This paper proposes a new way to give masses to all fermions in the Standard Model while at the same time protecting the axion, a hypothetical particle that could solve the strong CP problem. The authors add one extra gauge symmetry, called U(1)_{Y'}, plus new heavy fermions and new Higgs-like fields. These additions let the known fermions get masses through a “chain seesaw” instead of the usual direct couplings to the Higgs.

In the model, the usual direct Yukawa couplings between the Standard Model Higgs and fermions are forbidden by the extra gauge symmetry. To get masses, the left-handed and right-handed versions of each fermion are connected by a chain of heavy mediator fermions and new Higgs singlets. The mediators are vector-like fermions, meaning they come in matched pairs and do not spoil the gauge anomaly cancellation. The down-type and up-type quark chains can have different numbers of links because the mediators and singlets carry different charges under U(1)_{Y'}.

At a high level the mechanism works like this: the new Higgs singlets develop vacuum expectation values (VEVs) — that is, the fields take nonzero values in empty space. Those VEVs, together with the chain of heavy mediators, build effective interaction terms that act like the usual Yukawa couplings to the Standard Model Higgs. When the Standard Model Higgs later gets its VEV, the ordinary fermions acquire their Dirac masses. Because the masses arise through chains and heavy mediators, small neutrino masses can appear naturally without extremely tiny direct couplings.

The paper also addresses the axion quality problem. The axion is a particle tied to a global symmetry named Peccei–Quinn (PQ), introduced to solve the strong CP problem in quantum chromodynamics. Global symmetries can be spoiled by gravity through Planck-scale effects, which would ruin the axion solution unless the symmetry is extremely precise. In this model the PQ symmetry is an automatic or accidental feature of the added U(1)_{Y'} gauge symmetry. The authors argue that requiring gauge invariance under U(1)_{Y'} is enough to protect the PQ symmetry and give a high-quality axion.