质量起源和自然性问题
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摘要
粒子物理中粒子质量的起源是一个很重要的基本问题.在粒子物理的标准模型中,粒子通过电弱对称破缺机制得到质量.近年来希格斯粒子的发现对于检验以及人们更深入地理解电弱对称破缺机制起到了里程碑的作用,但是理论中仍旧有一些重要的问题亟待解决,其中最关键的是如何稳定电弱对称破缺的能标,即所谓的自然性问题.为了解决这一问题,需要引入新物理来屏蔽高能标物理对希格斯粒子的质量修正.其中有两大类新物理模型可以解决希格斯的自然性问题:第一类是超对称模型,这类模型是通过费米和玻色子之间的对称性来消除希格斯质量的二次发散;第二类是复合希格斯模型,这类模型是通过希格斯的束缚态的特性来降低希格斯对高能标物理的敏感度.在超对称模型中,每一个标准模型场都会有一个超对称伴随子,这使得整个理论非常复杂,而复合希格斯模型却可以非常简单地解决自然性问题.本文首先综述标准模型中的希格斯机制以讨论希格斯的自然性问题;然后一般性地讨论超对称模型及其唯象;最后主要集中讨论复合希格斯模型,基于复合希格斯粒子物理模型,对解决希格斯自然性问题的理论挑战、研究现状以及解决方案进行详细阐述.
Electroweak symmetry breaking is the key ingredient of the standard model responsible for the generation of all elementary particle masses. The discovery of the Higgs boson is a major milestone towards understanding the mechanism of electroweak symmetry breaking but several important issues remain unexplained. Among them the key mystery is how to stabilize the electroweak symmetry scale, called the naturalness problem. To solve this problem, some new physics should be introduced to screen quantum corrections from higher energy scale. There are two classes of new physics theories: one is super symmetry model in which Higgs quadratic divergence is cancelled through the extended space-time symmetry between scalars and fermions. The other one is composite Higgs model in which the sensitivity to higher energy scale is reduced by the composite nature of Higgs. In super symmetry model, every field in standard model should have a super symmetric partner, which makes this theory very complicated. However, the composite Higgs models can address the naturalness problem in a very simple way. In this article we first review the Higgs mechanism in standard model and explain Higgs naturalness problem. Then we generally review the super symmetry model and its phenomenology. It is found that the tuning of this kind of model is worse than 1% when confronts experimental measurements. In the remaining parts we focus on discussing the composite Higgs model. We first review the structure of composite Higgs models and then discuss how to reduce Higgs mass through some symmetry collectively breaking or extra dimension mechanism. It is found that, in this kind of models, to produce a light Higgs the composite quarks canceling Higgs quadratic divergences should be relatively light, around 1 TeV. But the constraints from Large Hadron Collider(LHC) indicate that these fermions should be much heavier than 1 Te V, which results the difficulty in achieving a light Higgs. Moreover, to evade precise electroweak tests, the electroweak scale should be separated with Higgs confinement scale, called the Little Hierarchy, requiring more tuning in this model. In order to produce light Higgs while keeping composite quarks heavy, we plan to find a general principle to realize neutral naturalness mechanism in which Higgs quadratic divergences are cancelled by hidden sector. And then find the UV completion for this mechanism and fully study its phenomenology. In order to naturally solve Little Hierarchy, we plan to construct a mechanism to produce Higgs tree level or loop level self-quartic coupling, so that the big separation between electroweak and confinement scale can be achieved by adjusting properly this coupling without introducing any tuning. After solving above two problems, we combine these two mechanisms to construct the super-natural composite Higgs model which can successfully achieve electroweak symmetry breaking without any tuning.
Electroweak symmetry breaking is the key ingredient of the standard model responsible for the generation of all elementary particle masses. The discovery of the Higgs boson is a major milestone towards understanding the mechanism of electroweak symmetry breaking but several important issues remain unexplained. Among them the key mystery is how to stabilize the electroweak symmetry scale, called the naturalness problem. To solve this problem, some new physics should be introduced to screen quantum corrections from higher energy scale. There are two classes of new physics theories: one is super symmetry model in which Higgs quadratic divergence is cancelled through the extended space-time symmetry between scalars and fermions. The other one is composite Higgs model in which the sensitivity to higher energy scale is reduced by the composite nature of Higgs. In super symmetry model, every field in standard model should have a super symmetric partner, which makes this theory very complicated. However, the composite Higgs models can address the naturalness problem in a very simple way. In this article we first review the Higgs mechanism in standard model and explain Higgs naturalness problem. Then we generally review the super symmetry model and its phenomenology. It is found that the tuning of this kind of model is worse than 1% when confronts experimental measurements. In the remaining parts we focus on discussing the composite Higgs model. We first review the structure of composite Higgs models and then discuss how to reduce Higgs mass through some symmetry collectively breaking or extra dimension mechanism. It is found that, in this kind of models, to produce a light Higgs the composite quarks canceling Higgs quadratic divergences should be relatively light, around 1 TeV. But the constraints from Large Hadron Collider(LHC) indicate that these fermions should be much heavier than 1 Te V, which results the difficulty in achieving a light Higgs. Moreover, to evade precise electroweak tests, the electroweak scale should be separated with Higgs confinement scale, called the Little Hierarchy, requiring more tuning in this model. In order to produce light Higgs while keeping composite quarks heavy, we plan to find a general principle to realize neutral naturalness mechanism in which Higgs quadratic divergences are cancelled by hidden sector. And then find the UV completion for this mechanism and fully study its phenomenology. In order to naturally solve Little Hierarchy, we plan to construct a mechanism to produce Higgs tree level or loop level self-quartic coupling, so that the big separation between electroweak and confinement scale can be achieved by adjusting properly this coupling without introducing any tuning. After solving above two problems, we combine these two mechanisms to construct the super-natural composite Higgs model which can successfully achieve electroweak symmetry breaking without any tuning.
引文
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2 CMS Collaboration.Observation of a new boson at a mass of 125 Ge V with the CMS experiment at the LHC.Phys Lett B,2012,716:30–61
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22 Kaul R K.Super symmetric solution of gauge hierarchy problem.Pramana,1982,19:183
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25 Gunion J F,Haber H E,Kane G L,et al.The Higgs hunter’s guide.Front Phys,2000,80:1–404
26 Weinberg S.Implications of dynamical symmetry breaking.Phys Rev D,1976,13:974–996
27 Susskind L.Dynamics of spontaneous symmetry breaking in the Weinberg-Salam theory.Phys Rev D,1979,20:2619–2625
28 Hill C T,Simmons E H.Strong dynamics and electroweak symmetry breaking.Phys Rept,2003,381:235–402
29 Kaplan D B,Georgi H.SU(2)?U(1)breaking by vacuum misalignment.Phys Lett B,1984,136:183–186
30 Csaki C,Ma T,Shu J.Maximally symmetric composite Higgs models.Phys Rev Lett,2017,119:131803
31 Panico G,Wulzer A.The composite nambu-goldstone Higgs.Lect Notes Phys,2016,913:1–316
32 Csaki C,Grojean C,Terning J.Alternatives to an elementary Higgs.Rev Mod Phys,2016,88:045001
33 Agashe K,Contino R,Pomarol A.The minimal composite Higgs model.Nucl Phys B,2005,719:165–187
34 De Curtis S,Redi M,Tesi A.The 4D composite Higgs.J High Energy Phys,2012,4:42
35 Chacko Z,Goh H S,Harnik R.The twin Higgs:Natural electroweak breaking from mirror symmetry.Phys Rev Lett,2006,96:231802
36 Chacko Z,Goh H S,Harnik R.A twin Higgs model from left-right symmetry.J High Energy Phys,2006,1:108
37 Csaki C,Ma T,Shu J.Trigonometric parity for the composite Higgs.2017,ar Xiv:1709.08636
2 CMS Collaboration.Observation of a new boson at a mass of 125 Ge V with the CMS experiment at the LHC.Phys Lett B,2012,716:30–61
3 ATLAS and CMS Collaboration.Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at s=7 and 8 Te V.J High Energy Phys,2016,8:45
4 Glashow S L.Partial symmetries of weak interactions.Nucl Phys,1961,22:579–588
5 Weinberg S.A model of leptons.Phys Rev Lett,1967,19:1264–1266
6 Glashow S L,Iliopoulos J,Maiani L.Weak interactions with lepton-hadron symmetry.Phys Rev D,1970,2:1285–1292
7 Englert F,Brout R.Broken symmetry and the mass of gauge vector mesons.Phys Rev Lett,1964,13:321–323
8 Higgs P W.Broken symmetries and the masses of gauge bosons.Phys Rev Lett,1964,13:508–509
9 Higgs P W.Spontaneous symmetry breakdown without massless bosons.Phys Rev,1966,145:1156–1163
10 Guralnik G S,Hagen C R,Kibble T W B.Global conservation laws and massless particles.Phys Rev Lett,1964,13:585–587
11 Cornwall J M,Levin D N,Tiktopoulos G.Derivation of gauge invariance from high-energy unitarity bounds on the matrix.Phys Rev D,1974,10:1145
12 Lewellyn Smith C H.High-energy behavior and gauge symmetry.Phys Lett B,1973,46:233–236
13 Lee B W,Quigg C,Thacker H B.Weak interactions at very high-energies:The role of the Higgs boson mass.Phys Rev D,1977,16:1519–1531
14 Wilson K G.The renormalization group and strong interactions.Phys Rev D,1971,3:1818
15 Wess J,Zumino B.Supergauge transformations in four-dimensions.Nucl Phys B,1974,70:39–50
16 Wess J,Zumino B.A Lagrangian model invariant under supergauge transformations.Phys Lett B,1974,49:52
17 Fayet P.Spontaneously broken supersymmetric theories of weak,electromagnetic and strong interactions.Phys Lett B,1977,69:489–494
18 Fayet P.Weak Interactions of a Light Gravitino:A lower limit on the gravitino mass from the decay psi→gravitino anti-photino.Phys Lett B,1979,84:421–426
19 Fayet P.Scattering cross-sections of the photino and the Goldstino(Gravitino)on matter.Phys Lett B,1979,86:272–278
20 Witten E.Dynamical breaking of supersymmetry.Nucl Phys B,1981,188:513
21 Kaul R K.Gauge hierarchy in a supersymmetric model.Phys Lett B,1982,109:19–24
22 Kaul R K.Super symmetric solution of gauge hierarchy problem.Pramana,1982,19:183
23 Susskind L.The gauge hierarchy problem,technicolor,supersymmetry,and all that.Phys Rept,1984,104:181–193
24 Haber H E,Kane G L.The search for supersymmetry:Probing physics beyond the standard model.Phys Rept,1985,117:75–263
25 Gunion J F,Haber H E,Kane G L,et al.The Higgs hunter’s guide.Front Phys,2000,80:1–404
26 Weinberg S.Implications of dynamical symmetry breaking.Phys Rev D,1976,13:974–996
27 Susskind L.Dynamics of spontaneous symmetry breaking in the Weinberg-Salam theory.Phys Rev D,1979,20:2619–2625
28 Hill C T,Simmons E H.Strong dynamics and electroweak symmetry breaking.Phys Rept,2003,381:235–402
29 Kaplan D B,Georgi H.SU(2)?U(1)breaking by vacuum misalignment.Phys Lett B,1984,136:183–186
30 Csaki C,Ma T,Shu J.Maximally symmetric composite Higgs models.Phys Rev Lett,2017,119:131803
31 Panico G,Wulzer A.The composite nambu-goldstone Higgs.Lect Notes Phys,2016,913:1–316
32 Csaki C,Grojean C,Terning J.Alternatives to an elementary Higgs.Rev Mod Phys,2016,88:045001
33 Agashe K,Contino R,Pomarol A.The minimal composite Higgs model.Nucl Phys B,2005,719:165–187
34 De Curtis S,Redi M,Tesi A.The 4D composite Higgs.J High Energy Phys,2012,4:42
35 Chacko Z,Goh H S,Harnik R.The twin Higgs:Natural electroweak breaking from mirror symmetry.Phys Rev Lett,2006,96:231802
36 Chacko Z,Goh H S,Harnik R.A twin Higgs model from left-right symmetry.J High Energy Phys,2006,1:108
37 Csaki C,Ma T,Shu J.Trigonometric parity for the composite Higgs.2017,ar Xiv:1709.08636