Low-energy hadronic cross sections measurements at BABAR and g-2 of the muon

The LO hadronic vacuum polarization (VP) contribution to the muon anomalous magnetic moment $a_\mu$ is obtained as the integral as a function of energy of an expression that involves the ratio of the $e^+e^- \rightarrow \mathrm{hadron}$ cross section to the pointlike muon pair cross section. The former is extracted from experimental data for individual hadronic final states at low energies, and from perturbative QCD at high energies. The BaBar experiment at SLAC has a programme of systematic measurement of the production of the lowest-rest-mass hadronic final states, those that contribute most significantly to the integral. To that purpose, we use a method in which, while the PEP-II storage ring is operated at a constant energy in the center of mass system, $\sqrt{s}$, of about 10.6 GeV, events are reconstructed and selected which have been produced with a hadronic final state together with a high-energy photon which may (photon tagging) or may not (no tagging) be observed. In our kinematic configuration the photon is almost always emitted by the electron or by the positron of the initial state, hence the name "initial-state radiation" (ISR). The cross section for the direct $e^+e^- \rightarrow f$ production of a final state $f$ at an energy $\sqrt{s'}$ is then extracted from the differential cross section of the ISR production of the state $f$ with invariant mass $\sqrt{s'}$. The programme is almost completed and has lead to a number of first measurements and to an improvement of up to a factor of three of the uncertainties on the contributions of individual channels to $a_\mu$.