A 2HDM from Strong Dynamics Kei Yagyu Seikei U arXiv: 1803.01865 [hep-ph] Collaboration with Stefania De Curtis, Luigi Delle Rose, Stefano Moretti 2018, 12 th May, 22nd NHWG Meeting
Introduction From LHC results At least 1 Higgs boson exists. It shows SU(2) L doublet nature. Its mass is 125 GeV. But, Higgs is still mystery…. In fact, we do not know The Nature of the Higgs boson. The reason for the small Higgs mass with respect to a NP scale. The true shape of the Higgs sector. 2 important paradigms (dynamics) Supersymmetry (weak) and Compositeness (strong) Both scenarios can provide a 2HDM as a low energy EFT . Can we distinguish these scenarios from the 2HDM property? 1
Plan of the talk Introduction Introduction to pNGB Higgs Composite 2HDM (C2HDM) Results Summary
Pion Physics ↔ Higgs Physics Georgi, Kaplan 80ʼs From now on, let me say “ Composite Higgs ” as pNGB Higgs . This scenario can be understood by analogy of the pion physics. Higgs Physics Pion Physics Fundamental QCD-like theory QCD Theory Spontaneous sym. SU(2) L ×SU(2) R → SU(2) V G → H breaking h ~ 125 GeV pNGB modes (π 0 , π ± ) ~ 135 MeV New spin 1 and ½ states Other resonances ρ ~ 770 MeV, … ~ Multi-TeV 2
Basic Rules for Composite Higgs Suppose there is a global symmetry G at scale above f (~TeV), which is spontaneously broken down into a subgroup H. The structure of the Higgs sector is determined by the coset G/H. H should contain the custodial SO(4) ≃ SU(2) L ×SU(2) R symmetry. The number of NGBs (dimG-dimH) must be 4 or lager. G f H G sm v EM 3
Basic Rules for Composite Higgs Suppose there is a global symmetry G at scale above f (~TeV), which is spontaneously broken down into a subgroup H. The structure of the Higgs sector is determined by the coset G/H. H should contain the custodial SO(4) ≃ SU(2) L ×SU(2) R symmetry. G The number of NGBs (dimG-dimH) should be 4 or lager. f H G sm v EM Table from Mrazek, Pomarol, Rattazi, Redi, Serra, Wulzer NPB 853 (2011) 1-48 4
Basic Rules for Composite Higgs Suppose there is a global symmetry G at scale above f (~TeV), which is spontaneously broken down into a subgroup H. The structure of the Higgs sector is determined by the coset G/H. H should contain the custodial SO(4) ≃ SU(2) L ×SU(2) R symmetry. G The number of NGBs (dimG-dimH) should be 4 or lager. f Agashe, Contino, Pomarol (2005) H 1 Doublet: Minimal Composite Higgs Model G sm v EM Table from Mrazek, Pomarol, Rattazi, Redi, Serra, Wulzer NPB 853 (2011) 1-48 4
Basic Rules for Composite Higgs Suppose there is a global symmetry G at scale above f (~TeV), which is spontaneously broken down into a subgroup H. The structure of the Higgs sector is determined by the coset G/H. H should contain the custodial SO(4) ≃ SU(2) L ×SU(2) R symmetry. G The number of NGBs (dimG-dimH) should be 4 or lager. f Gripaios, Pomarol, Riva, Serra (2009) H 1 Doublet + 1 Singlet Redi, Tesi (2012) G sm v EM Table from Mrazek, Pomarol, Rattazi, Redi, Serra, Wulzer NPB 853 (2011) 1-48 4
Basic Rules for Composite Higgs Suppose there is a global symmetry G at scale above f (~TeV), which is spontaneously broken down into a subgroup H. The structure of the Higgs sector is determined by the coset G/H. H should contain the custodial SO(4) ≃ SU(2) L ×SU(2) R symmetry. G The number of NGBs (dimG-dimH) should be 4 or lager. f H 2 Doublets Mrazek, Pomarol, Rattazi, Redi, Serra, Wulzer (2011) G sm 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 Suppose there is a global symmetry G at scale above f (~TeV), which is spontaneously broken down into a subgroup H. The structure of the Higgs sector is determined by the coset G/H. H should contain the custodial SO(4) ≃ SU(2) L ×SU(2) R symmetry. G The number of NGBs (dimG-dimH) should be 4 or lager. f H G sm v EM In this talk, I take SO(6) SO(4)×SO(2). 4
Construction of 2 pNGB Doublets 15 SO(6) generators: ^ (A=1-15, a=1-3, a=1-4) 6 SO(4) 1 SO(2) 8 Broken pNGB matrix: U is transformed non-linearly under SO(6): Linear rep. Σ(15): 15 = ( 6 , 1 ) ⊕ ( 4 , 2 ) ⊕ ( 1 , 1 ) under SO(4)×SO(2) Σ is transformed linearly under SO(6): Σ g Σ g -1 and Σ 0 h Σ 0 h -1 5
Higgs Potential The potential becomes 0 because of the shift symmetry of the NGB. the Higgs mass also becomes 0. We need to introduce the explicit breaking of G. NGB Higgs becomes p NGB with a finite mass. Kaplan, PLB365, 259 (1991) Explicit breaking can be realized by partial compositeness Linear mixing a Particle in Particles in elementary sector strong sector 6
Strategy SO(6) invariant Lagrangian Explicit Model with partial compositeness Integrating out heavy DOFs SU(2)×U(1) invariant Lag. Effective Lagrangian with form factors Coleman-Weinberg mechanism 2HDM potential with Effective Potential predicted parameters Higgs mass spectrum Phenomenology Higgs couplings, decays, etc… 7
Explicit Model Based on the 4DCHM, De Curtis, Redi, Tesi, JHEP04 (2012) 042 Strong Sector Elementary Sector SO(6)×U(1) X Mixing SU(2) L ×U(1) Y → SO(4)× SO(2)×U(1) X Partial Compositeness 8
Explicit Model Based on the 4DCHM, De Curtis, Redi, Tesi, JHEP04 (2012) 042 Strong Sector Elementary Sector SO(6)×U(1) X Mixing SU(2) L ×U(1) Y → SO(4)× SO(2)×U(1) X Partial Compositeness 8
Explicit Model Based on the 4DCHM, De Curtis, Redi, Tesi, JHEP04 (2012) 042 Strong Sector Elementary Sector SO(6)×U(1) X Mixing SU(2) L ×U(1) Y → SO(4)× SO(2)×U(1) X Partial Compositeness + (Σ-ρ) interactions 8
Explicit Model Based on the 4DCHM, De Curtis, Redi, Tesi, JHEP04 (2012) 042 C 2 symmetry (to avoid FCNCs) C 2 = diag(1,1,1,1,1,-1) Strong Sector Elementary Sector SO(6)×U(1) X Mixing SU(2) L ×U(1) Y → SO(4)× SO(2)×U(1) X Partial Compositeness + (Σ-ρ) interactions 8
Explicit Model Based on the 4DCHM, De Curtis, Redi, Tesi, JHEP04 (2012) 042 Embeddings into SO(6) multiplets︓ Strong Sector Elementary Sector SO(6)×U(1) X Mixing SU(2) L ×U(1) Y → SO(4)× SO(2)×U(1) X Partial Compositeness 8
Effective Lagrangian All the strong sector information are encoded into the form factors: We then calculate the 1-loop CW potential. K LL , K RR G LL , G RR K LR 9
Effective Potential + O(Φ 6 ) 2 and λ i are given as All the potential parameters m i a function of strong parameters: 10
Typical Prediction of Mass Spectrum E Ψ, ρ μ Y 1 : C 2 breaking term f H ± , H, A ★f ∞ : All extra Higgses are decoupled (elementary) SM limit h ~ 125 GeV ★To get M≠0, we need C 2 breaking (Yukawa alignment is required →A2HDM). 11
f VS tanβ 12
Correlation b/w f and m A 13
Correlation b/w m A and κ V (= g hVV /g hVV SM ) 14
Summary Higgs as pNGB scenarios give natural explanation for a light Higgs and are well motivated by the analogy of pion physics . Taking the SO(6)/SO(4)*SO(2) coset, we obtain C2HDMs as a low energy EFT , where 2HDM parameters can be predicted by the strong dynamics . To get larger extra Higgs masses, we need to introduce the C 2 breaking term Aligned 2HDM . C2HDMs predict delayed decoupling as compared to the MSSM. 15
Correlation b/w m A and κ V (= g hVV /g hVV SM )
Correlation b/w f and M T
Gauge Sector Lagrangian De Curtis, Redi, Tesi, JHEP04 (2012) 042 G 1 × G 2 × G 3 G i : Global SO(6) G V ʼ Σ 2 (8) U 1 (15=7+8) (gauged) mixed H [SO(4)×SO(2)] G V 8 + 8(Φ 1 , Φ 2 ) 7 + 8 NGBs are absorbed into the longitudinal components of gauge bosons of adj[SO(6)].
Gauge Sector Lagrangian (in unitary gauge) De Curtis, Redi, Tesi, JHEP04 (2012) 042 Elementary Sector (g W , W μ ) Strong Sector (g ρ , ρ μ ) SO(6) SO(6) U 1 Σ 2 SO(4)×SO(2) SU(2) L ×U(1) Y
Matching Conditions We need to reproduce the top mass and the weak boson mass. g 2 V sm 2 ~ (246 GeV) 2 Y t
Effective Lagrangian Integrating out the heavy degrees of freedom (ρ A and ψ 6 ), we obtain the effective low energy Lagrangian ≔ K ≔ G
Effective Lagrangian Integrating out the heavy degrees of freedom (ρ A and ψ 6 ), we obtain the effective low energy Lagrangian ≔ K ≔ G These coefficients can be expanded as c 1 , c 2 , … are determined by strong parameters.
Numerical Analysis Input parameters (to be scanned): Tadpole conditions: T 1 = T 2 = 0 165 GeV < m t < 175 GeV 120 GeV < m h < 130 GeV
Yukawa Interactions The structure of the Yukawa interaction is that in the Aligned 2HDM. t and tanβ can be predicted by strong dynamics, All M 1 t , M 2 so the ζ t factor is also predicted. 33
Yukawa Interactions
Spurion Method The Higgs potential is calculated only by using the spurion VEV Δ ψ and U. Merit: Quite General (but still we need to assume fermion rep. ) Demerit: Losing the correlation, O(1) uncertainties in pot. parameters. U T U 1
Spurion Method Mrazek, Pomarol, Rattazi, Redi, Serra, Wulzer NPB 853 (2011) 1-48 Fermionic contribution assuming r = 6 -plet of SO(6). Arbitral O(1) parameters appear in front of each operator. 36
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