Fermionic DM Higgs Portal � An EFT approach Michael A. Fedderke University of Chicago Based on 1404.2283 [hep-ph] (MF , Chen, Kolb, Wang) Unlocking the Higgs Portal ACFI, UMass, Amherst 2 May 2014
2012 discovery of (a) ~125GeV Higgs boson natural motivation for exploring Higgs Portal (HP) couplings � � L ⊃ H † H O New � One avenue for particle DM to couple to SM � � This talk � Bottom-up EFT analysis of the allowed parameter space for the lowest dimension ‘scalar’ and ‘pseudoscalar’ HP couplings of fermionic WIMP DM � in light of recent experimental limits. � � (See also results in Xiao-Gang He’s talk yesterday for scalar DM case) � � Previous similar work � 1112.3299 [Djouadi, et al.] � 1203.2064 [Lopez-Honorez, Schwetz, Zupan] � 1309.3561 [Greljo, et al.] � 1402.6287 [De Simone, Giudice, Strumia] � 2
Dimension 5 fermionic DM (WIMP) Higgs portal with scalar (CP-even) and pseudoscalar (CP-odd) couplings � ⇣ ⌘ ∂ − M 0 ) χ + H † H χ ( i/ � L = L SM + ¯ Λ 1 ¯ χχ + c 5 Λ 5 ¯ χ i γ 5 χ c 1 � Singlet Dirac fermion � χ ∼ ( 1 , 1 , 0) 1 (Majorana: ) � χ → 2 χ √ � Convenient re-parametrisation � ∂ − M 0 ) χ + 1 Λ H † H (cos θ ¯ � χ ( i/ L = L SM + ¯ χχ + sin θ ¯ χ i γ 5 χ ) � Good for numerical parameter scan � Mixes up suppression scales (NB for judging unitarity bounds) 3
Standard lore for WIMP direct detection bounds � � H † H ¯ The `pseudoscalar’ (C)P-odd coupling � χ i γ 5 χ is momentum-transfer suppressed � = velocity suppressed ( ) for elastic v 2 ∼ 10 − 6 scattering. � � H † H ¯ Only the ‘scalar’ (C)P-even coupling is � χχ relevant. � � Direct detection bounds strong. � � Pseudoscalar coupling strongly favoured ( ) � θ ∼ π / 2 � However… 4
…after EWSB, � χχ � h v i 2 ✓ ◆� � χ i/ L � ¯ ∂χ � M 0 ¯ χ i γ 5 χ cos θ ¯ χχ + sin θ ¯ 2 Λ � ✓ ◆ ✓ ◆ h v i h + 1 � + Λ − 1 2 h 2 χ i γ 5 χ . cos θ ¯ χχ + sin θ ¯ � Chiral rotation to real-mass basis. � � Modifies the couplings and mass. ✓ ◆ � h v i h + 1 χ M χ + Λ − 1 2 h 2 χ i/ L � ¯ ∂χ � ¯ χ i γ 5 χ , cos ξ ¯ χχ + sin ξ ¯ Scalar Pseudoscalar cos θ � h v i 2 � cos ξ = M 0 sin ξ = M 0 M sin θ 2 Λ M 0 M s✓ ◆ 2 ◆ 2 M 0 � h v i 2 ✓ h v i 2 sin 2 θ 2 Λ cos θ M = + 2 Λ 5
…after EWSB, � χχ � h v i 2 ✓ ◆� � χ i/ L � ¯ ∂χ � M 0 ¯ χ i γ 5 χ cos θ ¯ χχ + sin θ ¯ 2 Λ � ✓ ◆ ✓ ◆ h v i h + 1 � + Λ − 1 2 h 2 χ i γ 5 χ . cos θ ¯ χχ + sin θ ¯ � Chiral rotation to real-mass basis. � � Modifies the couplings and mass. ✓ ◆ � h v i h + 1 χ M χ + Λ − 1 2 h 2 χ i/ L � ¯ ∂χ � ¯ χ i γ 5 χ , cos ξ ¯ χχ + sin ξ ¯ Scalar Pseudoscalar cos θ � h v i 2 � cos ξ = M 0 sin ξ = M 0 M sin θ 2 Λ M 0 M s✓ ◆ 2 ◆ 2 M 0 � h v i 2 ✓ h v i 2 sin 2 θ 2 Λ cos θ M = + 2 Λ 6
Motivates a parameter scan of the low energy Lagrangian considering both couplings: � � ✓ ◆ � h v i h + 1 χ M χ + Λ − 1 2 h 2 χ i/ L � ¯ ∂χ � ¯ χ i γ 5 χ cos ξ ¯ χχ + sin ξ ¯ � � For the purposes of low energy phenomenology, need not explicitly account for the rotation: � so long as the WIMP DM freezes out after the EW phase transition ( ) don’t need to compute M/T F ∼ 20 relevant observables above EWSB scale. � � It is however still important in relating low energy limits to the gauge-invariant EFT operators, and the EFT to some renormalizable model of the HP. � � 7
Motivates a parameter scan of the low energy Lagrangian considering both couplings: � � ✓ ◆ � h v i h + 1 χ M χ + Λ − 1 2 h 2 χ i/ L � ¯ ∂χ � ¯ χ i γ 5 χ cos ξ ¯ χχ + sin ξ ¯ � � Analysis: � � WIMP freeze-out used to fix � Λ parameter space constrained by � ( M, ξ ) Invisible Higgs width � LUX direct detection bounds � 8
Annihilation cross-sections � � Only look at 2-body decays; 3- and 4-body decays phase-space suppressed. Only tree level. � � � Channels: f ¯ f hh ¯ f ( k ) χ h ( k ) ¯ ¯ h ( k ) χ χ ∆ h ( P 2 ) ∆ h ( P 2 ) [ hf ¯ + k ↔ k ′ f ] [ hhh ] h ( k ′ ) h ( k ′ ) χ χ f ( k ′ ) ¯ χ ⟨ v ⟩ ⟨ v ⟩ ZZ W + W − O ( Λ − 1 ) ¯ Z ν ( k ) W − ν ( k ) ¯ χ χ ∆ h ( P 2 ) ∆ h ( P 2 ) [ hZZ ] µ ν [ hWW ] µ ν Z µ ( k ′ ) W + µ ( k ′ ) χ χ ⟨ v ⟩ ⟨ v ⟩ 9
Also have contributions to via - and - O ( Λ − 2 ) hh t u channel diagrams ⟨ v ⟩ � Higher order h ( k ) ¯ χ - e ff ects are generally small + k ↔ k ′ - expect other corrections at same order from neglected operators h ( k ′ ) h ( k ′ ) χ We ‘ignore’ these. (see backup) ⟨ v ⟩ � 10 0 � χχ → ab ) In the NR limit 10 − 1 ( ) s ≈ 4 M 2 + M 2 v 2 10 − 2 hh BR (¯ relevant for W + W − 10 − 3 Z 0 Z 0 freeze-out away f f ¯ � f 10 − 4 from thresholds 10 1 10 2 10 3 and resonances. M [GeV] 10
Most of the annihilation (except contact) through s- channel Higgs. Scale as � � 2 + ( m h Γ h /s ) 2 i − 1 h� � 1 − m 2 h /s σ ∼ � � DM contribution to the Higgs width very important for : 2 M < m h Huge compared to SM width � ◆ 2 s 1 − 4 M 2 ✓ 1 TeV � 1 − 4 M 2 cos 2 ξ 3 . 034 × 10 2 MeV � � � Γ h → ¯ χχ = × m 2 m 2 Λ h h � (for Dirac; halved for Majorana) � Will return to this for constraints… 11
Gondolo and Gelmini, Nucl. Phys. B 360 (1991) 145-179. Srednicki, Watkins and Olive, Nucl. Phys. B 310 (1988) 693. Kolb and Turner, The Early Universe (Westview),1994. WIMP relic density from Boltzmann Equation � n 2 � n 2 ⇥ ⇤ n + 3 Hn = �h σ v Møller i ˙ EQ � Numerical solution, using full thermal averaging (important near resonances and below thresholds) � ⇤ − 1 Z ∞ 4 M 2 σ ( s ) ( s � 4 M 2 ) p s K 1 ( p s/T ) ds 8 M 4 TK 2 � ⇥ h σ v Møller i = 2 ( M/T ) � Defining , Y = n/s ⇢ 1 � � × Ms 0 self-conjugate DM Ω = Y ∞ � 2 non-self-conjugate DM ρ c � Use to fix . Ω DM h 2 � Planck = 0 . 1186(31) Λ Planck Collaboration, 1303.5076 [hep-ph] � 12
EFT suppression scale for correct relic abundance � � Dirac Majorana Dirac Majorana Scalar � 1 . 0 1 . 0 Λ < h v i 10 4 Λ < h v i Dirac 10 4 1 . 0 10 4 � 0 . 8 0 . 8 0 . 8 � 0 . 6 0 . 6 0 . 6 � Λ [GeV] Λ [GeV] Λ [GeV] cos 2 ξ cos 2 ξ cos 2 ξ � 0 . 4 0 . 4 0 . 4 10 3 10 3 10 3 � 0 . 2 0 . 2 0 . 2 � Ω h 2 = 0 . 1186 0 . 0 ⟨ v ⟩ 10 1 10 2 10 3 Pseudo- Ω h 2 = 0 . 1186 Ω h 2 = 0 . 1186 � M [GeV] ⟨ v ⟩ ⟨ v ⟩ 0 . 0 0 . 0 scalar 10 1 10 2 10 3 10 1 10 2 10 3 M [GeV] M [GeV] � � Λ = 2 M Λ = M � Now fix the suppression scale at this value. 13
EFT suppression scale for correct relic abundance 2 † h i 1 2 L � 3 ( H 1 � H ) ⇥ � v O 3 2 ⇤ h v i h + h O Λ χ Λ 2 Λ 2 χ � Dirac Majorana Dirac Majorana Scalar � 1 . 0 1 . 0 Λ < h v i 10 4 Λ < h v i Dirac 10 4 1 . 0 10 4 � 0 . 8 0 . 8 0 . 8 � 0 . 6 0 . 6 0 . 6 � Λ [GeV] Λ [GeV] Λ [GeV] cos 2 ξ cos 2 ξ cos 2 ξ � 0 . 4 0 . 4 0 . 4 10 3 10 3 10 3 � 0 . 2 0 . 2 0 . 2 � Ω h 2 = 0 . 1186 0 . 0 ⟨ v ⟩ 10 1 10 2 10 3 Pseudo- Ω h 2 = 0 . 1186 Ω h 2 = 0 . 1186 � M [GeV] ⟨ v ⟩ ⟨ v ⟩ 0 . 0 0 . 0 scalar 10 1 10 2 10 3 10 1 10 2 10 3 M [GeV] M [GeV] � � Λ = 2 M Λ = M � Now fix the suppression scale at this value. 14
Invisible width constraint � Already noted that invisible width SM width � � Recent limits on Higgs width � - Global fits to Higgs data Belanger et. al., 1306.2941 [hep-ph] � Γ h → ¯ @ 95% confidence χχ ≤ 0 . 19(0 . 38) B inv ≡ Γ SM + Γ h → ¯ χχ � for fit with SM couplings fixed (floating). � - CMS analysis of on-shell vs. o ff -shell Higgs CMS-PAS-HIG-14-002 and production and decay Caola and Melnikov, h → ZZ → llll, ll νν 1307.4935 [hep-ph] � @ 95% confidence. Γ h, tot ≤ 17 . 4MeV 15
Resulting limits on the DM mass � � � Invisible BR Invisible BR Direct limit [Belanger, et al.] [Belanger, et al.] [CMS] � � � � M & GeV � Couplings fixed Couplings floating — � to SM � 56.8 56.2 55.7 Dirac � � 55.3 54.6 53.8 Majorana � � � (Practically independent of S/PS nature: larger for Λ PS, but less phase-space suppression) 16
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