Colorful Mirror Solution to the Strong CP Problem.

We propose theories of a complete mirror world with parity (P) solving the strong CP problem. P exchanges the entire standard model with its mirror copy. We derive bounds on the two new mass scales that arise: v^{'} where parity and mirror electroweak symmetry are spontaneously broken, and v_{3} where the color groups break to the diagonal strong interactions.

Shift-Invariant Orders of an Axionlike Particle.

It is generally believed that global symmetries, in particular, axion shift symmetries, can only be approximate. This motivates one to quantify the breaking of the shift invariance that characterizes the flavorful effective couplings of an axionlike particle to standard model fermions. We identify a minimal set of Jarlskog-like flavor invariants that vanish if and only if the axion is shift symmetric.