Hadronic contribution to muon g-2 using dispersive approach*

The muon g-2, is one of the most precisely measured quantities in particle physics, both experimentally and theoretically. It represents a crucial test of the Standard Model (SM) and a sensitive probe for new physics, as any deviation between the experimental and theoretical values could indicate Beyond Standard Model physics contributions. Its SM evaluation is limited by current tensions in the evaluation of the leading order hadronic contributions (HVP). These have been tradionally computed by means of a dispersion relation technique involving experimental data measuring the cross section of electron positron annihilation into hadrons, e⁺e⁻→hadrons, (so-called "time-like” or “dispersive” approach). The calculation of HVP via time-like data is highly challenging, due to many hadron-production channels and different experiments with their own systematics and correlations between the involved datasets and a recent result from CMD3 experiment in Novosibirk is in significant discrepancy with previous measurements. In the last few years there has been a lot of progress on the first-principle calculation of HVP using lattice QCD  and a new precise evaluation from BMW collaboration is in closer agreement with the muon g-2 experimental value and with the value for HVP provided by CMD3 taken in isolation. I will review the status and the prospects of the HVP calculation using dispersive approach.