Dark-Sector Coupling Bounds from Existing Data: A Budget for the Kinetically Mixed Dark Photon

A light dark sector can communicate with ordinary matter only very weakly, and the quantitative statement of that weakness is distributed across stellar astrophysics, supernova observations, fixed-target and collider experiments, cosmology, and direct detection. This paper compiles the published bounds for one worked example, the dark photon with kinetic mixing parameter epsilon and mass m_A', into a single budget. All bounds are transcribed as cited inputs from published reviews and results; only comparisons and conversions are derived. At representative masses of 1e-6 eV, 1 keV, 1 MeV, and 1 GeV, the strongest unconditional bounds on epsilon are 1e-12 (horizontal-branch and red-giant cooling), 3e-13 (horizontal-branch and red-giant cooling), 1e-9 (the lower edge of the SN 1987A cooling band), and 7e-4 (the BaBar visible search), respectively. Against a thermal-relic target of epsilon = 1.27e-4 for the stated benchmark (dark coupling alpha_D = 0.5, mediator-to-dark-matter mass ratio 3, target variable y = 1e-10), the MeV bound lies 5.10 decades below the target, while at 1 GeV the target lies 0.74 decades below the bound, so that benchmark point is already probed. Finally, the Planck bound on extra radiation, Delta N_eff below 0.2792 (the Planck 2018 value N_eff = 2.99 plus or minus 0.17 implies Delta N_eff below 0.2792 at 95 per cent confidence, 1.96 sigma, relative to the Standard Model value 3.044), requires a thermalized light species to have decoupled while the entropy degrees of freedom of the plasma satisfied g_S above 18.4 for a real scalar, 28.0 for a Weyl fermion, 30.9 for a massless vector, and 41.9 for a massive vector; a species decoupling at g_S = 106.75 contributes only 0.027 to 0.080 to Delta N_eff. No new experiment is proposed; the contribution is the bookkeeping itself. Correction in this version: the first version of this paper computed the decoupling thresholds of Table 2 at an adopted bound of Delta N_eff = 0.30, inconsistent with the convention used elsewhere in this series of papers. This version corrects the table and the statements that quote it to the single convention Delta N_eff below 0.2792 (95 per cent confidence, 1.96 sigma, Standard Model value 3.044), giving minimum decoupling entropy counts of 18.4 for a real scalar, 28.0 for a Weyl fermion, 30.9 for a massless vector, and 41.9 for a massive vector. All other results are unchanged. Disclosure: This work was prepared with the assistance of Dave, an AI research system operated by Aldred Industries. All computations are reproducible from the accompanying script.