New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi In collaboration with Piero Ferrarese Open Questions in Particle Physics and Cosmology April 4, 2017 - Goettingen Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.1/34
New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion 1 Introduction: New Strong Dynamics 2 Fundamental Minimal Composite Higgs Model 3 Unitarity: Strong Vector Boson Scattering in CH 4 Experimental signatures 5 Conclusion Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.2/34
New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion New Strong Dynamics The Standard Model 1606.02266 • Last successful prediction of the SM: Discovered Higgs boson h very SM-like • Nevertheless SM suffers from several inconsistencies: naturalness/hierarchy, DM, neutrino masses, triviality, inflation, baryogenesis, ... Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.3/34
New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion New Strong Dynamics The Standard Model 1606.02266 • Last successful prediction of the SM: Discovered Higgs boson h very SM-like • Nevertheless SM suffers from several inconsistencies: naturalness/hierarchy, DM, neutrino masses, triviality, inflation, baryogenesis, ... • Implies new physics! Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.3/34
New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion New Strong Dynamics New Strong Dynamics • Technicolor (Weinberg 76, Susskind 79) is a gauge theory that is strongly coupled at ∼ 1 T eV and breaks Chiral symmetry through a condensate of techni-quarks - as in QCD • The techni-quarks carry electroweak charge, thus EW Symmetry breaking is embedded in chiral SB • Pros: naturalness, assymptonic freedom (or safety), DM candidates (techni-baryon number), unification (?), inflation, ... • Issues: large S -parameter, large Higgs mass, non SM Higgs couplings, fermion masses vs FCNC, ... Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.4/34
New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion New Strong Dynamics Is it dead?! Issues: fermion masses vs FCNC, large S -parameter, large Higgs mass, non SM Higgs couplings? Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.5/34
New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion New Strong Dynamics Is it dead?! Issues: fermion masses vs FCNC, large S -parameter, large Higgs mass, non SM Higgs couplings? The answer is NO!! A large number of theories unexplored Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.5/34
New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion New Strong Dynamics Fermion masses • Larger scale Λ > Λ TC generates low energy 4-fermion interactions, schematically: QQ ¯ ¯ ψψ ¯ ¯ QQ ¯ ¯ QQ ψψ + κ QQQ ψ ψψ α + β + h . c . + γ Λ 2 Λ 2 Λ 2 Λ 2 ETC PC FCNC • Extended Technicolor (ETC) (Dimopoulos, Susskind 79, Eichten, Lane 80) • Partial Compositeness (PC) Kaplan 91 - improved hierarchy and FCNC constraints • Light weak doublet scalar fundamental (e.g. Supersymmetric TC) or of composite nature... Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.6/34
New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion New Strong Dynamics Walking Technicolor • Realistic TC theories are quasi-conformal, since quasi-conformality suppress undesirable flavour changing neutral current and can reduce contribution to the S -parameter - Walking Technicolor (WTC) • � ¯ QQ � condensate enhanced. � � γ � � γ ( α ∗ ) � ¯ Λ ETC � ¯ Λ ETC � ¯ QQ ETC � ∼ ln QQ TC � ∼ QQ TC � Λ TC Λ TC Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.7/34
New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion New Strong Dynamics 4 light + 8 heavy techni-quarks in SU (3) (Brower, Hasenfratz, Rebbi, Weinberg, Witzel 16) • ensure chiral SB in the IR • walking is tunable by m h (heavy quark mass) • it is nevertheless hard to get large enough anomalous dimensions, e.g. Ratazzi, Rychkov, Tonni, Vichi 10 for ETC and Pica, Sannino et al. 16 for PC Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.8/34
New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion New Strong Dynamics Light scalar: Higgs boson mass • Techni-dilaton. In Walking dynamics it is expected a component of the Higgs to be a pseudo-Goldstone boson from the breaking of scale invariance. • Top-quark correction, H ) 2 + 3(4 πκ F π ) 2 / (16 π 2 v 2 )[ − 4 r 2 M 2 t m 2 H = ( M TC t + ... ]+non pert. Foadi, Frandsen, Sannino 12’ • Pseudo-Goldstone boson (“Composite Higgs”), - Higgs is the pseudo-GB of the breaking of a global symmetry Georgi, Kaplan 84’ Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.9/34
New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion New Strong Dynamics Higgs couplings • techni-dilaton component couples like SM Higgs (if F σ ∼ v ). • CH component couples like SM-Higgs → g hWW = g SM hWW cos θ • Techni- σ component unknown, but g σππ in QCD is mysteriously described by linear sigma model (Belyaev, Brown, Foadi, Frandsen, Sannino 13’) Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.10/34
New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Fundamental Minimal Composite Higgs Model Fundamental Minimal Composite Higgs Model • Possible SB patterns from fundamental fermions: SU ( N ) × SU ( N ) → SU ( N ), SU (2 N ) → SO (2 N ) or Sp (2 N ) Peskin 80, Preskill 80 • the so-called minimal CH model is based on the coset SO (5) / SO (4) - can be achieved via 4-fermion operators Gersdorff, Ponton, Rosenfeld 15 • Minimal custodial scenario SU(4)/Sp(4) Galloway et al 10’, Cacciapaglia, Sannino 14’ • UV completion example: 2 Dirac flavours fundamental of SU(2) gauge theory Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.11/34
New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Fundamental Minimal Composite Higgs Model • Vacuum misaligned with vacuum that breaks EW symmetry: Σ 0 = cos θ Σ B + sin θ Σ H • The 5 (pseudo-)NGB field is parametrized by the exponential map � � √ 5 � 2 i π a Y a U = exp f a =1 • CCWZ Lowest order NGB Lagrangian L = 1 2 f 2 � x µ x µ � − V • Dynamical generation of EW scale v = f sin θ Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.12/34
New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Fundamental Minimal Composite Higgs Model Scalar Sector • Scalar sector: 5 GB (3 eaten+ h , η ) + 1 σ mixing w/ h (Arbey et al. 15’) L σ = 1 2 κ ( σ ) f 2 � x µ x µ � + 1 2 ∂ µ σ∂ µ σ − 1 σ σ 2 − V 2 M 2 κ ( σ ) = 1 + κ ′ σ + · · · • Modification in the Higgs coupling, g hVV / g SM hVV ∼ cos θ . EWPO, sin θ � 0 . 2 • On the other hand, minimization of potential, e.g. cos θ → 2 C m / ( y ′ t C t ) top-loop and techni-quark mass. Indicates not so small angles - different origin C x ∼ 1 • η phenomenology hard, σ ∼ fb • First principle lattice calculation M σ = 4 . 7(2 . 6) / sin θ TeV (Arthur, Drach, Hietanen, Pica, Sannino, 16’) Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.13/34
New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Fundamental Minimal Composite Higgs Model Spin-1 sector • Local Hidden Symmetry construction (DBF, Cacciapaglia, Cai, Deandrea, Frandsen 16’) → LO parameters: ˜ g , r , M V , M A • First principle lattice calculation, M V = 3 . 2(5) / sin θ TeV, M A = 3 . 6(9) / sin θ TeV (Arthur et al. 16’) 10 5 � � V a A a F µ = V µ + A µ = µ V a + µ Y a . a =1 a =1 SU(2) V SU(2) L × SU(2) R TC CH − → → − v 0 , ± 3 ρ µ ρ µ µ (3,1) ⊕ (1,3) − → s 0 , ± 3 a µ µ V s 0 , ± ˜ 3 µ (2,2) v 0 ˜ 1 µ → − a 0 , ± 3 a µ µ (2,2) x 0 A 1 µ x 0 ˜ 1 (1,1) µ Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.14/34
New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Longitudinal Vector Boson Scattering Unitarity Longitudinal VBS Unitarity • Lattice provides good estimate of heavy vector mass; however it poorly provide scalar mass and other quantities of effective Lagrangian • Analiticity and unitarity of n -point functions can lead to further information on the spectra of strong dynamics, e.g. dispersion relations and Weinberg sum rules • Unitarity of Vector Boson Scattering is a powerful tool. A ( s ) ∼ s f 2 • What can it say about the spectra and couplings of CH models, M σ , κ ′ (scalar), ˜ g and r ? Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.15/34
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