One intriguing beyond-the-Standard-Model particle is the QCD axion , which could simultaneously provide a solution to the Strong CP problem and account for some , if not all , of the dark matter density in the universe .
This particle is a pseudo-Nambu–Goldstone boson of the conjectured Peccei–Quinn ( PQ ) symmetry of the Standard Model .
Its mass and interactions are suppressed by a heavy symmetry breaking scale , f _ { a } , whose value is roughly greater than 10 ^ { 9 } GeV ( or , conversely , the axion mass , m _ { a } , is roughly less than 10 ^ { 4 } \mu \text { eV } ) .
The density of axions in the universe , which can not exceed the relic dark matter density and is a quantity of great interest in axion experiments like ADMX , is a result of the early-universe interplay between cosmological evolution and the axion mass as a function of temperature .
The latter quantity is proportional to the second derivative of the temperature-dependent QCD free energy with respect to the CP-violating phase , \theta .
However , this quantity is generically non-perturbative and previous calculations have only employed instanton models at the high temperatures of interest ( roughly 1 GeV ) .
In this and future works , we aim to calculate the temperature-dependent axion mass at small \theta from first-principle lattice calculations , with controlled statistical and systematic errors .
Once calculated , this temperature-dependent axion mass is input for the classical evolution equations of the axion density of the universe , which is required to be less than or equal to the dark matter density .
Due to a variety of lattice systematic effects at the very high temperatures required , we perform a calculation of the leading small- \theta cumulant of the theta vacua on large volume lattices for SU ( 3 ) Yang–Mills with high statistics as a first proof of concept , before attempting a full QCD calculation in the future .
From these pure glue results , the misalignment mechanism yields the axion mass bound m _ { a } \geq ( 14.6 \pm 0.1 ) \mu \text { eV } when PQ-breaking occurs after inflation .