The mass of the η′ in self-dual QCD

The QCD gauge field is modeled as an ensemble of statistically independent self-dual and anti-self-dual regions. This model is motivated by instanton physics. The scale anomaly then allows one to relate the topological susceptibility to the gluon condensate. With the help of Wittenʹs formula for mη′ and an estimate of the suppression of the gluon condensate due to light quarks the mass of the η′ can be related to fπ and the physical gluon condensate. We obtain the quite satisfactory value mη′ = 884 ± 116 MeV. Using the physical η′ mass as an input it is in principle possible to obtain information about the interaction between instantons and anti-instantons.