Abstract
A known mechanism for obtaining naturally light Dirac neutrinos is implemented in the context of SU(6) → SU(5) × U(1)N.
Highlights
A known mechanism for obtaining naturally light Dirac neutrinos is implemented in the context of SU(6) → SU(5) × U(1)N
Instead of the ad hoc U(1)D symmetry, νR is identified as part of the fundamental representation of SU(6) which breaks to SU(5) × U(1)N
Following a recent analysis [9], it is shown how naturally small Dirac neutrino masses occur in this context
Summary
Starting with the well-known SU(5) model [10] of grand unification, an extension to SU(6) is straightforward [11, 12]. The scalars which break the SU(6) symmetry and allow these fermions to acquire masses are listed in table 2. The 6S breaks U(1)N at a lower scale Because it is charged under U(1)X , its only allowed coupling is 6∗S ×6∗F2 ×15F. The 15S × 15F × 15F term yields masses for ucu proportional to v2, whereas the 15S × 6∗F 1 × 6∗F 2 term yields masses for ννc, N E0 proportional to v3 Let these three Higgs doublets be named Φ1,2 and η respectively. The soft term μ2Φ†2η breaking U(1)X by 3 units is available to make the Dirac neutrino masses very small. Note that νc does not acquire a Majorana mass because of the absence of a scalar 21∗ with 4 units of charge under U(1)X. The two soft trilinear terms 84S ×6S ×15∗S break U(1)X by 3 and 6 units, whereas 6S ×6S ×21∗S does it by 6 units
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