The 4D Composite Higgs boson at the LHC and a LC Stefano Moretti - PowerPoint PPT Presentation

Outline 4DCHM Implementation LHC results LHC results LC results Conclusions Backup slides Backup slides The 4D Composite Higgs boson at the LHC and a LC Stefano Moretti (NExT Institute, Southampton & RAL) With D. Barducci, A. Belyaev, M.S. Brown, S. De Curtis and G.M. Pruna Based on arXiv:1302.2371, arXiv:1306.6876 & arXiv:1304.4639 B’ham, 29 Feb 2014

Outline 4DCHM Implementation LHC results LHC results LC results Conclusions Backup slides Backup slides Outline Preamble: • A Higgs(-like) signal has been observed at the LHC (supplemental earlier evidence from Tevatron as well) • Both ATLAS and CMS confirm it, very SM-like • Mass measurements around 125 GeV b and τ + τ − (in • Candidate data samples: γγ , ZZ ∗ , WW ∗ , b ¯ order of decreasing accuracy and/or significance) plus invisible Motivation: • Some inconsistency with the SM predictions existed (still exists), particularly in the (most significant) γγ channel • Either way, it is mandatory to explore BSM solutions • Whereas the ‘fundamental Higgs’ hypothesis is being quantitatively tested in several models, the ‘composite Higgs’ one has only been marginally studied in comparison • All (pseudo)scalar objects discovered in Nature have always been fermion composites

Outline 4DCHM Implementation LHC results LHC results LC results Conclusions Backup slides Backup slides Outline Desclaimer: • This talk is about a phenomenological analysis aimed at capturing the essentials of CHMs, it is not about building them and/or comparing their pros and cons • It thus adopts a specific CHM realisation that it is entirely calculable, the 4DCHM, apart from its UV structure • For an analysis of the Higgs data, knowledge of the latter is not strictly necessary Content: • The 4DCHM (touch and go) • Implementation (trust me, it is damn complicated but it is correct) • Results (not exciting as one might have hoped, yet not so frustrating as in many other BSM scenarios)

Outline 4DCHM Implementation LHC results LHC results LC results Conclusions Backup slides Backup slides 4DCHM Even with discovery of a Higgs particle, SM may not the end of the story (hierarchy and naturalness problems) Two possible scenarios Weak coupling Strong coupling • Supersymmetry • Technicolor • Extra dimensions • Composite Higgs A possible Composite Higgs scenario • Higgs doublet arise from a strong dynamics • Higgs as a (Pseudo) Nambu-Goldstone Boson (PNGB) Idea from the ’80s: spontaneous breaking of a symmetry G → H Georgi and Kaplan, Phys.Lett. B136, 183 (1984)

Outline 4DCHM Implementation LHC results LHC results LC results Conclusions Backup slides Backup slides 4DCHM Simplest example was considered by Agashe, Contino and Pomarol (arXiv:0412089) • Symmetry pattern SO (5) → SO (4) The coset SO (5) / SO (4) turn out to be one of the most economical: 4 Pseudo Nambu-Goldstone Bosons (PNGBs) (minimum number to be identified with the SM Higgs doublet) Potential generated by radiative corrections → light Higgs (a la Coleman, Weinberg ’73) Extra-particle content is present • Spin 1 resonances • Spin 1/2 resonances

Outline 4DCHM Implementation LHC results LHC results LC results Conclusions Backup slides Backup slides 4DCHM 4DCHM of De Curtis, Redi, Tesi (arXiv:1110.1613) : highly deconstructed 4D version of general 5D theory • Just two sites: Elementary and Composite sectors • Mechanism of partial compositness (e.g. mixing between elementary and composite states - 3 rd generation quarks, cfr γ − ρ mixing in QCD) Effective 4D model, hence needs UV completion, (largely) irrelevant for Higgs sector Minimal: single SO (5) multiplet of resonances from composite sector (only dof’s accessible at the LHC) The 4DCHM represents the framework to study CHMs in a complete and computable way Generic features of all relevant CHMs are captured

Outline 4DCHM Implementation LHC results LHC results LC results Conclusions Backup slides Backup slides 4DCHM Bosonic sector Elementary sector Composite Sector Ω 1 SO (5) ⊗ U (1) X SO (5) ⊗ U (1) X Φ 2 SU (2) L ⊗ U (1) Y SO (4) ⊗ U (1) X g 0 , ˜ g ∗ , ˜ A W De Curtis, Redi, Tesi ’11 Ω 1 = exp ( i Π 2 f ) Π Goldstone Matrix f scale of the symmetry breaking (compositeness scale) ϕ 0 = (0 , 0 , 0 , 0 , 1) = δ i 5 Φ 2 = Ω 1 ϕ 0 11 new gauge resonances 5 Neutral 6 Charged (c.c.)

Outline 4DCHM Implementation LHC results LHC results LC results Conclusions Backup slides Backup slides 4DCHM Bosonic sector mass spectrum s 2 Z ≃ f 2 ψ M 2 4 g 2 ∗ ( s 2 θ + 2 ) ξ Bosonic sector mass spectrum M 2 Z 1 = f 2 g 2 ∗ M ∗ ≃ 3 TeV tan θ = s θ / c θ = g 0 / g ∗ √ tan ψ = s ψ / c ψ = 2 g 0 Y / g ∗ ξ = sin ( v 2 f ) ≃ v 2 f v = ⟨ h ⟩ = 246 GeV m Z = 91 GeV Model parameters (gauge): m W = 80 GeV m γ = 0 f ≃ 1 TeV and g ∗ perturbative ( ≤ 4 π ) Gauge boson mass ≥ 1 . 5 TeV M ∗ = f g ∗ from EWPTs

Outline 4DCHM Implementation LHC results LHC results LC results Conclusions Backup slides Backup slides 4DCHM Fermionic sector Explicit breaking of SO (5) through ∆ b R b el Ψ ˜ R B Yukawas in composite sector Y T , Y B 20 new fermionic resonances Y B , m Y B • 10 in the top sector ∆ b L • 10 in the bottom sector Ψ B q el L Ψ T Model parameters (fermion sector) ∆ t L m ∗ Y T , m Y T ∆ tL , ∆ tR , Y T , m Y T , ∆ t R ∆ bL , ∆ bR , Y B , m Y B t el Ψ ˜ R T • Elementary(3 rd ) fermions mix with composites via link fields Ω 1 • First two generation quarks and all leptons considered as in SM

Outline 4DCHM Implementation LHC results LHC results LC results Conclusions Backup slides Backup slides 4DCHM Fermionic sector mass spectrum Top and bottom sector ( ˜ X = X / m ∗ ) b ∝ ξ m 2 Fermionic sector mass spectrum m 2 ∗ ∆ 2 ˜ b L ˜ ∆ 2 b R ˜ Y 2 B 2 m ∗ ≃ 1 TeV t ∝ ξ m 2 m 2 ∗ ∆ 2 ˜ t L ˜ ∆ 2 t R ˜ Y 2 T 2 T 1 ≃ m 2 ( ) √ m 2 ∗ 2 + ˜ M 2 Y T − ˜ 4 + ˜ M 2 M Y T Y T 2 B 1 ≃ m 2 ( ) m top = 172 GeV √ m 2 ∗ 2 + ˜ M 2 Y B − ˜ 4 + ˜ M 2 M Y B Y B 2 Fermionic resonance mass ≃ 1 TeV

Outline 4DCHM Implementation LHC results LHC results LC results Conclusions Backup slides Backup slides 4DCHM Recapping: Higgs sector at a glance • Four PNGBs in the vector representation of SO (4) one of which is composite Higgs boson • Physical Higgs particle acquires mass through one-loop generated potential (Coleman-Weinberg) • 4DCHM choice for fermionic sector gives finite potential, i.e., from location of minimum one extracts m H and ⟨ h ⟩ • Partial compositness: 1. SM gauge/fermion states couple to Higgs via mixing with composite particles 2. 4DCHM gauge/fermion resonances couple to Higgs directly • Zoo of new fermions and gauge bosons has potential to alter Higgs couplings via mixing and/or loops