Some current efforts to explain the theoretical underpinnings for observed neutrino masses are being developed in the context of supersymmetric flipped SU(5).[6]
Flipped SU(5) is not a fully unified model, because the U(1)Y factor of the
Standard Model gauge group is within the U(1) factor of the GUT group. The addition of states below Mx in this model, while solving certain threshold correction issues in
string theory, makes the model merely descriptive, rather than predictive.[7]
The model
The flipped SU(5) model states that the
gauge group is:
Fermions form three families, each consisting of the
representations
5−3 for the lepton doublet, L, and the up quarks uc;
101 for the quark doublet, Q, the down quark, dc and the right-handed neutrino, N;
15 for the charged leptons, ec.
This assignment includes three right-handed neutrinos, which have never been observed, but are often postulated to explain the lightness of the observed neutrinos and
neutrino oscillations. There is also a 101 and/or 10−1 called the Higgs fields which acquire a
VEV, yielding the
spontaneous symmetry breaking
The name "flipped" SU(5) arose in comparison to the "standard" SU(5)Georgi–Glashow model, in which uc and dc quark are respectively assigned to the 10 and 5 representation. In comparison with the standard SU(5), the flipped SU(5) can accomplish the spontaneous symmetry breaking using Higgs fields of dimension 10, while the standard SU(5) typically requires a 24-dimensional Higgs.[8]
The
sign convention for U(1)χ varies from article/book to article.
The hypercharge Y/2 is a linear combination (sum) of the following:
Calling the
representations for example, 5−3 and 240 is purely a physicist's convention, not a mathematician's convention, where representations are either labelled by
Young tableaux or
Dynkin diagrams with numbers on their vertices, and is a standard used by GUT
theorists.
The N = 1 superspace extension of 3 + 1 Minkowski spacetime
Spatial symmetry
N = 1 SUSY over 3 + 1 Minkowski spacetime with
R-symmetry
Gauge symmetry group
(SU(5) × U(1)χ)/Z5
Global internal symmetry
Z2 (matter parity) not related to U(1)R in any way for this particular model
Vector superfields
Those associated with the SU(5) × U(1)χ gauge symmetry
Chiral superfields
As complex representations:
label
description
multiplicity
SU(5) × U(1)χ rep
Z2 rep
U(1)R
10H
GUT Higgs field
1
101
+
0
10H
GUT Higgs field
1
10−1
+
0
Hu
electroweak Higgs field
1
52
+
2
Hd
electroweak Higgs field
1
5−2
+
2
5
matter fields
3
5−3
-
0
10
matter fields
3
101
-
0
1
left-handed positron
3
15
-
0
φ
sterile neutrino (optional)
3
10
-
2
S
singlet
1
10
+
2
Superpotential
A generic invariant renormalizable superpotential is a (complex) SU(5) × U(1)χ × Z2 invariant cubic polynomial in the superfields which has an R-charge of 2. It is a linear combination of the following terms:
The second column expands each term in index notation (neglecting the proper normalization coefficient). i and j are the generation indices. The coupling Hd10i10j has coefficients which are symmetric in i and j.
In those models without the optional φ sterile neutrinos, we add the
nonrenormalizable couplings instead.
^Barr, S.M. (1982). "A new symmetry breaking pattern for SO(10) and proton decay". Physics Letters B. 112 (3): 219–222.
doi:
10.1016/0370-2693(82)90966-2.