Accidental Peccei-Quinn symmetry protected to arbitrary order

Abstract

A $SU(N{)}_L\times SU(N{)}_R$ gauge theory for a scalar multiplet $Y$ transforming in the bi-fundamental representation $(N,\bar{N})$ preserves, for $N>4$, an accidental $U(1)$ symmetry firstly broken at operator dimension $N$. Two configurations are possible for the vacuum expectation value of $Y$, which correspond to the (maximal) little groups ${\mathcal{H}}_s=SU(N{)}_{L+R}$ and ${\mathcal{H}}_h=SU(N-1{)}_L\times SU(N-1{)}_R\times U(1{)}_{L+R}$. In the first case the accidental $U(1)$ gets also broken, yielding a pseudo Nambu-Goldstone boson with mass suppression controlled by $N$, while in the second case a global $U(1)$ remains unbroken. The strong CP problem is solved by coupling $Y$ to new fermions carrying color. The first case allows for a Peccei-Quinn solution with $U(1{)}_{PQ}$ protected up to order $N$ by the gauge symmetry. In the second case $U(1)$ can get broken by condensates of the new strong dynamics, resulting in a composite axion. By coupling $Y$ to fermions carrying only weak isospin, models for axion-like particles can be constructed.

Comments: 6 pages 1 figure