Measurement of hadronic cross-sections with the BaBar detector

A program of measuring the light hadrons production in exclusive $e^+e^-$ to hadrons processes is in place at BaBar with the aim to improve the calculation of the hadronic contribution to the muon $g-2$. We present the most recent results obtained by using the full data set of about $514 \mathrm{fb}^{-1}$ collected by the BaBar experiment at the PEP-II $e^+e^-$ collider at a center-of-mass energy of about $10.6$ GeV. In particular, we report the results on the channels $e^+e^-\rightarrow \pi^+ \pi^- 3\pi^0$, $e^+e^-\rightarrow \pi^+\pi^- 2\pi^0\eta$, and its resonant sub-states. These final states are studied in a wide mass range,from threshold production up to about $4 GeV/c^2$. In addition to the cross-sections, twelve $J/\psi$ and $\psi(2S)$ branching fractions were measured with ten of them be a first-time measurement.