Longitudinal double spin asymmetry $A_1^p$ and spin-dependent structure function $g_1^p$ of the proton at low $x$ and low $Q^2$ from COMPASS

The COMPASS experiment at CERN has collected a large sample of events of inelastic scattering of longitudinally polarised muons off longitudinally polarised protons in the non-perturbative region (four-momentum transfer squared $Q^2<1$~(GeV$^2$/$c^2$), with a Bjorken scaling variable in the range $4\times 10^{-5}<x<4\times 10^{-2}$. The data set is two orders of magnitude larger than the similar sample collected by the SMC experiment. These data complement our data for polarised deuterons. They allow the accurate determination of the longitudinal double spin asymmetry $A_1^p$ and of the spin-dependent structure function $g_1^p$ of the proton in the region of low $x$ and low $Q^2$. The preliminary results of the analysis of these data yield non zero and positive asymmetries and of the structure function $g_1^p$. This is the first time that spin effects are observed at such low $x$.