大统一理论和质子衰变
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摘要
自然界存在4种基本相互作用:强、弱、超荷和引力相互作用,故如何构造一种大统一理论来描述所有的基本相互作用是一个非常重要的基本问题.本文首先简单介绍了标准模型及其问题.考虑U(1)_Y超荷正则归一化因子和大沙漠假定(grand desert hypothesis),可以在TeV能标左右引入新的粒子来得到标准模型规范耦合常数的统一,其中特别解释了超对称标准模型.在四维大统一模型中,介绍了Pati-Salam SU(4)_C×SU(2)_L×SU(2)_R模型,Georgi-Glashow SU(5)模型,Flipped SU(5)×U(1)_X模型和SO(10)模型,其中详细介绍了非超对称和超对称SU(5)模型,并讨论了其正确的预言、存在的问题及其解决方案和质子衰变等.还简单介绍了高维Orbifold大统一模型和超弦模型.最后讨论了如何探寻大统一理论:在对撞机上寻找新的粒子及其粒子特性、质子衰变的现在和将来的实验检验以及可能的新探测方案.
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. Nordstr o¨m, Kaluza, and Klein for the first time proposed the extra dimension(s), and tried to unify the known gravity and electromagnetic interaction into a fivedimensional gravity. This idea is indeed great, but unfortunately does not describe Nature. The third unification was done by Glashow, Salam, and Weinberg, who described the 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 important and fundamental problem. As we know, strong, weak, and hypercharge interactions are gauge interactions, whose gauge groups are SU(3)_C × S U(2)_L × 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 Theories which 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 gravity is 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 unification by introducing new particles around Te V scale. Especially, we explain the supersymmetric Standard Models in details. We discuss the four-dimensional Pati-Salam SU(4)_C × SU(2)_L × SU(2)_R models, Georgi-Glashow S U(5) models, Flipped S U(5) × U(1)_X models, and S O(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 dimensional orbifold Grand Unified Theories and string models. Finally, we study how to probe these models: searches for the new particles with predicted properties at the colliders, as well as the current and future proton decay experiments and possible new proposals.
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. Nordstr o¨m, Kaluza, and Klein for the first time proposed the extra dimension(s), and tried to unify the known gravity and electromagnetic interaction into a fivedimensional gravity. This idea is indeed great, but unfortunately does not describe Nature. The third unification was done by Glashow, Salam, and Weinberg, who described the 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 important and fundamental problem. As we know, strong, weak, and hypercharge interactions are gauge interactions, whose gauge groups are SU(3)_C × S U(2)_L × 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 Theories which 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 gravity is 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 unification by introducing new particles around Te V scale. Especially, we explain the supersymmetric Standard Models in details. We discuss the four-dimensional Pati-Salam SU(4)_C × SU(2)_L × SU(2)_R models, Georgi-Glashow S U(5) models, Flipped S U(5) × U(1)_X models, and S O(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 dimensional orbifold Grand Unified Theories and string models. Finally, we study how to probe these models: searches for the new particles with predicted properties at the colliders, as well as the current and future proton decay experiments and possible new proposals.
引文
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12 Jiang J,Li T,Nanopoulos D V,et al.F-S U(5).Phys Lett B,2009,677:322-325
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19 Hebecker A,March-Russell J.A minimal S1/(Z2×Z′2)orbifold GUT.Nucl Phys B,2001,613:3-16
20 Li T.GUT breaking on M4×T2/(Z2×Z′2).Phys Lett B,2001,520:377-384
21 Li T.N=2 supersymmetric GUT breaking on T2orbifolds.Nucl Phys B,2001,619:75-104
22 Bionta R M,Blewitt G,Bratton C B,et al.A search for proton decay into e+π0.Phys Rev Lett,1983,51:27-30
23 Abe K,Hayato Y,Iyogi K.Search for proton decay via p→e+π0and p→μ+π0in 0.31 megaton years exposure of the Super-Kamiokande water Cherenkov detector.Phys Rev D,2017,95:012004
24 Yokoyama M T.The Hyper-Kamiokande experiment.2017,ar Xiv:1705.00306
2 Weinberg S.The cosmological constant problem.Rev Mod Phys,1989,61:1-23
3 Barger V,Jiang J,Langacker P,et al.Gauge coupling unification in the standard model.Phys Lett B,2005,624:233-238
4 Barger V,Jiang J,Langacker P,et al.Non-canonical gauge coupling unification in high-scale supersymmetry breaking.Nucl Phys B,2005,726:149-170
5 Li T,Liao W.Low-energy gauge unification theory.Mod Phys Lett A,2002,17:2393-2407
6 Pati J C,Salam A.Lepton number as the fourth color.Phys Rev D,1974,10:275-289
7 Georgi H,Glashow S L.Unity of all elementary particle forces.Phys Rev Lett,1974,32:438-441
8 Barr M S.A new symmetry breaking pattern for S O(10)and proton decay.Phys Lett B,1982,112:219-222
9 Derendinger J P,Kim J E,Nanopoulos D V.Anti-S U(5).Phys Lett B,1984,139:170-176
10 Antoniadis I,Ellis J R,Hagelin J S,et al.The flipped S U(5)×U(1)string model revamped.Phys Lett B,1989,231:65-74
11 Jiang J,Li T,Nanopoulos D V.Testable flipped S U(5)×U(1)Xmodels.Nucl Phys B,2007,772:49-66
12 Jiang J,Li T,Nanopoulos D V,et al.F-S U(5).Phys Lett B,2009,677:322-325
13 Jiang J,Li T,Nanopoulos D V,et al.Flipped S U(5)×U(1)Xmodels from F-theory.Nucl Phys B,2010,830:195-220
14 Kawamura Y.Gauge symmetry breaking from extra space S1/Z2.Prog Theor Phys,2000,103:613-619
15 Kawamura Y.Triplet doublet splitting,proton stability and extra dimension.Prog Theor Phys,2001,105:999-1006
16 Kawamura Y.Split multiplets,coupling unification and extra dimension.Prog Theor Phys,2001,105:691-696
17 Altarelli G,Feruglio F.S U(5)grand unification in extra dimensions and proton decay.Phys Lett B,2001,511:257-264
18 Hall L J,Nomura Y.Gauge unification in higher dimensions.Phys Rev D,2001,64:055003
19 Hebecker A,March-Russell J.A minimal S1/(Z2×Z′2)orbifold GUT.Nucl Phys B,2001,613:3-16
20 Li T.GUT breaking on M4×T2/(Z2×Z′2).Phys Lett B,2001,520:377-384
21 Li T.N=2 supersymmetric GUT breaking on T2orbifolds.Nucl Phys B,2001,619:75-104
22 Bionta R M,Blewitt G,Bratton C B,et al.A search for proton decay into e+π0.Phys Rev Lett,1983,51:27-30
23 Abe K,Hayato Y,Iyogi K.Search for proton decay via p→e+π0and p→μ+π0in 0.31 megaton years exposure of the Super-Kamiokande water Cherenkov detector.Phys Rev D,2017,95:012004
24 Yokoyama M T.The Hyper-Kamiokande experiment.2017,ar Xiv:1705.00306