### Susy, or not susy (SO(10) grand unification): that is the question

**Is ignoring SUSY a risky business for model builders beyond the standard model?**

*A paper skeleton*(the spectral physicist?* ;-)

*in the office of CERN theorist John Ellis is a grave warning against opponents of supersymmetry (Image: Maximilien Brice/CERN)*

Models based on SO(10) gauge symmetry are especially attractive since quarks, leptons, anti-quarks, and anti-leptons of a family are uniﬁed in a single 16-dimensional spinor representation of the gauge group [39]. This explains the quantum numbers (electric charge, weak charge, color charge) of fermions, as depicted in Table 1. SO(10) symmetry contains ﬁve independent internal spins, denoted as + or − signs (for spin–up and spin–down) in Table 1. Subject to the condition that the number of down spins must be even, there are 16 combinations for the spin orientations, each corresponding to one fermionic degree. The ﬁrst three spins denote color charges, while the last two are weak charges. In addition to the three independent color spins (r, b, g), there is a fourth color (the fourth row), identiﬁed as lepton number [18]. The ﬁrst and the third columns (and similarly the second and the fourth) are left–right conjugates. Thus SO(10) contains quark–lepton symmetry as well as parity. A right–handed neutrino state ... is predicted because it is needed to complete the multiplet. Being a singlet of the Standard Model, it naturally acquires a superheavy Majorana mass and leads in a compelling manner to the generation of light neutrino masses via the seesaw mechanism.Hypercharge of each fermion follows from the formula Y =⅓Σ(C) −½Σ(W), where Σ(C) is the summation of color spins (ﬁrst three entries) and Σ(W) is the sum of weak spins (last two entries).This leads to quantization of hypercharge, and thus of electric charge. Such a simple organization of matter is remarkably beautiful and can be argued as a hint in favor of GUTs based on SO(10).

Table 1

As in the case of SU(5),when embedded with low energy supersymmetry so that the mass of the Higgs boson is stabilized, the three gauge couplings of the Standard Model (SM) nearly unify at an energy scale of M_{X}≈ 2 · 10^{16}GeV in SO(10) models.The light neutrino masses inferred from neutrino oscillation data (m_{v3}∼ 0.05 eV) suggest the Majorana mass of the heaviest of the three νc’s to be M_{vc}∼ 10^{14}GeV, which is close to M_{X}. In a class of SO(10) models discussed further here, M_{vc}∼ M^{2}_{X}/M_{Pl}∼ 10^{14}GeV quite naturally. The lepton number violating decays of νc can elegantly explain the observed baryon asymmetry of the universe via leptogenesis. Furthermore, the uniﬁed setup of quarks and leptons in SO(10) serves as a powerful framework in realizing predictive schemes for the masses and mixings of all fermions, including the neutrinos, in association with ﬂavor symmetries in many cases. All these features make SUSY SO(10) models compelling candidates for the study of proton decay.

Even without supersymmetry, SO(10) models are fully consistent with the uniﬁcation of the three gauge couplings and the experimental limit on proton lifetime, unlike non–SUSY SU(5). This is possible since SO(10) can break to the SM via an intermediate symmetry such asSU(4)_{C}×SU(2)_{L}×SU(2)_{R}[56]. Such models would predict that a proton would decay predominantly to e+π_{0}with a lifetime in the range 10^{33}−10^{36}yrs, depending on which intermediate gauge symmetry is realized [57]. If the intermediate symmetry isSU(4)_{C}×SU(2)_{L}×SU(2)_{R}×D with D being the discrete parity symmetry, then taking all the relevant threshold eﬀects into account an upper limit on the lifetime τ(p → e+π_{0}) < 5×10^{35}yrs has been derived in [58]. It has been shown in [59] that with the intermediate symmetrySU(4)_{C}×SU(2)_{L}×SU(2)_{R}(without discrete parity), SO(10) models can also explain the strong CP problem via the axion solution, although τ(p → e+π_{0}) in this case can exceed 5×10^{35}yrs.

Conveners: K.S. Babu, E. Kearns, November 21st 2013

***No the spectral physicist does not (need to) speak bad about SUSY!**

The derivation of the full Standard Model from noncommutative geometry has been a promising sign for possible applications of the latter in High Energy Physics. Many believe, however, that the Standard Model cannot be the ﬁnal answer.We translate several demands whose origin lies in physics to the context of noncommutative geometry and use these to put constraints on the fermionic content of models. We show that the Standard Model only satisﬁes these demands provided it has a right-handed neutrino in each ‘generation’.Furthermore, we show that the demands can be met upon extending the SM with a copy of the representation (1, 2, 1/2) but this has consequences for the number of particle generations.We ﬁnally prove that the Minimal Supersymmetric Standard Model is not among the models that satisfy our constraints, but we pose a solution that is a slight extension of the MSSM.

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