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The MUonE experiment aims to provide a new, independent measurement of the hadronic vacuum polarisation (HVP) contribution to the muon $g-2$. Considering the disagreement between some recent lattice calculations and dispersive determinations, a third and fully independent result is extremely important. However, MUonE will require an unprecedented precision of $10^{-5}$ to solve this disagreement.
I will introduce the MUonE experiment and explain the theory behind the our recent NNLO calculation as well as some future developments towards N${}^3$LO.