Phenomenology of classical scale invariant models for electroweak - PowerPoint PPT Presentation

Phenomenology of classical scale invariant models for electroweak symmetry breaking Katsuya Hashino (University of Toyama) ] Based on 1. K. Hashino, S. Kanemura, Y. Orikasa Phys. Lett. B 752, 217 (2016). 2. K. Hashino, M. Kakizaki, S. Kanemura, T. Matsui, arXiv:1604.02069. 2016/05/07-08 New Higgs Working Group 17

Contents 1. Introduction 2. Models for electroweak symmetry breaking based on classical scale invariance 3. Discriminative phenomenological features for the models 4. Summary 2

1. Introduction ● The Higgs boson (125GeV) was found in 2012. The Standard Model (SM) was successful. But Higgs sector remains unknown!! ● For example... negative mass term is introduced by hand in the potential. ● In order to avoid the problem, we consider massless model. ● The massless model is based on chiral symmetry, Classical Scale Invariance (CSI), and so on. We consider the models based on CSI. 3

2. Model for EWSB based on CSI −α x , ∂ μ → e 4 x √ − g → e 4 x √ − g α Φ , ∫ d − 4 α ∫ d α ∂ μ , Φ → e x → e ● CSI prohibits mass term at the tree level. 2 | ϕ | 2 +λ | ϕ | 4 V SM (ϕ)=−μ ● Electroweak symmetry breaking (EWSB) cannot happen at the tree level. V SM (Φ) Φ O ● EWSB can happen by Coleman-Weinberg mechanism (CWM). [S. R. Coleman and E. J. Weinberg, Phys. Rev. D 7, 1888(1973)] ● But the SM with CWM cannot explain the data. 4

Non-minimal model for EWSB based on CSI ● We consider the non-minimal Higgs model with Gildener-Weinberg method. Gildener-Weinberg method(GWM) [E. Gildener and S. Weinberg, Phys. Rev. D 13, 3333(1976)] • The GWM supposes that there is the flat direction in the tree-level potential. • On the flat direction EWSB occurs by CWM. • When we use the GWM, the effective potential is written as • All masses are proportional to the vacuum expectation value.

3. Discriminative phenomenological features for the models ● The models have three discriminative features. [K. Hashino, S. Kanemura and Y. Orikasa, Phys. Lett. B 752, 217 (2016)] CSI 1) A general upper bound on the mass of the lightest of m 1 the scalar bosons is CSI ≤ 543GeV m 1 CSI κ γ h γ γ 2) The scaling factor of the coupling is CSI ≃ 1 − n 16 − m κ γ 4 � where n and m are the numbers of singly- and doubly- charged scalar bosons, respectively. CSI Γ hhh 3) T he triple Higgs boson coupling is universally predicted at the leading order. CSI = 5 SM tree Γ hhh 3 × Γ hhh 6 From now we will discuss these features one after another.

CSI 1) A general upper bound on the mass m 1 • The Higgs mass is • We consider a case including N extra scalar bosons and the masses can be written as CSI . CSI ≤ m 2 CSI ⋯≤ m N m 1 N 4 = ∑ CSI ) 4 ≥ N ( m 1 CSI ) 4 ( m n Tr M s n = 1 7

CSI 1) A general upper bound on the mass m 1 • The Higgs mass is • We consider a case including N extra scalar bosons and the masses can be written as CSI . CSI ≤ m 2 CSI ⋯≤ m N m 1 N 4 = ∑ CSI ) 4 ≥ N ( m 1 CSI ) 4 ( m n Tr M s CSI ≤ C ≤ 543 ( GeV ) m 1 n = 1 √ N 4 8 CSI • m 1 is generally less than 543 GeV !

CSI κ γ 2) The scaling factor of the coupling h γ γ CSI κ γ 2 / m h 2 τ x = 4m x n (m) is the number of singly- (doubly- ) charged scalar bosons and . The loop effect of ... A 1 / 2 (τ t )=− 1.4 top quark A 1 (τ W )= 8.4 W boson Charged scalar A 0 (τ i )=− 1 / 3 m h ≪ m i boson ( ) The characteristics of the model for EWSB based on CSI CSI ≃ 1 − n 16 − m κ γ 4 Non-decoupling effects 9

CSI κ γ 2) The scaling factor of the coupling h γ γ [V. Khachatryan et al. [CMS Collaboration], Eur. Phys.J. C75, no.5, 212(2015)] CSI κ γ FIG : Behavior of in specific (n,m) is expressed by charged scalar boson mass M ϕ of the horizontal axis. CSI κ γ will be measured with the 5-7% accuracy at the LHC Run-2. • [S. Dawson et al. arXiv:1310.8361] • We expect that the number of the charged scalar bosons in the model will be determined by LHC Run-2 ! 10

3) The triple Higgs boson coupling CCI Γ hhh • All models for EWSB based on CSI is universally 3 ∣ 3 V eff 2 CSI ≡ ∂ = 5m h = 5 SM tree Γ hhh 3 × Γ hhh v ∂φ φ= v [K. Hashino, S. Kanemura and Y. Orikasa, Phys. Lett. B 752, 217 (2016)] • O(N) extended Higgs model that does not based on CSI, the triple Higgs boson coupling is [ M. Kakizaki, S. Kanemura and T. Matsui, Phys. Rev. D 92, no. 11, 115007 (2015)] 2 3m h CSI Γ hhh SM tree = Γ hhh • The deviation of from is universally about 67% ! v • The deviation will be measured with the 10% accuracy at the ILC. [T.Barklow et al., arXiv:1506.07830] • We able to check whether the model is true in the future !! 11

Landau pole (CSI O(N) models) Λ • We calculate the Landau pole Λ of the CSI O(N) models. TABLE : The energy scale of the Landau pole Λ in the CSI O(N) models for N = 1,4,12 and 60. [K. Hashino, M. Kakizaki, S. Kanemura and T. Matsui, arXiv:1604.02069 ] • T he renormalization scale Q is decided by the stationary condition. • T he cutoff scale Λ is defined as the scale where any of the scalar couplings diverges. 12

4. Summary ● We have discussed the model for electroweak symmetry breaking based on Classical Scale Invariance. ● The models have three discriminative features. 1) A general upper bound on the mass of the lightest CSI ≤ 543GeV m 1 of the extra scalar bosons is CSI ≃ 1 − n 16 − m κ γ 2) The scaling factor of the h� � coupling is 4 CSI = 5 SM tree Γ hhh 3 × Γ hhh 3) T he triple Higgs boson coupling is universally ● These features will be tested by the future experiments. 13

CSI m 1 Upper bound on the mass in 2HDM For a specific model • We rewrite N as which is the number of scalar fields with isospin I and hypercharge Y. N I ,Y N = N 0,0 + 2N 0,1 + 4N 1 + 3N 1,0 + 6N 1,1 + ・ ・ ・ 2 , 1 2 I = 1 2 ,Y = 1 • When we consider the extensions for doublets( ), this upper bound is stronger! 2 14

Gildener - Weinberg method � The GWM supposes that there is the f lat direction in the tree-level Φ potential V 0 ( ). 4 V 0 (Φ) ∂ V 0 (Φ)= 1 f ijkl ≡ 24 f ijkl Φ i Φ j Φ k Φ l , ∂Φ i ∂Φ j ∂Φ k ∂Φ l � The f l at direction is decided by Φ i = n i φ . n i φ The unit vector represents the direction of f l at direction and is order parameter. V 0 ( n i φ)= 0 � On the f l at direction, � � � � � , and� EWSB occurs by CWM. � � � � � � 15

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Comment Our result cannot be applied to the models where a negative mass term appears after symmetry breaking of a symmetry by CWM. 17