Scale and quality of Peccei-Quinn symmetry and weak gravity conjectures

Wen Yin

doi:10.1007/jhep10(2020)032

Abstract

The promising solution to the strong CP problem by a Peccei-Quinn (PQ) symmetry may introduce quality and hierarchy problems, which are both relevant to Planck physics. In this paper, we study whether both problems can be explained by introducing a simple hidden gauge group which satisfies the WGC or its variant. As a concrete example, we point out that a weakly-coupled hidden SU(N ) gauge symmetry, which is broken down to SO(N ), can do this job in the context of a Tower/sub-Lattice WGC. Cosmology is discussed.

Highlights

JHEP10(2020)032 to extend the PQ sector to make the scale of the classical axion window natural, e.g. the axion is composite [38, 39], or with supersymmetry
It may be important to discuss the scale of the PQ symmetry in the context of the weakgravity conjecture (WGC) via the gauge symmetry introduced for the quality problem
We find that by introducing a U(1) gauge symmetry in a KSVZ axion model [5, 6], the hierarchy between the scale of axion window and the Planck scale can be explained within the context of the WGC, which restricts an unbroken abelian gauge symmetry

Summary

Scale of fundamental axion and WGC

2.1 Hierarchy problem of the PQ scale Let us consider a KSVZ model with the following particle contents q : (1, rSM), q : (0, rSM), HPQ : (−1, 1). By assuming the cutoff scale Λc.o ∼ Mpl, the radiative correction is 1017 GeV for O(1) couplings This implies that m2PQ in the conventional axion window (2.7) requires fine-tuning of m2PQ/δm2PQ 10−10 between the bare mass squared and δm2PQ. The WGC states that gravity is the weakest long-range force It says that in the effective theory of U(1) gauge symmetry consistent with the quantum gravity, there is at least a charged particle with mass m and charge q satisfying [55]. Let us rewrite the gauge coupling fg Notice that this bound is from the consistency condition with quantum gravity if the WGC is correct, and the naıve radiative instability discussion neglecting quantum gravity does not apply. In the context of the mild version of the WGC, an unbroken U(1) symmetry can solve the hierarchy problem of the PQ symmetry but cannot solve the quality problem.

PQ scale and quality with non-abelian hidden gauge symmetry

Cosmology

Conclusions and discussion

A Alternative models with sLWGC