On The Sensitivity of Spin-Precession Axion Experiments

A leading direction in the hunt for axion dark-matter is to search for its influence on nuclear spins. The detection scheme involves polarizing a sample of nuclei within a strong static magnetic field and then looking for a spin precession induced by the oscillating axion field. We study the axion signal and background contributions that arise in such experiments (a prominent example being CASPEr), finding key differences with the existing literature. Most importantly, in the limit where the transverse spin-relaxation time of the material is the largest timescale of the problem, we show that the induced signal continues to grow even beyond the coherence time of the axion field. As a result, we find that spin-precession instruments are much more sensitive than what has been previously estimated in a sizable range of axion masses, with sensitivity improvement of up to a factor of 100 at an axion mass of $100~{\rm neV} $ using a ${}^{129}{\rm Xe} $ sample. This improves the detection prospects for the QCD axion and we estimate the experimental requirements to reach this motivated target.Our results apply to both the axion electric and magnetic dipole moment operators