Thanks 王磊 Little Higgs 为了自然地得到一个较轻的Higgs粒子，人们早在二十世纪七十年代就提出了把Higgs粒子看作赝哥德斯通粒子，以保持它的小质量，这就是小Higgs理论最初的思想(Georgi) 八十年代Georgi和Kaplan以这个思想构造了一个这样的模型，但是从电弱标度到该模型的截断标度仍然需要精细调节 二十世纪初，受“Dimension（De)Construction”(Arkani-Hamed, Cohen, Georgi) 的启发，人们引进了协同对称破缺机制，将Higgs粒子构造成赝哥德斯通粒子的小黑格斯模型成功建立起来(Arkani-Hamed,Cohen,Georgi,Katz,Nelson)

No one-loop quadratic divergence of Higgs mass Motivation: No one-loop quadratic divergence of Higgs mass What is little Higgs ？ Higgs boson is a pseudo Nambu-Goldstone boson of an approximate global symmetry At least two sets of interactions are needed to break this global symmetry -- collective symmetry breaking N. Arkani-Hamed, A. G. Cohen, A.E. Nelson, hep-ph/0105239

Collective Symmetry Breaking 根据哥德斯通定理:   比如 14 Goldstone boson fields  

      此时Higgs粒子变成赝哥德斯通粒子，在单圈获得了质量： 但这是单圈二次发散的质量。所以我们必须做的更多才行啊

        具有二次发散贡献的Higgs质量在两圈出现

Collective Symmetry Breaking 协同对称破缺   In the following we take littlest Higgs model to show how the quadratic divergences can be avoided at one loop level

Littlest Higgs Model         14 Goldstones

g1, g2 分别是两个SU(2)的耦合 g’1, g’2 分别是两个U(1)的耦合 Gauge bosons: cause no quadratic divergence at 1-loop M. Perelstein，hep-ph/0512128 Each of these two terms (like in SM) will cause quadratic divergence But collective symmetry breaking forbid their existence because each of them only contains one kind of interactions g1, g2 分别是两个SU(2)的耦合 g’1, g’2 分别是两个U(1)的耦合

Equivalently, in mass eigenstates ： Each term contains two kinds of interactions (enough to break global symmetry to give Higgs mass)   Equivalently, in mass eigenstates ： Quadratic divergences from two diagrams cancel

Top quark Yukawa interaction: (i, j, k=1, 2, 3，x, y =4, 5)

Top quark对Higgs质量单圈二次发散的抵消

Phenomenology of little Higgs (1) The diphoton signal is suppressed   Wang, Yang, Zhu, PRD88, 075018 (2013) Han, Wang, Yang, Zhu, PRD87, 055004(2013) Wang, Yang, PRD84, 075024(2011)

(2) T-odd particles in LHT Belyaev, Chen, Tobe, Yuan, PRD74, 115020 (2006) The T-odd gauge bosons: Dark matter The T-odd fermions: Signal of T-odd particles generally contains , similar to SUSY Production processes at LHC The decay modes have LHC has reported constraints on

(3) Dark matter in LHT Wu, Yang, Zhang, JHEP1612, 152 (2016)

Belyaev, Chen, Tobe, Yuan, PRD74, 115020 (2006) (4) Top-partners in LHT