Singlet scalars are among the most promising candidates of new physics. Standard (minimal) assumptions in the study of this framework might however hide a large parameter space of solutions to different puzzles in the SM which can limit our discovery potential. In the first part of the talk, I will consider the impact of scalar mixing in the standard singlet axion mechanism to solve the strong CP problem. I will show that the canonical axion mass-scale relation can be modified within QCD and multiple signals may be required to reconstruct the solution to the strong CP problem. These signals are constrained by a sum rule that I will derive, which applies to arbitrary scalar potentials. In the second part of the talk, I will consider the impact of operator mixing, via RGEs, in the singlet parameter space. Such effects can change the stability of UV scenarios and give additional constraints on the parameter space.
DFA and INFN, Sezione di Padova