Composite 2 Higgs doublet models Kei Yagyu Seikei

Composite 2 Higgs doublet models Kei Yagyu Seikei U ar. Xiv: 1803. 01865 [hep-ph] Collaboration with Stefania De Curtis, Luigi Delle Rose, Andrea Tesi (U of Florence), Stefano Moretti (U of Southampton) 2018, 31 st May, ALCW 18, Fukuoka

Introduction Higgs boson was found at 125 Ge. V at the LHC, but … The Higgs sector is still mystery…. In fact, we do not know p The Nature of the Higgs boson. p The true shape of the Higgs sector. p The reason for the small Higgs mass with respect to a NP scale. 2 important paradigms (dynamics) p Supersymmetry (weak) and Compositeness (strong) Both scenarios can provide a 2 HDM as a low energy EFT. Can we distinguish these scenarios from the 2 HDM property? 1

Plan of the talk p Introduction to composite (p. NGB) Higgs p Composite 2 HDM (C 2 HDM) p Results p Summary

Pion Physics ↔ Higgs Physics p From now on, let me say “Composite Higgs” as p. NGB Higgs. Georgi, Kaplan 80’s p This scenario can be understood by analogy of the pion physics. Pion Physics Fundamental Theory Spontaneous sym. breaking p. NGB modes Other resonances QCD SU(2)L×SU(2)R → SU(2)V (π0, π±) ~ 135 Me. V ρ ~ 770 Me. V, … Higgs Physics QCD-like theory G→H h ~ 125 Ge. V New spin 1 and ½ states ~ Multi-Te. V 2

Basic Rules for Composite Higgs p Suppose there is a global symmetry G at scale above f (~Te. V), which is spontaneously broken down into a subgroup H. p The structure of the Higgs sector is determined by the coset G/H. p H should contain the custodial SO(4) ≃ SU(2)L×SU(2)R symmetry. p The number of NGBs (dim. G-dim. H) must be 4 or lager. G f H Gsm v EM 3

Basic Rules for Composite Higgs p Suppose there is a global symmetry G at scale above f (~Te. V), which is spontaneously broken down into a subgroup H. p The structure of the Higgs sector is determined by the coset G/H. p H should contain the custodial SO(4) ≃ SU(2)L×SU(2)R symmetry. G p The number of NGBs (dim. G-dim. H) should be 4 or lager. f H Gsm v EM Table from Mrazek, Pomarol, Rattazi, Redi, Serra, Wulzer NPB 853 (2011) 1 -48 4

Basic Rules for Composite Higgs p Suppose there is a global symmetry G at scale above f (~Te. V), which is spontaneously broken down into a subgroup H. p The structure of the Higgs sector is determined by the coset G/H. p H should contain the custodial SO(4) ≃ SU(2)L×SU(2)R symmetry. G p The number of NGBs (dim. G-dim. H) should be 4 or lager. f 1 Doublet: Minimal Composite Higgs Model H Gsm Agashe, Contino, Pomarol (2005) Kanemura, Kaneta, Machida, Shindou (2014) v EM Table from Mrazek, Pomarol, Rattazi, Redi, Serra, Wulzer NPB 853 (2011) 1 -48 4

Basic Rules for Composite Higgs p Suppose there is a global symmetry G at scale above f (~Te. V), which is spontaneously broken down into a subgroup H. p The structure of the Higgs sector is determined by the coset G/H. p H should contain the custodial SO(4) ≃ SU(2)L×SU(2)R symmetry. G p The number of NGBs (dim. G-dim. H) should be 4 or lager. f H 1 Doublet + 1 Singlet Gsm Gripaios, Pomarol, Riva, Serra (2009) Redi, Tesi (2012) v EM Table from Mrazek, Pomarol, Rattazi, Redi, Serra, Wulzer NPB 853 (2011) 1 -48 4

Basic Rules for Composite Higgs p Suppose there is a global symmetry G at scale above f (~Te. V), which is spontaneously broken down into a subgroup H. p The structure of the Higgs sector is determined by the coset G/H. p H should contain the custodial SO(4) ≃ SU(2)L×SU(2)R symmetry. G p The number of NGBs (dim. G-dim. H) should be 4 or lager. f 2 Doublets H Gsm Mrazek, Pomarol, Rattazi, Redi, Serra, Wulzer (2011) Bertuzzo, Ray, Sandes, Savoy (2013) v EM Table from Mrazek, Pomarol, Rattazi, Redi, Serra, Wulzer NPB 853 (2011) 1 -48 4

Basic Rules for Composite Higgs p Suppose there is a global symmetry G at scale above f (~Te. V), which is spontaneously broken down into a subgroup H. p The structure of the Higgs sector is determined by the coset G/H. p H should contain the custodial SO(4) ≃ SU(2)L×SU(2)R symmetry. G p The number of NGBs (dim. G-dim. H) should be 4 or lager. f H Gsm v EM In this talk, I take SO(6) SO(4)×SO(2). 4

Construction of 2 p. NGB Doublets p 15 SO(6) generators: ^ (A=1 -15, a=1 -3, a=1 -4) 6 SO(4) 1 SO(2) 8 Broken p p. NGB matrix: U is transformed non-linearly under SO(6): p Linear rep. Σ(15): 15 = (6, 1) ⊕ (4, 2) ⊕ (1, 1) under SO(4)×SO(2) 5

Higgs Potential p The potential becomes 0 because of the shift symmetry of the NGB. the Higgs mass also becomes 0. p We need to introduce the explicit breaking of G. NGB Higgs becomes p. NGB with a finite mass. Kaplan, PLB 365, 259 (1991) p Explicit breaking can be realized by partial compositeness Linear mixing a Particle in elementary sector strong sector 6

Strategy Explicit Model Integrating out SO(6) invariant Lagrangian with partial compositeness heavy DOFs Effective Lagrangian SU(2)×U(1) invariant Lag. with form factors Coleman-Weinberg mechanism Effective Potential Phenomenology 2 HDM potential with predicted parameters Higgs mass spectrum Higgs couplings, decays, etc… 7

Explicit Model Based on the 4 DCHM, De Curtis, Redi, Tesi, JHEP 04 (2012) 042 Strong Sector Elementary Sector SU(2)L×U(1)Y Mixing SO(6)×U(1)X → SO(4)× SO(2)×U(1)X Partial Compositeness 8

Explicit Model Based on the 4 DCHM, De Curtis, Redi, Tesi, JHEP 04 (2012) 042 Embeddings into SO(6) multiplets： Strong Sector Elementary Sector SU(2)L×U(1)Y Mixing SO(6)×U(1)X → SO(4)× SO(2)×U(1)X Partial Compositeness 8

Effective Lagrangian p All the strong sector information are encoded into the form factors: p We then calculate the 1 -loop CW potential. KLL, KRR GLL, GRR KLR 9

Effective Potential + O(Φ 6) All the potential parameters mi 2 and λi are given as a function of strong parameters: 10

Matching Conditions p We need to reproduce the top mass and the weak boson mass. g 2 Vsm 2 ~ (246 Ge. V)2 Yt 11

Typical Prediction of Mass Spectrum Energy Ψ, ρμ f ~ Te. V H±, H, A ★ The Higgs mass mh is naturally explained by gρ ~ 5. ★f ∞ : All extra Higgs bosons are decoupled. (elementary) SM limit. h ~ 125 Ge. V 12

f VS tanβ 13

Correlation b/w f and m. A 14

Correlation b/w m. A and κV (= gh. VV/gh. VVSM) 15

Correlation b/w m. A and κV (= gh. VV/gh. VVSM) E 2 HDM C 2 HDM 16

Ratio of σ(e+e- Zhh) @ √s = 1 Te. V De Curtis, Moretti, KY, Yildirim, PRD 95 095026 Δσ = σ(C 2 HDM)/σ(E 2 HDM) - 1 sinθ < 0 sinθ > 0 = v 2/f 2 17

Summary p Composite (=p. NGB) Higgs can naturally explain the light Higgs. p Taking the SO(6)/SO(4)*SO(2) coset, we obtain C 2 HDMs as a low energy EFT, where 2 HDM parameters can be predicted by the strong dynamics. p The MSSM and C 2 HDM can be distinguished by looking at the decoupling behavior (κV-m. A). p The C 2 HDM can be further distinguished from E 2 HDMs from the decoupling behaviour or by looking at e+e- → Zhh process. 18

Gauge Sector Lagrangian (in unitary gauge) De Curtis, Redi, Tesi, JHEP 04 (2012) 042 Elementary Sector (g. W, Wμ) Strong Sector (gρ, ρμ) SO(6) U 1 SU(2)L×U(1)Y Σ 2 SO(4)×SO(2)

Explicit Model Based on the 4 DCHM, De Curtis, Redi, Tesi, JHEP 04 (2012) 042 Strong Sector Elementary Sector SU(2)L×U(1)Y Mixing SO(6)×U(1)X → SO(4)× SO(2)×U(1)X Partial Compositeness 8

Explicit Model Based on the 4 DCHM, De Curtis, Redi, Tesi, JHEP 04 (2012) 042 Strong Sector Elementary Sector SU(2)L×U(1)Y Mixing SO(6)×U(1)X → SO(4)× SO(2)×U(1)X Partial Compositeness + (Σ-ρ) interactions 8

Explicit Model Based on the 4 DCHM, De Curtis, Redi, Tesi, JHEP 04 (2012) 042 C 2 symmetry (to avoid FCNCs) C 2 = diag(1, 1, 1, -1) Strong Sector Elementary Sector SU(2)L×U(1)Y Mixing SO(6)×U(1)X → SO(4)× SO(2)×U(1)X Partial Compositeness + (Σ-ρ) interactions 8

Correlation b/w m. A and κV (= gh. VV/gh. VVSM)

Correlation b/w f and MT

Gauge Sector Lagrangian De Curtis, Redi, Tesi, JHEP 04 (2012) 042 G 1 × G 2 × U 1(15=7+8) GV G 3 GV ’ (gauged) Gi : Global SO(6) Σ 2(8) mixed H [SO(4)×SO(2)] 8 + 8(Φ 1, Φ 2) 7 + 8 NGBs are absorbed into the longitudinal components of gauge bosons of adj[SO(6)].

Effective Lagrangian p Integrating out the heavy degrees of freedom (ρA and ψ6), we obtain the effective low energy Lagrangian ≔G ≔K

Effective Lagrangian p Integrating out the heavy degrees of freedom (ρA and ψ6), we obtain the effective low energy Lagrangian ≔G These coefficients can be expanded as c 1, c 2, … are determined by strong parameters. ≔K

Numerical Analysis Input parameters (to be scanned): Tadpole conditions: T 1 = T 2 = 0 165 Ge. V < mt < 175 Ge. V 120 Ge. V < mh < 130 Ge. V

Yukawa Interactions p The structure of the Yukawa interaction is that in the Aligned 2 HDM. p All M 1 t, M 2 t and tanβ can be predicted by strong dynamics, so the ζt factor is also predicted. 35

Yukawa Interactions