Spectral distortions in the decaying QCD dark matter scenario

We study the QCD--DM scenario by analyzing the imprint of energy injection from decaying dark-sector particles on the spectral distortions (SDs) of the Cosmic Microwave Background (CMB). We adopt a unified framework capable of describing both relativistic and non-relativistic particles, as well as fast and slow decay regimes. Within this approach, we model exponential, power-law, oscillatory, and two-step decays, computing the resulting $\mu$- and $y$-type distortions across the parameter space spanned by the confinement scale $a_c$, decay rate $\Gamma_\chi$, energy-transfer efficiency $\Sigma_\chi$, and velocity $v_{\chi c}$. We find that power-law, oscillatory, and cascade decays can be effectively mapped onto exponential models with appropriate rescaling. The dominant factors controlling SDs are the decay epoch and lifetime, with $v_{\chi c}$ becoming relevant only in the ultra-relativistic limit. FIRAS observations impose tight constraints on early energy injection, with $\mu$-type distortions placing the strongest bounds on $\Sigma_\chi$. Simultaneous matching of both $\mu_{\rm firas}$ and $y_{\rm firas}$ breaks the degeneracy between $\Gamma_\chi$ and $\Sigma_\chi$, localizing preferred decay rates around $\Gamma_\chi \lesssim (3.3-4.4)\times10^{-3}~{\rm yr}^{-1}$ and $\Sigma_\chi \lesssim 8.5\times10^{-4}$ for relativistic particles, while fast decays with $\Gamma_\chi \gtrsim 6.5~{\rm yr}^{-1}$ become observationally negligible. Our results show that CMB spectral distortions are a powerful probe of dark-sector dynamics. Future missions such as PIXIE or PRISM could extend current limits by several orders of magnitude and test previously inaccessible regions of parameter space.