Scale and quality of Peccei-Quinn symmetry and weak gravity conjectures
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Received: August 17, 2020 Accepted: September 10, 2020 Published: October 6, 2020
Wen Yin Department of Physics, Faculty of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
E-mail: [email protected] 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. Keywords: Beyond Standard Model, Cosmology of Theories beyond the SM, Global Symmetries ArXiv ePrint: 2007.13320
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)032
JHEP10(2020)032
Scale and quality of Peccei-Quinn symmetry and weak gravity conjectures
Contents 1
2 Scale of fundamental axion and WGC 2.1 Hierarchy problem of the PQ scale 2.2 WGC and PQ scale: case of U(1)0
2 2 3
3 PQ 3.1 3.2 3.3
5 5 7 8
scale and quality with non-abelian hidden gauge symmetry A hidden SU(N ) gauge model for precise PQ symmetry WGC and PQ scale: case of SO(N ) Cosmology
4 Conclusions and discussion
9
A Alternative models with sLWGC
1
10
Introduction
A global Peccei-Quinn (PQ) symmetry, U(1)PQ , is a leading candidate to solve a finetuning problem, the strong CP problem, of the standard model (SM) [1, 2]. Through the spontaneously breaking of U(1)PQ , an axion, which is a pseudo-Nambu Goldstone boson (pNGB), arises [3–8]. Since the anomaly of U(1)PQ -SU(3)2C is non-vanishing, the axion gets a potential with a CP-conserving minimum due to the non-perturbative effect of the QCD, and thus at the vacuum the strong CP problem is solved. Because of the coherent oscillation in the early universe, the axion condensate can contribute to the matter density and hence can explain the dark matter [9–11]. (See e.g. refs. [12–19] for reviews.) The solution, however, suffers from hierarchy and quality problems. The first problem is due to that the PQ scale, or the decay constant of the QCD axion, fa , is constrained to be within the so-called classical axion window: 108 GeV . fa . 1012 GeV,
(1.1)
which is smaller than the reduced Planck scale, Mpl = 2.4 × 1018 GeV. The lower bound comes from the duration of the neutrino burst in the SN1987a [20] (See also refs. [21, 22]). The upper bound comes from the axion abundance constraint. One simple way to address this hierarchy is to open the window. This is possible if the Hubble parameter during the inflation, which lasts long enough, is lower than the QCD scale [23, 24].1 Another way is 1
This low scale inflation can also alleviate the moduli problem at the same time [25]. See also related top
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