Spontaneous mass generation suggests small dimension of the SM group U(1)xSU(2)xSU(3)

TL;DR

The paper explores why the Standard Model's gauge group has low dimensionality, suggesting that larger groups would produce extremely heavy fermions due to strong antiscreening effects, explaining the observed gauge structure.

Contribution

It proposes a dynamical mass generation mechanism that favors small gauge groups like the Standard Model over larger ones based on fermion mass scales.

Findings

Fermions charged under larger groups acquire exponentially larger masses.

Large groups become strongly coupled near the GUT scale, preventing their low-energy realization.

Small gauge groups are favored due to their lighter fermions and weaker coupling effects.

Abstract

The reasons behind the gauge symmetry of the Standard Model, U(1)xSU(2)xSU(3), are still unsettled. One obvious feature is the low dimensionality of all its subgroups. Under certain conditions, a negative answer to the question "why not larger groups like SU(15), or for that matter, SP(26) or E7?" is possible. We have recently observed that fermions charged under large groups acquire much bigger dynamical masses, all things being equal at a high e.g. GUT scale, than ordinary quarks. Should such multicharged fermions exist, they are just too heavy to be observed today (and have either decayed early on if coupled to the rest of the Standard Model, or become reliquial dark matter if uncoupled). Their mass scale is dictated by strong antiscreening of the running coupling for those larger groups (with an appropriately small number of flavors) together with scaling properties of the Dyson-Schwinger equation for the fermion mass. The generated fermion mass (assuming only few flavors, to avoid spoiling antiscreening) grows exponentially with the number of colors as M(N_c) ~ exp(N_c) for scales much below the GUT scale. Large groups would be strongly coupled already near the GUT scale and fermions charged thereunder have correspondingly large masses.