Small instanton-induced flavor invariants and the axion potential
Guilherme Guedes (DESY)

In this talk, I will go over the role of small instantons (SI) in increasing the axion mass. These SI will also enhance the effect of CP-violating operators which shift the axion potential minimum by an amount proportional to the flavorful couplings of the theory. Since physical observables must be flavor basis independent, we construct a basis of determinant-like flavor invariants that arise in instanton calculations containing the effects of dimension-six CP-odd operators. This new basis provides a more reliable estimate of the shift of the minimum of the axion potential, which is severely constrained by neutron electric dipole moment experiments. We show explicitly how these quantities arise in the case of 4-quark and semi-leptonic operators, and how they can be used to constrain the ratio of the scales of SI and CP-violation. More generally, the flavor invariants introduced, together with an instanton NDA, can be used to more accurately estimate small instanton effects in the axion potential arising from any effective operator. We will also discuss how other shift-breaking effects can be enhanced in the presence of SI.