the Standard Model, and is expected to provide an even more stringent test in the next few years with the experimental error reducing by a factor of four. In parallel the theoretical error need to be reduced. It is dominated by the...

The muon anomaly, $𝑎_𝜇=\frac{(𝑔−2)}{2}$, is a low-energy observable which can be both measured and computed to high precision, making it a sensitive test of the Standard Model and a probe for new physics. The current discrepancy between the Standard Model calculation from the Muon $𝑔−2$ Theory Initiative [T. Aoyama et al. - Phys. Rept. 887 (2020), 1-166] and the experimental value is...

We present our previous and ongoing lattice QCD efforts to determine thehadron vacuum polarization contribution to the muon magnetic moment.

We discuss a novel approach, based on spectral reconstruction techniques, which circumvents the well-known problem of the analytic continuation from Minkowskian to Euclidean time for hadronic processes above kinematical thresholds. The approach is discussed for the specific case of the radiative decays of pseudoscalar mesons $P\to \ell \nu_{\ell} \gamma^{}$, where $\gamma^{}$ is a virtual...

As the number of fermion fields is increased, gauge theories are expected to undergo a transition from a QCD-like phase, characterised by confinement and chiral symmetry breaking, to a conformal phase, where the theory becomes scale-invariant at large distances. In this paper, we discuss some properties of a third phase, where spontaneously broken conformal symmetry is characterised by its...

We discuss how a recently discovered non-perturbative field-theoretical mechanism giving mass to elementary fermions can be extended to generate a mass for the electro-weak bosons, when weak interactions are introduced, and can thus be used as a viable alternative to the Higgs scenario. We will show that this new scheme, successfully tested in extensive lattice simulations, offers a solution...

I will overview the interplay between QCD axion properties and Lattice QCD inputs and discuss open questions in axion phenomenology and cosmology.

High-statistics measurements in peripheral photon-induced scattering using relativistic heavy-ion beams provide a precise and unique opportunity to investigate extensions of the Standard Model. New measurements of exclusive dilepton production (electron, muon, and tau pairs) are discussed. In particular, the tau-pair production measurement is used to constrain tau lepton's anomalous magnetic...