| Abstract |
The Standard Model (SM) is a chiral theory, where right- and left-handed fermion fields transform differently under the gauge group. Extra fermions, if they do exist, need to be heavy otherwise they would have already been observed. With no complex mechanisms at work, such as confining interactions or extra-dimensions, this can only be achieved if every extra right-handed fermion comes paired with a left-handed one transforming in the same way under the Standard Model gauge group, otherwise the new states would only get a mass after electroweak symmetry breaking, which would necessarily be small (similar to 100 GeV). Such a simple requirement severely constrains the fermion content of Grand Unified Theories (GUTs). It is known for example that three copies of the representations (5) over bar + 10 of SU(5) or three copies of the 16 of SO(10) can reproduce the Standard Model's chirality, but how unique are these arrangements? In a systematic way, this paper looks at the possibility of having non-standard mixtures of fermion GUT representations yielding the correct Standard Model chirality. Family unification is possible with large special unitary groups for example, the 171 representation of SU(19) may decompose as 3(16) + 120 + 3(1) under SO(10). |
