Correlation Between X-Ray and Cosmic Neutrino Sources: From Obscured AGN to Blazars

The origin of high-energy astrophysical neutrinos remains a key open question in multimessenger astrophysics. A correlation between unabsorbed hard X-ray emission and high-energy neutrino luminosity has been reported in a sample of six active galactic nuclei with the highest individual IceCube significances, linking neutrino production to compact, photon-rich environments near supermassive black holes. In this work we study whether the threshold-near IceCube excesses associated with seven NuSTAR-observed blazars are statistically consistent with that established relation. Calibrating the relation between the neutrino and hard X-ray luminosities as $\log L_\nu = \alpha + \beta \log L_\mathrm{hX} + \mathcal{N}(0, \sigma_{\rm int}^2)$ on the six published sources via a Bayesian regression with errors on both axes, the recovered slope is consistent with $\beta = 1$, and the intrinsic scatter is $\sim 0.6$\,dex. All seven new blazars are posterior-predictively consistent with this calibration ($\chi^2_7 = 1.58$, $p = 0.98$) under the working hypothesis that the published IceCube best-fit neutrino numbers $\hat{n}_s$ values reflect the signal. A null-injection test confirms that, given the present calibration sample size, the consistency test does not by itself adjudicate between signal and selected-background origins. A distance-free $L_\mathrm{hX}/L_\nu$ ratio diagnostic places both populations within the photohadronic prediction band, statistically indistinguishable. A flux-space permutation test on the 13-source joint sample, with construction-controlled $d_L^{\,2}$ distance bias, rejects random pairing $L_\mathrm{hX}$--$L_\nu$ with $p = 6.3 \times 10^{-4}$ ($3.23\,\sigma$). We interpret these results as a conditional consistency check; a detection-level statement requires either an enlarged calibration set or an X-ray-weighted IceCube stacking likelihood with internal data.