Dark QCD Origin of the NANOGrav Signal and Self-Interacting Dark Matter

Abstract

The NANOGrav 15-year stochastic gravitational wave background (SGWB) amplitude $A_{\mathrm{yr}}\approx 2.4\times 10^{-15}$ lies at the upper edge of population synthesis predictions for supermassive black hole binaries (SMBHBs), motivating exploration of additional cosmological sources. We present a phenomenological framework based on an $\text{SU}(3{)}_D$ gauge theory that can simultaneously accommodate the gravitational wave signal and resolve small-scale structure anomalies via Self-Interacting Dark Matter (SIDM). The dark matter candidate is a heavy dark baryon $\chi =QQQ$ with mass $m_{\chi }\approx 40$~GeV, which self-interacts through a light pseudo-dilaton $d$ $m_d\approx 20$--$50$~MeV as a pseudo-Goldstone boson of approximate scale invariance arising in near-conformal gauge theories with $N_f\sim 6$--$8$ light flavors. A first-order phase transition at the MeV scale, enabled by walking dynamics near the conformal window, produces gravitational waves in the PTA band. For representative parameters $T_n\approx 5$--$6$~MeV, $\alpha \sim 500$--$1000$, $\beta /H_{\ast }\sim 30$--$50$, the model provides a fit to NANOGrav data comparable to SMBHB while naturally connecting the gravitational wave amplitude to the dark matter relic density through entropy dilution $D\approx {\alpha }^{3/4}$. We present explicit calculations of the bounce action, bubble wall velocity, and $\Delta N_{\mathrm{eff}}$, demonstrating that the benchmark parameters are theoretically consistent and cosmologically safe ($\Delta N_{\mathrm{eff}}\lesssim 0.1$ for $m_{\pi }>2m_d$). The distinctive spectral shape ($f^3\to f^{-4}$) provides a robust prediction testable with future PTAs.