Introduction School of Physics, the University of Melbourne December 2016 Triplet-Quadruplet Fermionic Dark Matter Zhao-Huan Yu (Melbourne) 1 December, 2016 CosPA 2016, Sydney Based on Tim Tait and ZHY, arXiv:1601.01354, JHEP ARC Centre of Excellence for Particle Physics at the Terascale, Model Details Zhao-Huan Yu ( 余钊焕 ) Triplet-Quadruplet Fermionic Dark Matter Backups Conclusion Constraints Mass corrections 1 / 28
Introduction Spiral galaxy M33 December 2016 Triplet-Quadruplet Fermionic Dark Matter Zhao-Huan Yu (Melbourne) as suggested by astrophysical and cosmological observations Dark matter (DM) makes up most of the matter component in the Universe, [1502.01589] Planck 2015 CMB Model Details Spiral galaxy M33 CMB Bullet Cluster Bullet Cluster Mass corrections Constraints Conclusion Backups Dark Matter in the Universe 2 / 28 M33 dark matter halo stellar disk gas Cold DM ( 25.8% ) Ω c h 2 = 0.1186 ± 0.0020 Baryons ( 4.8% ) Ω b h 2 = 0.02226 ± 0.00023 Dark energy ( 69.3% ) Ω Λ = 0.692 ± 0.012
Introduction Model Details December 2016 Triplet-Quadruplet Fermionic Dark Matter Zhao-Huan Yu (Melbourne) Weakly interacting massive particles (WIMPs) A very attractive class of DM candidates: we have , for gauge coupling the Assuming the annihilation process consists of two weak interaction vertices with 3 / 28 [Feng, arXiv:1003.0904] would be determined by the annihilation DM Relic Abundance Backups Conclusion Constraints Mass corrections If DM particles ( χ ) were thermally produced in the early Universe, their relic abundance cross section 〈 σ ann v 〉 : Ω χ h 2 ≃ 3 × 10 − 27 cm 3 s − 1 〈 σ ann v 〉 Observation value Ω χ h 2 ≃ 0.1 〈 σ ann v 〉 ≃ 3 × 10 − 26 cm 3 s − 1 ⇒
Introduction would be determined by the annihilation December 2016 Triplet-Quadruplet Fermionic Dark Matter Zhao-Huan Yu (Melbourne) Weakly interacting massive particles (WIMPs) A very attractive class of DM candidates: Assuming the annihilation process consists of two weak interaction vertices with Model Details 3 / 28 DM Relic Abundance [Feng, arXiv:1003.0904] Mass corrections Constraints Conclusion Backups If DM particles ( χ ) were thermally produced in the early Universe, their relic abundance cross section 〈 σ ann v 〉 : Ω χ h 2 ≃ 3 × 10 − 27 cm 3 s − 1 〈 σ ann v 〉 Observation value Ω χ h 2 ≃ 0.1 〈 σ ann v 〉 ≃ 3 × 10 − 26 cm 3 s − 1 ⇒ the SU ( 2 ) L gauge coupling g ≃ 0.64 , for m χ ∼ O ( TeV ) we have g 4 ∼ O ( 10 − 26 ) cm 3 s − 1 〈 σ ann v 〉 ∼ 16 π 2 m 2 χ ⇒
Introduction multiplets , whose December 2016 Triplet-Quadruplet Fermionic Dark Matter Zhao-Huan Yu (Melbourne) Doublet-triplet DM model [Dedes & Karamitros, 1403.7744] D’Eramo, 0705.4493; Cohen et al. , 1109.2604] Singlet-doublet DM model [Mahbubani & Senatore, hep-ph/0510064; symmetry is usually needed 2 types of multiplets: an artifjcial (DM stability is explained by an accidental symmetry) minimal DM model [Cirelli et al. , hep-ph/0512090] 1 multiplet in a high-dimensional representation: neutral components could provide a viable DM candidate extending the SM with a dark sector consisting of Model Details For DM phenomenology, it is quite natural to construct WIMP models by WIMPs are typically introduced in the extensions of the Standard Model (SM) WIMP Models Backups Conclusion Constraints Mass corrections 4 / 28 aiming at solving the gauge hierarchy problem χ 0 Supersymmetry (SUSY): the lightest neutralino ( ˜ 1 ) Universal extra dimensions: the lightest KK particle ( B ( 1 ) , W 3 ( 1 ) , or ν ( 1 ) )
Introduction Model Details December 2016 Triplet-Quadruplet Fermionic Dark Matter Zhao-Huan Yu (Melbourne) Doublet-triplet DM model [Dedes & Karamitros, 1403.7744] D’Eramo, 0705.4493; Cohen et al. , 1109.2604] Singlet-doublet DM model [Mahbubani & Senatore, hep-ph/0510064; (DM stability is explained by an accidental symmetry) minimal DM model [Cirelli et al. , hep-ph/0512090] 1 multiplet in a high-dimensional representation: neutral components could provide a viable DM candidate 4 / 28 For DM phenomenology, it is quite natural to construct WIMP models by WIMPs are typically introduced in the extensions of the Standard Model (SM) WIMP Models Backups Conclusion Constraints Mass corrections aiming at solving the gauge hierarchy problem χ 0 Supersymmetry (SUSY): the lightest neutralino ( ˜ 1 ) Universal extra dimensions: the lightest KK particle ( B ( 1 ) , W 3 ( 1 ) , or ν ( 1 ) ) extending the SM with a dark sector consisting of SU ( 2 ) L multiplets , whose 2 types of multiplets: an artifjcial Z 2 symmetry is usually needed ··· ···
Introduction Bino-higgsino sector in the MSSM December 2016 Triplet-Quadruplet Fermionic Dark Matter Zhao-Huan Yu (Melbourne) Triplet-quadruplet fermionic DM model: no analogue in usual SUSY models Doublet-triplet fermionic DM model: higgsino-wino sector in the MSSM Model Details Singlino-higgsino sector in the NMSSM 5 / 28 Singlet-doublet fermionic DM model: Backups Conclusion Constraints Mass corrections of more complete models, but the model parameters are much more free Connection to SUSY models The above models with SU ( 2 ) L multiplets can be understood as simplifjcations d ) + g ′ v d d − g ′ v u L mass ⊃ − 1 2 M 1 ˜ B ˜ B − µ ( ˜ H + u ˜ H − d − ˜ H 0 u ˜ H 0 B ˜ ˜ H 0 ˜ B ˜ H 0 � � u + h.c. 2 2 L mass ⊃ − κ v s ˜ S ˜ S − λ v s ( ˜ H + u ˜ H − d − ˜ H 0 u ˜ H 0 d ) + λ v u ˜ S ˜ H 0 d + λ v d ˜ S ˜ H 0 u + h.c. d ) − gv d L mass ⊃ − 1 W 0 ˜ W 0 − M 2 ˜ W + ˜ W − − µ ( ˜ W 0 ˜ 2 M 2 ˜ H + u ˜ H − d − ˜ H 0 u ˜ H 0 ˜ H 0 � d 2 + gv u W − − gv d ˜ W 0 ˜ W + ˜ ˜ H 0 u − gv u ˜ H + u ˜ H − � d + h.c. 2
Introduction Model Details December 2016 Triplet-Quadruplet Fermionic Dark Matter Zhao-Huan Yu (Melbourne) Yukawa couplings: Covariant kinetic and mass terms: 6 / 28 Backups Mass corrections Introduce left-handed Weyl fermions in the dark sector: Constraints Triplet-Quadruplet Fermionic DM Model Conclusion Q + Q ++ T + 1 2 Q 0 Q + � � � � 4 , − 1 4 , + 1 ∈ ( 3 ,0 ) , T 0 1 ∈ 2 ∈ T = Q 1 = , Q 2 = Q − Q 0 2 2 T − 1 2 Q −− Q − 1 2 σ µ D µ T − 1 L T = iT † ¯ 2 ( m T T T + h.c. ) L Q = iQ † σ µ D µ Q 1 + iQ † σ µ D µ Q 2 − ( m Q Q 1 Q 2 + h.c. ) 1 ¯ 2 ¯ k H l − y 2 ( Q 2 ) jk L HTQ = y 1 ϵ jl ( Q 1 ) jk k H † i T i i T i j + h.c. Z 2 symmetry: odd for dark sector fermions, even for SM particles forbids operators like T LH , Te c H † H † , Q 1 L † HH † , Q 2 LHH † , ... ⇒
Introduction Model Details December 2016 Triplet-Quadruplet Fermionic Dark Matter Zhao-Huan Yu (Melbourne) 3 Majorana fermions, 3 singly charged fermions, 1 doubly charged fermion 7 / 28 Backups Conclusion State Mixing Constraints Mass corrections T 0 T + L mass = − 1 − ( T − , Q − − m Q Q −− 2 ( T 0 , Q 0 1 , Q 0 Q 0 1 , Q − Q + 1 Q ++ 2 ) M N 2 ) M C + h.c. 1 1 2 Q 0 Q + 2 2 3 3 = − 1 ∑ ∑ i χ − i χ + i + h.c. − m Q χ −− χ ++ i χ 0 i χ 0 i − m χ 0 m χ ± 2 i = 1 i = 1 1 − 1 1 − 1 m T 3 y 1 v 3 y 2 v m T 2 y 1 v 6 y 2 v � � � � 1 − 1 − m Q M N = 3 y 1 v 0 m Q , M C = 6 y 1 v 0 � � − 1 1 − m Q � 3 y 2 v m Q 0 � 2 y 2 v 0 T 0 χ 0 T + χ + T − χ − 1 1 1 Q 0 = N χ 0 Q + = C L χ + Q − = C R χ − , , 1 2 1 2 1 2 Q + χ + Q − χ − Q 0 χ 0 2 3 2 3 2 3 χ −− ≡ Q −− χ ++ ≡ Q ++ 1 , 2 χ 0 1 would be an excellent DM candidate if it is the lightest dark sector fermion
Introduction Model Details December 2016 Triplet-Quadruplet Fermionic Dark Matter Zhao-Huan Yu (Melbourne) This approximate symmetry leads to special mixing patterns : 8 / 28 Backups Mass corrections Conclusion Constraints y 1 = y 2 : Custodial Symmetry When the two Yukawa couplings are equal ( y = y 1 = y 2 ), the Lagrangian has an SU ( 2 ) L × SU ( 2 ) R global symmetric form: k − 1 σ µ D µ ( Q A ) i j 2 [ m Q ϵ AB ϵ il ( Q A ) i j L Q + L HTQ = i ( Q † A ) k k ( Q B ) lk j + h.c. ] i j ¯ +[ y ϵ AB ( Q A ) jk i T i k ( H B ) j + h.c. ] � � � � ( Q 1 ) i j H † SU ( 2 ) R doublets: ( Q A ) i j i k k = , ( H A ) i = ( Q 2 ) i j H i k This is a custodial symmetry, explicitly broken by U ( 1 ) Y gauge interactions Identical magnitudes of Q 1 and Q 2 components in χ 0 i and χ ± i
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