2,788 research outputs found
On the chirality of the SM and the fermion content of GUTs
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
(). 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 of
or three copies of the of 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 representation of may decompose as
under
.Comment: Minor changes; matches publication in Nuclear Physics
Systematic classification of three-loop realizations of the Weinberg operator
We study systematically the decomposition of the Weinberg operator at
three-loop order. There are more than four thousand connected topologies.
However, the vast majority of these are infinite corrections to lower order
neutrino mass diagrams and only a very small percentage yields models for which
the three-loop diagrams are the leading order contribution to the neutrino mass
matrix. We identify 73 topologies that can lead to genuine three-loop models
with fermions and scalars, i.e. models for which lower order diagrams are
automatically absent without the need to invoke additional symmetries. The 73
genuine topologies can be divided into two sub-classes: Normal genuine ones (44
cases) and special genuine topologies (29 cases). The latter are a special
class of topologies, which can lead to genuine diagrams only for very specific
choices of fields. The genuine topologies generate 374 diagrams in the weak
basis, which can be reduced to only 30 distinct diagrams in the mass eigenstate
basis. We also discuss how all the mass eigenstate diagrams can be described in
terms of only five master integrals. We present some concrete models and for
two of them we give numerical estimates for the typical size of neutrino masses
they generate. Our results can be readily applied to construct other
neutrino mass models with three loops.Comment: Erratum added, published version in JHE
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