The QCD Axion Window as Bookkeeping: How Much of the Motivated Parameter Space Has Been Covered at Band Coupling?

The QCD axion is specified, up to model-dependent factors of order unity, by a single scale, the decay constant f_a. Its mass obeys m_a = 5.70 micro-eV x (10^12 GeV / f_a) and its photon coupling obeys g = (alpha / 2 pi f_a) x (E/N - 1.92), so that motivated models occupy a narrow diagonal strip in the mass-coupling plane. This note prices the published experimental coverage of that strip in logarithmic units. Taking the classic window to be 1 micro-eV to 1 meV (three decades in mass), haloscopes have excluded the full strip, down to the more weakly coupled DFSZ benchmark, over 0.099 decades (3.3 per cent of the window), and have tested the strip at the more strongly coupled KSVZ benchmark over 0.304 decades (10.1 per cent). The remaining 89.9 per cent of the classic window is untested at KSVZ coupling, and 96.7 per cent is untested at DFSZ coupling. HAYSTAC, ORGAN, CAST and ALPS II have published limits in or near the window, but at couplings above the strip, by factors ranging from about 3 to about 38,000 depending on mass and experiment, so they contribute no coverage at band coupling under the definitions used here. Horizontal-branch star limits likewise meet the strip only near 0.17 eV, outside the classic window; the supernova 1987A statement m_a below about 0.01 eV is the only astrophysical argument that maps onto band masses inside the window, and it is model-dependent. Projected sensitivities, in particular for IAXO, are listed separately and are not counted as coverage. Most of the classic window remains open at band coupling.