SU(5) GUT and Proton Decay

A contribution to the October-November 2006 DPF meeting in Hawaii by Goran Senjanovic entitled "Grand unification and proton decay: fact and fancy" has an abstract that stated:

 "… I review the minimal grand unification based on SU(5) and SO(10) groups, with and without supersymmetry. I discuss the predictions for the proton decay and show how they depend crucially on the fermion (and sfermion) masses and mixings. …".

Since the conventional view has been for years that proton decay experimental observations have ruled out SU(5) GUT, and since I saw no full copy of Senjanovic's Hawaii contribution,

I looked up his arXiv postings, and found hep-ph/0204311 by Borut Bajc, Pavel Fileviez Perez, and Goran Senjanovic with an abstract that stated:

"… We systematically study proton decay in the minimal supersymmetric SU(5) grand unified theory. We find that although the available parameter space of soft masses and mixings is quite constrained, the theory is still in accord with experiment. …".

A couple of years later, coauthor of hep-ph/0204311, Pavel Fileviez Perez, wrote a paper (with Ilja Dorsner) at hep-ph/0410198 whose abstract stated:

"… We investigate model independent upper bounds on total proton lifetime in the context of Grand Unified Theories with the Standard Model matter content. … Our result implies that a large class of non-supersymmetric Grand Unified models, with typical values alpha_GUT = [about] 1/39, still satisfies experimental constraints on proton lifetime. …".

In an even more recent paper, hep-ph/0601023, Pran Nath and Pavel Fileviez Perez say in sections 9 and 5.6 and 6.6:

"… In non-supersymmetric models proton decay proceeds via dimension six operators which are induced by gauge interactions and via exchange of scalar lepto-quarks. In these models one needs an extreme fine tuning to get light Higgs doublets ... An analysis of proton lifetime requires that one first address properly the fermion mass and mixing issues to predict in a realistic fashion proton lifetime. ... some of the non-supersymmetric unified models may still pass the stringent experimental proton lifetime constraints. As an example one may consider a simple extension of the Georgi-Glashow model with a Higgs sector composed of 5H, 24H, and 15H. In this case one finds an upper-bound on the total proton decay lifetime in this scenario of [aboput] 1.4 x 10^36 years ...

In this section [5.6] we discuss the possibility of finding an upper bound on the total proton decay lifetime … one may focus on the gauge d = 6 contributions since all other contributions can be set to zero in searching for upper limits …

any non-supersymmetric theory with alpha_GUT = 1/39 is eliminated if its unifying scale is below 4.9 x 10^13 GeV regardless of the exact form of the Yukawa sector of the theory.

Further, a majority of non-supersymmetric extensions of the Georgi-Glashow SU(5) model yield a GUT scale which is slightly above 10^14 GeV.

Hence, as far as the experimental limits on proton decay are concerned, these extensions still represent viable scenarios of models beyond the SM. …

For example in a minimal non-supersymmetric GUT based on SU(5) the upper bound on the total proton decay lifetime is …[less than or equal to]… 1.4 x 10^36 years

Proton decay in universal extra dimension (UED) models ... In these models it is possible to control proton decay via the use of extra symmetries that might arise in models with universal extra dimensions ... Thus in six dimensions with two universal extra dimensions the standard model particles are charged under the U(1) symmetry which arises due to the extra dimensions x4 and x5 and thus this symmetry may be labeled as U(1)45. Even after compactification a discrete Z8 symmetry survives. The symmetry allows only very high dimension baryon and lepton number violating operators, i.e., dimension sixteen or higher which leads to a suppression of proton decay. ... In summary in UED models a discrete subgroup of the Lorentz symmetry in six dimensions continues to forbid dangerous proton decay operators when reduction to four dimension is carried out. ...

Proton decay from black hole and wormhole effects ... Quantum gravity does not conserve baryon number and thus can catalyze proton decay. Such an effect can arise from virtual black hole exchange and wormhole tunneling. It is then possible that the two quarks in the proton might end up falling into the mini black hole and since one expects black holes not to conserve baryon number, a process such as this can lead to baryon number violation through q + q to l + nu and q + q to qbar + l and consequently to proton decay. If the scale of quantum gravity M_QG = M_Pl, the proton lifetime will be very high, i.e., [about] 10^45 yr and outside the realm of experimental observation. However, such lifetimes still have significance in determining the ultimate fate of the universe. ... ".


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