On the chirality of the SM and the fermion content of GUTs

Renato M Fonseca

doi:10.1016/j.nuclphysb.2015.06.012

Renato M Fonseca

Open Access

https://doi.org/10.1016/j.nuclphysb.2015.06.012

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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 (∼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¯+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).

Highlights

There is currently no explanation for the flavor structure of the Standard Model (SM) and GrandUnified Theories (GUTs) developed over the past decades have failed to shed light on this issue since particles with different flavors are usually assigned to distinct copies of a single representation of the enlarged gauge group
How unique is the standard fermion content 3 5 + 3 (10) in SU (5) Grand Unified Theories (GUTs)? This is an important question which we address in this work, noting that the normalization of the SM hypercharge depends on its answer
With larger GUT groups the situation becomes even more complicated if we do not make assumptions about the GUT representations where the SM fields are embedded, since there are more U (1) factors to consider. This situation is not insurmountable, but it does require adaptations to the analysis suggested in section 2, since it cannot be carried out unless we know the hypercharge y of the representations (all that is known is that y = i αiyi where yi are the charges under U (1)m, and the αi are to be determined)

Summary

23 June 2015 Abstract

The Standard Model (SM) is a chiral theory, where right- and left-handed fermion fields transform differently under the gauge group. 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 (∼ 100 GeV). Such a simple requirement severely constrains the fermion content of Grand Unified Theories (GUTs).

Introduction

The chirality of GUT models and representations

GUTs with the correct chirality

GUTs with the SM chirality

Concluding remarks