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Consistent explanation for the cosmic-ray positron excess in $p$-wave Breit-Wigner enhanced dark matter annihilation

Dark matter (DM) annihilation in the galactic halo can be enhanced relative to that in the early Universe due to the Breit-Wigner enhancement, if the DM particles annihilate through a narrow resonance. Although the $s$-wave Breit-Wigner enhancement can provide a consistent explanation for both the observed cosmic-ray (CR) positron excess and the DM thermal relic density, it is severely constrained by the observations of gamma rays from dwarf spheroidal satellite galaxies (dSphs) and the cosmic microwave background (CMB), which have relatively lower allowed DM annihilation cross section and typical DM velocities than that in the galactic halo. Furthermore, in the $s$-wave Breit-Wigner enhancement, the case where the resonance mass is below a threshold (twice the DM mass) is ruled out due to the monotonically increasing annihilation cross section with decreasing DM velocity. In this work, we consider Breit-Wigner enhanced $p$-wave DM annihilation. We explore the parameter regions which can simultaneously account for the CR positron excess and DM thermal relic density without violating the constraints from dSphs gamma rays and CMB. We show that the velocity-dependent cross section in this scenario can peak around the typical DM velocity in the galactic halo for the resonance mass both above and below the threshold. Moreover, the highly suppressed annihilation cross section at extremely low DM velocity can evade the constraints from dSphs gamma rays and CMB easily, which results in larger allowed parameter regions than that in the $s$-wave case.