Cosmic-ray antiproton constraints on light dark matter candidates

Some direct detection experiments have recently collected excess events that could be interpreted as a dark matter (DM) signal, pointing to particles in the $\sim$10 GeV mass range. We show that scenarios in which DM can self-annihilate with significant couplings to quarks are likely excluded by the cosmic-ray (CR) antiproton data, provided the annihilation is S-wave dominated when DM decouples in the early universe. These limits apply to most of supersymmetric candidates, eg in the minimal supersymmetric standard model (MSSM) and in the next-to-MSSM (NMSSM), and more generally to any thermal DM particle with hadronizing annihilation final states.