Dark matter in three Higgs doublet models Diana Rojas University of - PowerPoint PPT Presentation

Dark matter in three Higgs doublet models Diana Rojas University of Southampton & NExT Institute January 15, 2019 Diana Rojas DM in the 3HDM

N-Higgs Doublet Models (NHDM) N copies of the Higgs doublet with identical quantum numbers: � � φ + α Φ α = , α = 1 , 2 , . . . , N 1 2 ( ρ α + i η α ) √ The most general potential V = Y ab (Φ † a Φ b ) + Z abcd (Φ † a Φ b )(Φ † c Φ d ) contains N 2 ( N 2 + 3) / 2 free parameters. All Abelian symmetries realisable in NHDM have been found. [Ivanov, et al., J.Phys.A 45,215201 (2012)] Diana Rojas DM in the 3HDM

IDM * Amongst 2HDMs, the IDM has the advantage of including DM candidates * Characteristic: An unbroken Z n symmetry is imposed * Is an example of the Higgs-portal DM models 1 Figure: Higgs-portal Feynman diagrams. LEFT: DM annihilation produce SM particles (astrophysical observation). MIDDLE: nucleon-DM scattering (direct detection). RIGHT: Higgs decaying to DM pair (collider signature). 1B. Patt and F. Wilczek, hep-ph/0605188. Diana Rojas DM in the 3HDM

3HDM · Motivations richer symmetry groups than the 2HDMs richer particle spectrum possible update to 6HDM it resembles the 3 generation of fermions in this talk 3HDMs with Two inert plus One Higgs doublet, I(2+1)HDM One inert plus Two Higgs doublets, I(1+2)HDM CPC and CPV versions Previous work from: Adriana Cordero-Cid, Jaime Hernandez-Sanchez, Venus Keus, Steve King, Stefano Moretti, Dorota Sokolowska, Kei Yagyu Diana Rojas DM in the 3HDM

I(1+2)HDM May be regarded as an extension to the 2HDM by the addition of an extra inert scalar doublet Symmetry: Z 2 × ˜ Z 2 . We assign Z 2 = +1 : active doublets, Z 2 = − 1 : inert doublets. ˜ Z 2 in the active sector to avoid FCNCs Theoretical restrictions similar to I(2 + 1)HDM However, one should be careful with unitarity, in fact we have stronger bounds than in 2HDM and I(2+1)HDM 2 2 S. Moretti , K. Yagyu Phys.Rev. D91 (2015) 055022 Diana Rojas DM in the 3HDM

Charge assignments under Z 2 × ˜ Z 2 ( Z 2 , ˜ Z 2 ) charge Φ 1 Φ 2 η Q L L L u R d R e R Type-I (+ , +) (+ , − ) ( − , +) (+ , +) (+ , +) (+ , − ) (+ , − ) (+ , − ) Type-II (+ , +) (+ , − ) ( − , +) (+ , +) (+ , +) (+ , − ) (+ , +) (+ , +) Type-X (+ , +) (+ , − ) ( − , +) (+ , +) (+ , +) (+ , − ) (+ , − ) (+ , +) Type-Y (+ , +) (+ , − ) ( − , +) (+ , +) (+ , +) (+ , − ) (+ , +) (+ , − ) Φ 1 , Φ 2 are the active doublets η is the inert doublet Symmetries: Z 2 (unbroken) guarantees stability of DM ˜ Z 2 (soflty-broken) forbids FCNC at tree level Diana Rojas DM in the 3HDM

Scalar potential The most general phase invariant part of a 3HDM potential is 3 V 0 = − µ 2 i (Φ † i Φ i ) + λ ij (Φ † i Φ i )(Φ † ij (Φ † i Φ j )(Φ † j Φ j ) + λ ′ j Φ i ) and, considering an unbroken Z 2 symmetry we add the terms: 2 Φ 2 ) 2 + λ 2 (Φ † 2 Φ 3 ) 2 + λ 3 (Φ † 3 Φ 1 ) 2 + h.c. V Z 2 = − µ 2 12 (Φ † 1 Φ 2 ) + λ 1 (Φ † where g Z 2 = (+ , + , − ) and � � H ± α Φ α = , α = 1 , 2 , 3 1 2 ( H α + iA α ) √ 1,2 are the actives and 3 is the inert 3V. Keus, S. F. King and S. Moretti, Phys. Rev. D 90 , no. 7, 075015 (2014) doi:10.1103/PhysRevD.90.075015 [arXiv:1408.0796 [hep-ph]]. Diana Rojas DM in the 3HDM

Why studying the H ± W ∓ Z /γ vertex? To test the structure of the Higgs sector Not at tree-level in NHDMs An enhancement due to non-decoupling effects Measure of custodial symmetry violation → NP Diana Rojas DM in the 3HDM

The vertex HW ± Z /γ Loop amplitude of H ± → W ± V ( V = Z , γ ) i M ( H ± → W ± V ) = igm W V µν V ǫ W µ ( p W ) ǫ V ν ( p V ) with V µν written in terms of dimensionless form factors: V = g µν F V + p µ V p ν G V + i ǫ µνρσ p V ρ p W σ V µν W H V V m 2 m 2 W W V incoming momenta for W ± and V . with p µ W and p µ For the case of V = γ , Waard identity V µν γ p γν = 0 implies � � 1 − m 2 F γ = G γ H ± m 2 2 W W and ( p W + p γ ) 2 = m 2 where p 2 W = m 2 H ± . Diana Rojas DM in the 3HDM

The vertex HW ± Z /γ Loop amplitude of H ± → W ± V ( V = Z , γ ) i M ( H ± → W ± V ) = igm W V µν V ǫ W µ ( p W ) ǫ V ν ( p V ) with V µν written in terms of dimensionless form factors: V = g µν F V + p µ V p ν G V + i ǫ µνρσ p V ρ p W σ V µν W H V V m 2 m 2 W W V incoming momenta for W ± and V . with p µ W and p µ The effective lagrangian: µ Z µ + g V H + F µν L eff = f Z H + W − W F V µν + ih V ǫ µνρσ H + F µν W F ρσ + h.c. V where F µν W and F µν are the field strength tensors. V The coefficient f Z has mass dimension one whereas g V and h V have mass dimension minus one. Diana Rojas DM in the 3HDM

Figure: The 1PI diagrams for the HWZ and HW γ vertices. The diagrams which vanish in the limit sin( β − α ) = 1 are not displayed. Diana Rojas DM in the 3HDM

Form Factors Calculations are made in Type I and X where m H ± can be light m H = m H ± , − 400 2 GeV 2 < M 2 < 400 2 GeV 2 , 100 GeV < m A < 260 (350) GeV, m η A = 400 GeV Diana Rojas DM in the 3HDM

The I(2+1)HDM May be regarded as an extension to the IDM by the addition of an extra inert scalar doublet The work we did Could the DM pheno distinguish CPC and CPV inert sectors? Which pheno is interesting to study at the LHC? Can it be differenciated from IDM in experiments? Diana Rojas DM in the 3HDM

Constructing the ( Z 2 symmetric) I(2+1)HDM The most general phase invariant part of a 3HDM potential is 4 V 0 = − µ 2 i (Φ † i Φ i ) + λ ij (Φ † i Φ i )(Φ † ij (Φ † i Φ j )(Φ † j Φ j ) + λ ′ j Φ i ) and, considering an unbroken Z 2 symmetry we add the terms: 1 Φ 2 ) 2 + λ 2 (Φ † 2 Φ 3 ) 2 + λ 3 (Φ † 3 Φ 1 ) 2 + h.c. V Z 2 = − µ 2 12 (Φ † 1 Φ 2 ) + λ 1 (Φ † where g Z 2 = ( − , − , +) and � � H ± α Φ α = , α = 1 , 2 , 3 1 2 ( H α + iA α ) √ 1,2 are the inerts and 3 is the active 4V. Keus, S. F. King and S. Moretti, Phys. Rev. D 90 , no. 7, 075015 (2014) doi:10.1103/PhysRevD.90.075015 [arXiv:1408.0796 [hep-ph]]. Diana Rojas DM in the 3HDM

Dark democracy limit To obtain the mass spectrum → solve analytically or numerically. We simplify the model 5 µ 2 1 = µ 2 λ ′ 31 = λ ′ 2 , λ 3 = λ 2 , λ 31 = λ 23 , 23 Note: if µ 2 12 = 0 → doubled IDM! Two DM candidates, difficult to satisfy both relic density and LHC (invisible channel) constraints Then only two complex parameters: µ 2 12 = | µ 2 12 | e i θ 12 , λ 2 = | λ 2 | e i θ 2 5B. Grzadkowski, O. M. Ogreid, P. Osland, A. Pukhov and M. Purmohammadi, JHEP 1106 , 003 (2011) doi:10.1007/JHEP06(2011)003 [arXiv:1012.4680 [hep-ph]]. Diana Rojas DM in the 3HDM

Neutral mass spectrum v 2 m 2 2 ( λ ′ 23 + λ 23 ) − Λ − µ 2 = 2 S 1 v 2 m 2 2 ( λ ′ 23 + λ 23 ) + Λ − µ 2 = S 2 2 v 2 23 + λ 23 ) − Λ ′ − µ 2 m 2 2 ( λ ′ = S 3 2 v 2 23 + λ 23 ) + Λ ′ − µ 2 m 2 2 ( λ ′ = S 4 2 where � v 4 | λ 2 | 2 + | µ 2 12 | 2 − 2 v 2 | λ 2 || µ 2 Λ = 12 | cos( θ 12 + θ 2 ) � v 4 | λ 2 | 2 + | µ 2 12 | 2 + 2 v 2 | λ 2 || µ 2 Λ ′ = 12 | cos( θ 12 + θ 2 ) For S 1 to be DM, θ 2 + θ 12 in 2nd quadrant and λ 2 < 0. Diana Rojas DM in the 3HDM

Potential parameters 12 | = 1 | µ 2 2( m 2 2 − m 2 1 ) , S ± S ± m 2 2 + m 2 λ 23 = 2 µ 2 S ± S ± 2 1 v 2 + , v 2 23 = 1 λ ′ v 2 ( m 2 S 2 + m 2 S 1 − m 2 2 − m 2 1 ) , S ± S ± − m 2 S 2 + m 2 2 = v 2 v 2 | λ 2 | � � 4 α sin θ 2 + 2( α 2 − 1) cos θ 2 µ 2 S 1 2 g S 1 S 1 h − , 2(1 + α 2 ) 2 | λ 2 | = 1 | µ 2 � 12 | cos( θ 2 + θ 12 ) v 2 � � 2 � � m 2 S 2 − m 2 � 12 | 2 cos 2 ( θ 2 + θ 12 ) + S 1 12 | 2 ] . � | µ 2 − | µ 2 + 2 where α = −| µ 2 12 | cos θ 12 + v 2 | λ 2 | cos θ 2 − Λ | µ 2 12 | sin θ 12 + v 2 | λ 2 | sin θ 2 Diana Rojas DM in the 3HDM

Physical parameters Parameters of V: µ 2 2 , | λ 2 | , | µ 2 12 | , λ 23 , λ ′ 23 , θ 12 , θ 2 DM mass: m S 1 mass splittings: δ 12 = m S 2 − m S 1 δ 1 c = m S ± 1 − m S 1 δ c = m S ± 2 − m S ± 1 Higgs-DM coupling: g S 1 S 1 h CPV phases: θ 12 , θ 2 We recover CPC when θ 2 + θ 12 = π , where cos( θ 2 + θ 12 ) = − 1 and Λ = v 2 | λ 2 | + | µ 2 12 | , Λ = v 2 | λ 2 | − | µ 2 12 | and α, β → ∞ . Diana Rojas DM in the 3HDM

Benchmark scenarios A1: δ 12 = 125 GeV, δ 1 c = 50 GeV, δ c = 50 GeV, θ 2 = θ 12 = 0 . 5 m S 1 < m 2 , 3 , 4 , m S ± 1 , 2 (no co-annihilation) B1: δ 12 = 125 GeV, δ 1 c = 50 GeV, δ c = 50 GeV, θ 2 = θ 12 = 0 . 82 m S 1 ≈ m S 3 < m 2 , 4 , m S ± 1 , 2 C1: δ 12 = 12 GeV, δ 1 c = 100 GeV, δ c = 1 GeV, θ 2 = θ 12 = 1 . 57 m S 1 ≈ m S 2 ≈ m S 3 ≈ m S 4 < m S ± 1 , 2 G1: δ 12 = 2 GeV, δ 1 c = 1 GeV, δ c = 1 GeV, θ 2 = θ 12 = 0 . 82 m S 1 ≈ m S 2 ≈ m S 3 ≈ m S 4 ≈ m S ± 1 ≈ m S ± 2 H1: δ 12 = 50 GeV, δ 1 c = 1 GeV, δ c = 50 GeV, θ 2 = θ 12 = 0 . 82 m S 1 ≈ m S 3 ≈ m S ± 1 < m S 4 ≈ m S 2 ≈ m S ± 2 A. Cordero-Cid, J. Hern´ andez-S´ anchez , V. Keus, S. F. King, S. Moretti , D. Rojas and D. Soko� lowska, JHEP 1612 , 014 (2016) Diana Rojas DM in the 3HDM