Two-Higgs-doublet Models Pseudo-Nambu-Goldstone Dark Matter and - PowerPoint PPT Presentation

Thermal DM Based on Xue-Min Jiang, Chengfeng Cai, Zhao-Huan Yu, Yu-Pan Zeng, and Dec 2019 pNGB DM and 2HDMs Zhao-Huan Yu (SYSU) December 8, 2019 Beijing Normal University, Zhuhai 3rd BNU Dark Matter Workshop Hong-Hao Zhang, 1907.09684, PRD School of Physics, Sun Yat-Sen University pNGB DM Zhao-Huan Yu （余钊焕） Two-Higgs-doublet Models Pseudo-Nambu-Goldstone Dark Matter and Backups Conclusions Parameter Scan pNGB DM & 2HDMs 1 / 26

Thermal DM pNGB DM Dec 2019 pNGB DM and 2HDMs Zhao-Huan Yu (SYSU) matter paradigm Great challenge to the thermal dark No robust signal found so far Direct detection for WIMPs “WIMPs” “Weakly interacting massive particles” DM relic abundance observation from the early Universe assumed to be a thermal relic remaining Conventionally, dark matter (DM) is [XENON Coll., 1805.12562, PRL] 2 / 26 pNGB DM & 2HDMs Parameter Scan Conclusions Backups Thermal Dark Matter DM freeze out, m χ = 100 GeV, g * = 86 10 -7 10 -7 10 3 10 3 10 -8 10 -8 10 2 10 2 10 -9 10 -9 10 1 10 1 Y = n / s 10 -10 10 -10 3 × 10 -27 Ω χ h 2 10 0 10 0 10 -11 10 -11 〈 σ v 〉 = 3 × 10 -26 cm 3 /s 10 -1 10 -1 10 -12 10 -12 3 × 10 -25 10 -2 10 -2 Particle mass m χ ∼ O ( GeV ) − O ( TeV ) 10 -13 10 -13 Equilibrium 10 -3 10 -3 10 -14 10 -14 Interaction strength ∼ weak strength 10 10 1 1 0.1 0.1 T (GeV)

Thermal DM pNGB DM Dec 2019 pNGB DM and 2HDMs Zhao-Huan Yu (SYSU) Han et al. , 1810.04679, JHEP; Cai, ZHY , Zhang, 1705.07921, NPB; Cheung et al. , 1211.4873, JHEP; “Blind spots”: particular parameter values lead to suppression Feng et al. , 1102.4331 PLB; Isospin-violating interactions with protons and neutrons Suppress DM-nucleon scattering at zero momentum transfer Coannihilation, resonance efgect, Sommerfeld enhancement, etc. Enhance DM annihilation at the freeze-out epoch [Cai, ZHY , Zhang, 1705.07921, NPB] 3 / 26 [Frandsen et al. , 1107.2118, JHEP] Backups pNGB DM & 2HDMs Parameter Scan Conclusions Save the Thermal DM Paradigm Frandsen et al. , 1107.2118, JHEP; ··· Altmannshofer, et al. , 1907.01726, PRD; ··· QSDM, λ + = 1, λ − = 0 1.00 1.00 0.80 0.80 Current CEPC-B I - C P E C 0.60 0.60 λ 3 CP-even 0.40 0.40 LZ 0.20 0.20 500 m DM = 1000 GeV XENON 1T 0.00 0.00 300 300 400 400 500 500 600 600 700 700 800 800 900 1000 1100 1200 900 1000 1100 1200 m X (GeV)

Thermal DM Dedes & Karamitros, 1403.7744, PRD; Suppress DM-nucleon scattering at zero momentum transfer Mediated by pseudoscalars: velocity-dependent SD scattering Ipek et al. , 1404.3716, PRD; Berlin et al. , 1502.06000, PRD; Goncalves, et al. , 1611.04593, PRD; Bauer, et al. , 1701.07427, JHEP; Relevant DM couplings vanish due to special symmetries Tait & ZHY , 1601.01354, JHEP; pNGB DM Cai, ZHY , Zhang, 1611.02186, NPB; Triplet-quadruplet fermionic DM model DM-nucleon scattering vanishes at tree level DM particle is a pseudo-Nambu-Goldstone boson (pNGB) protected Zhao-Huan Yu (SYSU) pNGB DM and 2HDMs Dec 2019 [Cai, ZHY , Zhang, 1611.02186, NPB] 4 / 26 pNGB DM & 2HDMs Parameter Scan Conclusions Backups Save the Thermal DM Paradigm ··· ··· TQFDM, y 1 = y 2 = 1 10 4 10 4 CEPC-I C E P Current C - B m χ 0 1 = 1000 GeV 10 3 10 3 Custodial symmetry limit y 1 = y 2 m T (GeV) 200 10 2 10 2 50 DD-SI 20 DM couplings to h and Z vanish for m Q < m T 50 20 10 1 10 1 10 1 10 1 10 2 10 2 10 3 10 3 10 4 10 4 m Q (GeV) by an approximate global symmetry [Gross, Lebedev, Toma, 1708.02253, PRL]

Thermal DM pNGB DM Dec 2019 pNGB DM and 2HDMs Zhao-Huan Yu (SYSU) 5 / 26 Parameter Scan Conclusions pNGB DM & 2HDMs Backups pNGB Dark Matter [Gross, Lebedev, Toma, 1708.02253, PRL] Standard model (SM) Higgs doublet H , complex scalar S (SM singlet) Scalar potential respects a softly broken global U ( 1 ) symmetry S → e i α S µ 2 µ 2 2 | S | 2 + λ H 2 | H | 4 + λ S 2 | H | 2 − 2 | S | 4 + λ HS | H | 2 | S | 2 H S U ( 1 ) symmetric V 0 = − µ ′ 2 4 S 2 + H.c. S Soft breaking V soft = − Soft breaking parameter µ ′ 2 S can be made real and positive by redefjning S V soft can be justifjed by treating µ ′ 2 S as a spurion from an underlying theory H and S develop vacuum expectation values (VEVs) v and v s � � H → 1 0 S = 1 ( v s + s + i χ ) � , � v + h 2 2 The soft breaking term V soft give a mass to χ : m χ = µ ′ S χ is a stable pNGB , acting as a DM candidate

Thermal DM pNGB DM Dec 2019 pNGB DM and 2HDMs Zhao-Huan Yu (SYSU) Higgs portal interactions 6 / 26 Backups pNGB DM & 2HDMs Conclusions Parameter Scan Scalar Mixing and Interactions [Gross, Lebedev, Toma, 1708.02253, PRL] Mixing of the CP-even Higgs bosons h and s � � � m 2 � λ H v 2 λ HS vv s M 2 O T M 2 O = h 1 h , s = , λ S v 2 m 2 λ HS vv s s h 2 � � 2 λ HS vv s c θ s θ O = c θ ≡ cos θ , s θ ≡ sin θ , tan2 θ = , − s θ c θ λ S v 2 s − λ H v 2 � � � � � λ S v 2 s − λ H v 2 � h h 1 h 1 , h 2 = 1 λ H v 2 + λ S v 2 m 2 = O s ∓ , s h 2 cos2 θ 2 m f L ⊃ − λ HS v h χ 2 − λ S v s s χ 2 − ∑ v h ¯ f f 2 2 f m 2 m 2 h 1 s θ h 2 c θ m f h 1 χ 2 − h 2 χ 2 − ∑ v ( h 1 c θ + h 2 s θ ) ¯ = f f 2 v s 2 v s f

Thermal DM [Gross, Lebedev, Toma, 1708.02253, PRL] Dec 2019 pNGB DM and 2HDMs Zhao-Huan Yu (SYSU) Beyond capability of current and near future direct detection experiments Ishiwata & Toma, 1810.08139, JHEP] [Azevedo et al. , 1810.06105, JHEP; Tree-level interactions of a pNGB are generally momentum suppressed DM-nucleon scattering cross section vanishes at tree level pNGB DM DM-quark scattering amplitude from Higgs portal interactions DM-quark interactions induce DM-nucleon scattering in direct detection 7 / 26 pNGB DM & 2HDMs DM-nucleon Scattering Backups Conclusions Parameter Scan χ χ m 2 m 2 � � m q s θ c θ h 1 h 2 M ( χ q → χ q ) ∝ − t − m 2 t − m 2 vv s h 1 h 2 h 1 , h 2 k → 0 = 0 t ( m 2 h 1 − m 2 h 2 ) m q s θ c θ = . ( t − m 2 h 1 )( t − m 2 vv s h 2 ) q q Zero momentum transfer limit t = k 2 → 0 , M ( χ q → χ q ) → 0 One-loop corrections typically lead to σ SI χ N ≲ O ( 10 − 50 ) cm 2

Thermal DM Multiple pNGBs constituting multi-component dark matter Dec 2019 pNGB DM and 2HDMs Zhao-Huan Yu (SYSU) How are the constraints from indirect detection ? Can the observed relic abundance be obtained via the thermal mechanism? LHC experiments constrain such a model? How do current Higgs measurements in the zero momentum transfer? Does DM-nucleon scattering still vanish at We extend the study to two-Higgs-doublet models (2HDMs) Karamitros, 1901.09751, PRD] pNGB DM [Alanne et al. , 1812.05996, PRD; Generalizations Backups Conclusions Parameter Scan pNGB DM & 2HDMs 8 / 26 Generalize the softly broken global U ( 1 ) to O ( N ) , SU ( N ) or U ( 1 ) × S N Φ 1 Φ 2 H →

Thermal DM Two common assumptions for 2HDMs Dec 2019 pNGB DM and 2HDMs Zhao-Huan Yu (SYSU) pNGB DM 9 / 26 pNBG DM and Two Higgs Doublets pNGB DM & 2HDMs Parameter Scan Conclusions Backups Two Higgs doublets Φ 1 and Φ 2 with Y = 1 / 2 , complex scalar singlet S Scalar potential respects a softly broken global U ( 1 ) symmetry S → e i α S CP is conserved in the scalar sector There is a Z 2 symmetry Φ 1 → − Φ 1 or Φ 2 → − Φ 2 forbidding quartic terms that are odd in Φ 1 or Φ 2 , but it can be softly broken by quadratic terms Scalar potential constructed with Φ 1 and Φ 2 2 Φ 1 ) + λ 1 2 | Φ 1 | 4 + λ 2 11 | Φ 1 | 2 + m 2 22 | Φ 2 | 2 − m 2 V 1 = m 2 12 ( Φ † 1 Φ 2 + Φ † 2 | Φ 2 | 4 1 Φ 2 | 2 + λ 5 + λ 3 | Φ 1 | 2 | Φ 2 | 2 + λ 4 | Φ † 1 Φ 2 ) 2 + ( Φ † 2 [( Φ † 2 Φ 1 ) 2 ] U ( 1 ) symmetric potential terms involving S S | S | 2 + λ S 2 | S | 4 + κ 1 | Φ 1 | 2 | S | 2 + κ 2 | Φ 2 | 2 | S | 2 V 2 = − m 2 m ′ 2 4 S 2 + H.c. S Quadratic term softly breaking the global U ( 1 ) : V soft = −

Thermal DM pNGB DM Dec 2019 pNGB DM and 2HDMs Zhao-Huan Yu (SYSU) 10 / 26 Scalars pNGB DM & 2HDMs Conclusions Parameter Scan Backups Φ 1 , Φ 2 , and S develop VEVs v 1 , v 2 and v s � � � � ϕ + ϕ + S = v s + s + i χ 1 � 2 � Φ 1 = Φ 2 = � , , ( v 1 + ρ 1 + i η 1 ) / 2 ( v 2 + ρ 2 + i η 2 ) / 2 2 χ is a stable pNGB with m χ = m ′ S , acting as a DM candidate Mass terms for charged scalars and CP -odd scalars �� �� ϕ + � � �� − 1 12 − 1 v 2 / v 1 ϕ − ϕ − m 2 1 − L mass ⊃ 2 ( λ 4 + λ 5 ) v 1 v 2 1 , ϕ + 2 − 1 v 1 / v 2 2 �� �� � + 1 v 2 / v 1 − 1 η 1 � 2 ( m 2 12 − λ 5 v 1 v 2 ) η 1 , η 2 − 1 v 1 / v 2 η 2 � � � � � � � � � � ϕ + G + G 0 η 1 − s β tan β = v 2 c β 1 = R ( β ) , = R ( β ) , R ( β ) = , ϕ + H + η 2 a s β c β v 1 2 G ± and G 0 are massless Nambu-Goldstone bosons eaten by W ± and Z H ± and a are physical states v 2 1 + v 2 v 2 1 + v 2 � � m 2 m 2 12 − 1 m 2 v 1 v 2 ( m 2 12 − λ 5 v 1 v 2 ) H + = 2 2 ( λ 4 + λ 5 ) v 1 v 2 , a = 2 v 1 v 2