Longitudinal double-spin asymmetry $A_1^{\mathrm{p}}$ and spin-dependent structure function $g_1^{\mathrm{p}}$ of the proton at small values of $x$ and $Q^2$

We present a precise measurement of the proton longitudinal double-spin asymmetry $A_1^{\mathrm{p}}$ and the proton spin-dependent structure function $g_1^{\mathrm{p}}$ at photon virtualities $0.006~({\rm GeV}/c)^2<Q^2 < 1~({\rm GeV}/c)^2$intheBjorken$x$rangeof$4 \times 10^{-5} < x < 4 \times 10^{-2}$. The results are based on data collected by the COMPASS Collaboration at CERN using muon beam energies of $160\mathrm{G}\mathrm{e}\mathrm{V}$ and $200\mathrm{G}\mathrm{e}\mathrm{V}$. The statistical precision is more than tenfold better than that of the previous measurement in this region. In the whole range of $x$, the measured values of $A_1^{\mathrm{p}}$ and $g_1^{\mathrm{p}}$ are found to be positive. It is for the first time that spin effects are found at such low values of $x$.