Exploring sub-GeV dark matter via $s$-wave, $p$-wave, and resonance annihilation with CMB data

We revisit constraints on sub-GeV dark matter (DM) annihilation via $s$-wave, $p$-wave, and resonance processes using current and future CMB data from Planck, FIRAS, and upcoming experiments such as LiteBIRD, CMB-S4, PRISTINE, and PIXIE. For $s$-wave annihilation, we provide updated limits for both $e^{+}e^{-}$ and $\pi\pi$ channels, with the profile likelihood method yielding stronger constraints than the marginal posterior method. In the $p$-wave case, we comprehensively present a model-independent inequality for the $95\%$ upper limits from FIRAS, PRISTINE, and PIXIE, with future experiments expected to surpass current BBN limits. For resonance annihilation, we report -- for the first time -- the $95\%$ upper limits on the decay branching ratio of the mediator particle, when the resonance peaks during the recombination epoch. Overall, our study highlights the complementary strengths of $\mu$-distortion and CMB anisotropies in probing sub-GeV DM annihilation.