Hidden two-higgs doublet model C, Uppsala and Lund University SUSY10, Bonn, 2010-08-26 1 Two Higgs doublet models () 2 3 4 Phenomenological consequences 5
Two Higgs doublet models () Work together with Rikard Enberg and Glenn Wouda (Uppsala) C potential EWSB Why? Simplest non-trivial extension of the SM Higgs sector Realized in the MSSM (type II) Interesting phenomenology Here: Hidden where softly broken Z 2 symmetry imposed in Higgs basis (cf. Inert Doublet Model (IDM) by Barbieri, Hall and Rychkov) A and H ± have no tree-level couplings to fermions usual couplings to h, H and γ, Z, W Interesting phenomenology: electroweak precision tests can be fulfilled also with heavy h non-std decays of A/H ± such as H + W + γ can dominate essentially no limits on A, H ± from low-energy flavour experiments (B-decays etc)
General two Higgs doublet model potential Two complex SU(2) L doublets with hypercharge Y=1: Φ 1,Φ 2 C potential EWSB Invariance under global SU(2): Φ a U ab Φ b General potential [ ] V =m11φ 2 1 Φ 1 + m22φ 2 2 Φ 2 m12φ 2 1 Φ 2 + h.c. + 1 ( ) 2 2 λ 1 Φ 1 Φ 1 + 1 ( ) 2 ( ) ( ) ( ) ( ) 2 λ 2 Φ 2 Φ 2 + λ3 Φ 1 Φ 1 Φ 2 Φ 2 + λ 4 Φ 1 Φ 2 Φ 2 Φ 1 { 1 ( ) 2 ( ) ( )] ( ) } + 2 λ 5 Φ 1 Φ 2 + [λ 6 Φ 1 Φ 1 + λ 7 Φ 2 Φ 2 Φ 1 Φ 2 + h.c. Potential real {m 2 11, m2 22, λ 1 4} real, {m 2 12, λ 5 7} complex No explicit CP-violation {m 2 12, λ 5 7} real Exact Z 2 symmetry (as in IDM) Demanding that the potential is symmetric under Φ 1 Φ 1, Φ 2 Φ 2 m 2 12 = 0, λ 6 7 = 0 in general basis
Electroweak symmetry breaking Higgs basis EW symmetry broken by non-zero vev of Φ 1 C potential EWSB Φ 1 = 1 2 ( 2G + v h sin α + H cos α + ig 0 Minimization Φ 2 = 1 2 ( 2H + h cos α + H sin α + ia { m 2 11 = 1 2 v 2 λ 1 m 2 12 = 1 2 v 2 λ 6 (v 246 GeV ) Three Goldstone bosons: G ±, G 0 masses to W and Z Five Higgs boson states: two CP-even, h, H with mixing angle α, one CP-odd A, and two charged H ± sin α m 2 12 (m2 12 = 0 restores Z 2 symmetry) Higgs-gauge couplings from s α sin α (tan β = 0) No hard breaking of Z 2 symmetry λ 2, λ 7 fixed Parameterisation of potential: { m 2 22, m h, m H, m A, m H ±, s α } ) )
C In order for fermions to get mass they have to couple to Φ 1 To avoid non-mfv CC and FCNC at tree-level, each fermion type can only couple to one Higgs doublet (Glashow & Weinberg) fermions cannot couple to Φ 2 Yukawa couplings for SM fermions with mass eigenstates D = {d, s, b}, U = {u, c, t}, L = {e, µ, τ} and massless neutrinos ( L Y = 1 Dm D D + Um U U + ) Lm L L (sin αh cos αh) v U L D
Theoretical constraints C TH constraints Positivity of potential Demanding that the potential is bounded from below λ 1 > 0, λ 2 > 0, λ 3 > λ 1 λ 2, λ 3 + λ 4 λ 5 > λ 1 λ 2 plus more complicated expressions Perturbativity Cross-section for 2 2 Higgs scattering processes λ2 HHHH 16π 2 the quartic Higgs couplings λ HHHH cannot be too large for the perturbative series to make sense Tree-level unitarity requiring tree-level unitarity for HH and HV L scattering limits on eigenvalues of the corresponding scattering matrices
C Improved naturalness Non-standard decays Improved naturalness Naturalness (Barbieri, Hall, Rychkov) The physics that cancels the quadratic corrections to m 2 h must enter at a scale obtained from ( δm 2 h )top = 3m2 t 2π 2 v 2 Λ2 t < m 2 h Λ t 4πm h SM more natural (less fine-tuned) if m h larger But EW precision measurements restrict m h severely in SM χ 2 6 5 4 3 2 1 July 2010 Theory uncertainty α (5) had = 0.02758±0.00035 0.02749±0.00012 incl. low Q 2 data Excluded Preliminary 0 30 100 300 m H [GeV] m Limit = 158 GeV
Oblique parameters S, T, U sensitive to new physics Fixing the SM Higgs mass and U = 0 gives region of allowed (90% CL) points in the S - T plane C 1.00 0.75 0.50 0.25 Γ Z, σ had, R l, R q asymmetries M W ν scattering Q W E 158 Improved naturalness Non-standard decays T 0.00-0.25-0.50 all: M H = 117 GeV -0.75 all: M H = 340 GeV all: M H = 1000 GeV -1.00-1.25-1.00-0.75-0.50-0.25 0.00 0.25 0.50 0.75 1.00 1.25 If new physics increase T and/or decrease S lightest CP-even Higgs can be much heavier S possible with an additional Higgs doublet (also in IDM and λsusy)
Examples of allowed regions from S,T as well as positivity, perturbativity and tree-level unitarity in m A -m H ± plane C m h = 150 GeV m H = 200 GeV sin α = 1/ 2 m 22 = 50 GeV (GeV) + mh 800 700 600 500 400 300 200 100 Improved naturalness Non-standard decays m h = 400 GeV m H = 200 GeV sin α = 0.3 m 22 = 100 GeV (GeV) + mh 800 700 600 500 400 300 200 100 100 200 300 400 500 600 700 800 0 ma (GeV) 100 200 300 400 500 600 700 800 0 ma (GeV) points with an custodial global SU(2) symmetry allowed m H ± m A or m 2 H ± m 2 H sin2 α + m 2 h cos2 α
Non-standard H + decays C Basic decay vertex H + h/h/a cosα / sinα / 1 W + Decays into fermions and SM gauge bosons (m H ± < m A ) Improved naturalness Non-standard decays H + h/h H + h/h H + h/h W + W + W + H + h/h H + h / H Z / W + W + W + W + / γ Note: all diagrams proportional to sin(2α) vanish in no-mixing limit sin α 0 or cos α 0
C Improved naturalness Non-standard decays Example: m H ± = 300 GeV m H = 600 GeV m A = 400 GeV sin α = 0.3 m 22 = 0 H + 4f dominates for m h 2m V GeV H + VV ( ) 2f dominates for 2m V m h m H ± m V Γ (H + X) [ GeV ] BR (H + X) 4f 4f WW 2f ZZ2f tb WW 2f ZZ 2f WZ Wγ WZ Wγ M h [ GeV ] H + WZ dominates for m h > m H ± m V For smaller m H ± ( 100 GeV) tb H + W γ dominate for all m h M h [ GeV ]
C Hidden two Higgs Doublet model softly broken Z 2 symmetry in Higgs basis no Yukawa couplings for A and H ± Phenomenological consequences offers improved naturalness (m h larger) non-standard decay modes of A and H ± can dominate Next step look at lighter A and H ± and see possible effects on LEP searches