Grand unified theories and proton decay

Abstract

There exists four fundamental interactions in Nature: strong, weak, hypercharge, and gravity interactions.Based on the conjecture that all the fundamental interactions have the same origin,physicists have explored the Grand Unified Theories,which describes the most fundamental laws in the Universe. From the historical point of view,the first unification was done by Newton, who unified the celestial and terrestrial gravity.The second unification was done by Maxwell, who unified the electric and magnetic interactions into an electromagnetic interaction.Nordstrom, Kaluza, and Klein for the first time proposed the extra dimension(s),and tried to unify the known gravity and electromagnetic interaction into a five-dimensional gravity.This idea is indeed great, but unfortunately does not describe Nature.The third unification was done by Glashow, Salam, and Weinberg, who describedthe electromagnetic and weak interactions via an electroweak theory. Therefore,how to construct the Grand Unified Theories to describe all the fundamental interactions is a very importantand fundamental problem. As we know, strong, weak, and hypercharge interactionsare gauge interactions, whose gauge groups are $SU(3)_C\times~SU(2)_L\times~U(1)_Y$.Thus, we believe they have the same origin: a high scale Grand Unified Theory with gauge group $SU(5)$ or $SO(10)$, etc.Exactly speaking, there are two kinds of definitions for the Grand Unified Theories: (1) Gauge interaction unification;(2) Fermion unification. In this paper, we only consider the first definition, and do not consider the Grand Unified Theorieswhich unify three generations of the Standard Model fermions. However, the Grand Unified Theories do not include gravity.Especially, gravity quantization is another important problem in physics. Right now, the most promising theory for quantum gravityis string theory. Therefore, the models, which can unify all the four fundamental interactions in Nature, are probably the string models.In particular, string models can solve the major problems in the four-dimensional Grand Unified Theories naturally.Thus, the Grand Unified Theories and string models will give us a Theory of Everthing. In principle,it can explain all the phenomena in the Universe, and thus it is the final goal of the physics.Historically, many great physicists such as Einstein et al have studied the Grand Unified Theories. Right now.we have constructed various Grand Unified Theories and string models, and thus need further experiments to test them.In this paper, we first briefly explain the Standard Model and its problems.With the canonical normalized $U(1)_Y$ and Grand Desert Hypothesis, we can achieve the gauge coupling unificationby introducing new particles around TeV scale. Especially, we explain the supersymmetric Standard Models in details.We discuss the four-dimensional Pati-Salam $SU(4)_C\times~SU(2)_L\times~SU(2)_R$ models,Georgi-Glashow $SU(5)$ models, Flipped $SU(5)\times~U(1)_X$ models, and $SO(10)$ models.We explain the non-supersymmetric and supersymmetric $SU(5)$ models in details, including its correct predictions,the main problems and solutions, as well as proton decays, etc. We also briefly discuss the high dimensionalorbifold Grand Unified Theories and string models. Finally, we study how to probe these models: searches for the new particles withpredicted properties at the colliders, as well as the current and future proton decay experiments and possible new proposals.