generated for the QCD axion. Of course, the scalar field $a$ in Eq.  does not have to be the QCD axion. If not, it would be a type of ALP. Most considerations of ALPs have focused on fields that couple to electromagnetism through the coupling in Eq. . However there is no reason that an ALP has to couple only, or at all, through the electromagnetic coupling. The space of ALPs that have EDM couplings as in Eq.  is a new parameter space that is worth exploring since this coupling motivates new experimental signatures and appears promising for axion detection. Figure \[Fig:EDM\] shows the parameter space for an ALP in the space of the EDM coupling $g_d$ in Eq.  versus the mass of the ALP.

![ \[Fig:EDM\] ALP parameter space in EDM coupling Eq.  vs mass of ALP. The green region is excluded by excess cooling in SN1987A. The blue regions are excluded by the best static nucleon EDM experiments. The purple band is the QCD axion region, with dark purple showing the most theoretically-motivated region for QCD axion dark matter. The width of the band shows the uncertainty in the calculation of the axion-induced EDM and the axion mass. The ADMX region shows the part of QCD axion parameter space which has been covered (darker blue) [@Asztalos:2009yp] or will be covered in the near future (lighter blue) [@ADMXwebpage; @snowdarktalk] by ADMX. For the static EDM and ADMX bounds we assume that the ALP makes up all of the dark matter. See also Figure 2 of [@NMR; @paper] for sensitivity of the proposed NMR experiment.](dipoleplot.pdf){width="6"}

The QCD axion may lie anywhere on the purple line in Figure \[Fig:EDM\]. It lies on a line because it has only one free parameter, $f_a$, which determines its mass and $g_d$ as in Eqs.  and . The width of the QCD axion line shows an estimate of the theoretical uncertainty in the calculation of these quantities, as described above. The darker purple section of the line shows where the QCD axion may make up the dark matter. For values of $m_a \gtrsim$ meV the QCD axion cannot have enoug