Inert Doublet Model:

Inert Doublet Model: Dark Matter Implication and Collider Phenomenology Shufang Su U. of Arizona S. Su In collaboration with E. Dolle, X. Miao and B. Thomas

Inert Doublet Model Introduce another Higgs field that only couples to gauge sector impose Z2 parity: SM particles +, extra Higgs: ( ) H H 1 = H + SM H 2 = (S + ia)/ 2 lightest one: DM candicate Inert Doublet Model (IDM) V = µ 2 1 H 1 2 + µ 2 2 H 2 2 + λ 1 H 1 4 + λ 2 H 2 4 + λ 3 H 1 2 H 2 2 + λ 4 H 1 H 2 2 + λ 5 2 [ ] (H 1 H 2) 2 + h.c.. (µ 2 1, µ2 2, λ 1, λ 2, λ 3, λ 4, λ 5 ). (v, m h, m S, δ 1, δ 2, λ 2, λ L ). S. Su 2

Inert Doublet Model Introduce another Higgs field that only couples to gauge sector impose Z2 parity: SM particles +, extra Higgs: ( ) H H 1 = H + SM H 2 = (S + ia)/ 2 lightest one: DM candicate Inert Doublet Model (IDM) V = µ 2 1 H 1 2 + µ 2 2 H 2 2 + λ 1 H 1 4 + λ 2 H 2 4 + λ 3 H 1 2 H 2 2 + λ 4 H 1 H 2 2 + λ 5 2 [ ] (H 1 H 2) 2 + h.c.. (µ 2 1, µ2 2, λ 1, λ 2, λ 3, λ 4, λ 5 ). (v, m h, m S, δ 1, δ 2, λ 2, λ L ). δ1=mh±ms S. Su 2

Inert Doublet Model Introduce another Higgs field that only couples to gauge sector impose Z2 parity: SM particles +, extra Higgs: ( ) H H 1 = H + SM H 2 = (S + ia)/ 2 lightest one: DM candicate Inert Doublet Model (IDM) V = µ 2 1 H 1 2 + µ 2 2 H 2 2 + λ 1 H 1 4 + λ 2 H 2 4 + λ 3 H 1 2 H 2 2 + λ 4 H 1 H 2 2 + λ 5 2 [ ] (H 1 H 2) 2 + h.c.. (µ 2 1, µ2 2, λ 1, λ 2, λ 3, λ 4, λ 5 ). (v, m h, m S, δ 1, δ 2, λ 2, λ L ). δ1=mh±ms δ2=mams S. Su 2

Inert Doublet Model Introduce another Higgs field that only couples to gauge sector impose Z2 parity: SM particles +, extra Higgs: ( ) H H 1 = H + SM H 2 = (S + ia)/ 2 lightest one: DM candicate Inert Doublet Model (IDM) V = µ 2 1 H 1 2 + µ 2 2 H 2 2 + λ 1 H 1 4 + λ 2 H 2 4 + λ 3 H 1 2 H 2 2 + λ 4 H 1 H 2 2 + λ 5 2 [ ] (H 1 H 2) 2 + h.c.. (µ 2 1, µ2 2, λ 1, λ 2, λ 3, λ 4, λ 5 ). (v, m h, m S, δ 1, δ 2, λ 2, λ L ). δ1=mh±ms δ2=mams SSh coupling λ L = λ 3 + λ 4 + λ 5 S. Su 2

Constraints Vacuum stability Perturbativity Dark matter direct detection W and Z decay width W S/A + H ±, Z S+A, H + H LEP II constraints Neutral and charged Higgs searches at LEP and Tevatron: does not apply rely on VVh coupling and the couplings of Higgses to fermions S. Su 3

Constraints LEP II constraints MSSM searches: e + e χ1 0 χ2 0 with χ2 0 χ1 0 qq/µµ/ee similar to e + e SA with A Sqq/µµ/ee 110 100 LEP excluded mass H 0 [GeV] 90 80 70 60 50 40 LEP II energy reach 30 20 10 LEP I excluded 0 0 50 100 150 200 mass A 0 [GeV] E. Lundstrom, M. Gustafsson and J. Edsjo, 0810.3924 MSSM searches: e + e χ1 + χ1 similar to e + e H + H mh± 70 GeV S. Su 4

Constraints LEP II constraints MSSM searches: e + e χ1 0 χ2 0 with χ2 0 χ1 0 qq/µµ/ee similar to e + e SA with A Sqq/µµ/ee 110 100 LEP excluded mass H 0 [GeV] 90 80 70 60 50 40 LEP II energy reach LEP I ms +ma < mz excluded 30 20 10 LEP I excluded 0 0 50 100 150 200 mass A 0 [GeV] E. Lundstrom, M. Gustafsson and J. Edsjo, 0810.3924 MSSM searches: e + e χ1 + χ1 similar to e + e H + H mh± 70 GeV S. Su 4

Constraints LEP II constraints MSSM searches: e + e χ1 0 χ2 0 with χ2 0 χ1 0 qq/µµ/ee similar to e + e SA with A Sqq/µµ/ee 110 100 LEP excluded 90 mass H 0 [GeV] 80 70 60 50 40 30 LEP II energy reach LEP II δ2 > 8 GeV ms < 80 GeV ma < 100 GeV excluded LEP I ms +ma < mz excluded 20 10 LEP I excluded 0 0 50 100 150 200 mass A 0 [GeV] E. Lundstrom, M. Gustafsson and J. Edsjo, 0810.3924 MSSM searches: e + e χ1 + χ1 similar to e + e H + H mh± 70 GeV S. Su 4

Constraints LEP II constraints MSSM searches: e + e χ1 0 χ2 0 with χ2 0 χ1 0 qq/µµ/ee similar to e + e SA with A Sqq/µµ/ee 110 100 LEP excluded 90 δ2 < 8 GeV ms +ma > mz allowed mass H 0 [GeV] 80 70 60 50 40 30 LEP II energy reach LEP II δ2 > 8 GeV ms < 80 GeV ma < 100 GeV excluded LEP I ms +ma < mz excluded 20 10 LEP I excluded 0 0 50 100 150 200 mass A 0 [GeV] E. Lundstrom, M. Gustafsson and J. Edsjo, 0810.3924 MSSM searches: e + e χ1 + χ1 similar to e + e H + H mh± 70 GeV S. Su 4

Electroweak Precision Test Electroweak precision test H 2 = ( H + (S + ia)/ 2 ) 400 mh=120 GeV 0.4 m t = 172.7 ± 2.9 GeV m h = 114...1000 GeV 400 mh=500 GeV 350 300 10 GeV 40 GeV 75 GeV 600 GeV 0.2 U=0 350 300 10 GeV 40 GeV 75 GeV 600 GeV! 2 [GeV] 250 200 150 100 T 0 0.2! 2 [GeV] 250 200 150 m t 100 50 0.4 0.4 0.2 0 0.2 0.4 0 0 50 100 150 200 250 300 350 400! 1 [GeV] m h 50 68 % CL 0 0 50 100 150 200 250 300 350 400! 1 [GeV] S. Su 5 gure 1: (Adapted from [8].) Dependence of the S, T parameters on the Higgs mass. The thick

Electroweak Precision Test Electroweak precision test H 2 = ( H + (S + ia)/ 2 ) mh=120 GeV mh=500 GeV 400 400 350 300 10 GeV 40 GeV 75 GeV 600 GeV 350 300 10 GeV 40 GeV 75 GeV 600 GeV! 2 [GeV] 250 200 150! 2 [GeV] 250 200 150 100 100 50 50 0 0 50 100 150 200 250 300 350 400! 1 [GeV] 0 0 50 100 150 200 250 300 350 400! 1 [GeV] S. Su 5

Dark matter relic density coannihilation of S, A coannihilation of S, H ± δ2=mams δ1=mh±ms δ2 A S δ1 H ± Use MicrOMEGA /CalCHEP to calculate the relic density low mass region: ms < 100 GeV high mass region: ms > 400 GeV S. Su 6

Low mass region: vary δ2 δ1=mh±ms = 50 GeV, λl=0.01 0.3 0.25 10 7 5 0.2! h 2 0.15 0.1 δ2=mams = 10 GeV 0.05 0 δ2=mams = 7 GeV mh=120 δ2=mams = 5 GeV 10 20 30 40 50 60 70 80 90 100 m S S. Su 7

Low mass region: vary δ2 δ1=mh±ms = 50 GeV, λl=0.01 0.3 10 A 0.25 q 7 5 0.2 S! h 2 0.15 Z q 0.1 0.05 0 δ2=mams = 10 GeV coannihilation δ2=mams = 7 GeV mh=120 δ2=mams = 5 GeV 10 20 30 40 50 60 70 80 90 100 m S zpole S. Su 7

Low mass region: vary δ2 δ1=mh±ms = 50 GeV, λl=0.01 0.3 0.25 10 7 5 0.2! h 2 0.15 0.1 0.05 0 δ2=mams = 10 GeV coannihilation δ2=mams = 7 GeV mh=120 δ2=mams = 5 GeV 10 20 30 40 50 60 70 80 90 100 m S zpole S. Su 7

Low mass region: vary δ2 δ1=mh±ms = 50 GeV, λl=0.01 0.3 Ŝ q, l 10 0.25 h SM 7 5 0.2 Ŝ q, l! h 2 0.15 0.1 0.05 0 δ2=mams = 10 GeV coannihilation δ2=mams = 7 GeV mh=120 δ2=mams = 5 GeV 10 20 30 40 50 60 70 80 90 100 m S zpole S. Su 7 hpole

Low mass region: vary δ2 δ1=mh±ms = 50 GeV, λl=0.01 0.3 0.25 10 7 5 0.2! h 2 0.15 0.1 0.05 0 δ2=mams = 10 GeV coannihilation δ2=mams = 7 GeV mh=120 δ2=mams = 5 GeV 10 20 30 40 50 60 70 80 90 100 m S zpole S. Su 7 hpole

Low mass region: vary δ2 δ1=mh±ms = 50 GeV, λl=0.01 S W 0.3 0.25 10 S 7 5 S H W W S W H ± 1 0.2 S W S W! h 2 0.15 0.1 0.05 0 δ2=mams = 10 GeV coannihilation δ2=mams = 7 GeV mh=120 δ2=mams = 5 GeV 10 20 30 40 50 60 70 80 90 100 m S zpole S. Su 7 hpole

Low mass region: vary δ2 δ1=mh±ms = 50 GeV, λl=0.01 S W 0.3 0.25 10 S 7 5 S H W W S W H ± 1 0.2 S W S W! h 2 0.15 0.1 0.05 0 δ2=mams = 10 GeV coannihilation SS ZZ δ2=mams = 7 GeV mh=120 δ2=mams = 5 GeV 10 20 30 40 50 60 70 80 90 100 m S zpole S. Su 7 hpole

Low mass region: vary δ2 δ1=mh±ms = 50 GeV, λl=0.01 0.3 0.25 10 7 5 0.2! h 2 0.15 0.1 0.05 0 δ2=mams = 10 GeV coannihilation SS ZZ δ2=mams = 7 GeV mh=120 δ2=mams = 5 GeV 10 20 30 40 50 60 70 80 90 100 m S zpole S. Su 7 hpole

Viable region for relic density DM SM h ms δ1, δ2 λl (I) low ms low mh 30 60 GeV 50 90 GeV 0.2 to 0 (II) 60 80 GeV at least one is large (III) high mh 50 75 GeV large δ1 δ2 < 8 GeV 0.2 to 0.2 1 to 3 (IV) 75 GeV large δ1, δ2 1 to 3 (V) high ms low mh 500 1000 GeV small δ1, δ2 0.2 to 0.3 most of the m S region between 40 GeV and 60 GeV, the relic density for the dark matter is too small due to the large coannihilation SA cross section. However, there is a viable region for 60 GeV < m S < 80 GeV with λ L in the region of ±0.1.! L 0.5 0.4 0.3 0.2 0.1 0!0.1!0.2!0.3!0.4!0.5 10 0.5 10 0.5 10 +3, (I) 8 0.4 8 0.4 8 +3* 6 0.3 (II) 6 0.3 (III) 6 (IV) +34 (V) 4 0.2 4 0.2 4 +32 2 0.1 2 0.1 2 +31 0 0 0 0 0 +!2!0.1!2!0.1!2!+31!4!0.2!4!0.2!4!+32!6!0.3!6!0.3!6!+34!8!0.4!8!0.4!8!+3* 10 20 30!10!0.5!10!0.5!10!+3, 40 50 60 70 80 90 100 10 201030204030 5040 6050 7060 8070 9080 100 90 100 10 2010 3020 40 30 50 40 60 50 70 60 80 70 90 80 100 90 100 10 20 30 40 50 60 70 80 90 100 *++,++ ++.++ /++ 0++ 1+++ 11++ 12++ m [GeV] m [GeV] m [GeV] m [GeV] S! #$%&'( S m S [GeV] S m S [GeV] S "! L! L! L! L! L! ) blue curves) in m S λ L plane for mfig. h =120 6: FIG. GeV. WMAP 4: WMAP 3σ allowed 3σ allowed region region (enclosed (enclosed by blue by blue curves) curves) in min S m S λ L plane λ L plane for for m h m=500 h =120 GeV. GeV. 50, 50) GeV (left plot), (70,70) GeV (right plot). ical and experimental constraints; see Shaded caption Shaded regions of regions are excluded are excluded by various by various theoretical theoretical and and experimental constraints; see see caption caption of of Fig. 3 for Fig. explanation. 3 for explanation. S. Su The mass Thesplittings mass splittings are chosen are chosen to be (δ to 1, be δ 2 )(δ = 1, (250, δ 2 ) = 110) (10, 50) GeV GeV (left (left plot), plot), (180,8) (10,10) GeV GeV (right (right plot). plot). 8

Collider signatures +W (*) H ± A + Z (*) +W (*) pp SA SSZ ( ), SSW ( ) W ( ) S pp SH ± SSW ( ), SSZ ( ) W ( ) pp AH ± SSZ ( ) W ( ), SSZ ( ) Z ( ) W ( ), SSW ( ) W ( ) W ( ) pp H + H SSW ( ) W ( ), SSW ( ) W ( ) Z ( ), SSW ( ) W ( ) Z ( ) Z ( ). Signatures: jets + leptons + missing ET jets and leptons could be soft for small splittings S. Su 9

Leptonic signals Focus on purely leptonic signals single lepton: SH ± dilepton: SA, H + H trilepton: AH ±... Benchmark points Dominant background WW, ZZ/γ, WZ/γ, tt,... mh (GeV) ms (GeV) (δ1, δ2) (GeV) λl LH1 150 40 (100,100) 0.275 LH2 120 40 (70,70) 0.15 LH3 120 82 (50,50) 0.2 LH4 120 73 (10,50) 0 LH5 120 79 (50,10) 0.18 HH1 500 76 (250,100) 0 HH2 500 76 (200,30) 0 S. Su 10

Dilepton signal from Z* Dilepton signals: pp SA SSZ (*) SSl + l pp H + H SSW (*) W (*) SSl + l νν Signal: pp SA SSZ (*) SSl + l Two isolated opposite charge e or µ with missing ET, no hard jets. Background: from IDM pp H + H SSW (*) W (*) SSl + l νν from SM pp WW l + l νν pp ZZ/γ l + l νν tt, WZ, Wt, Zt... with missing lepton or jets S. Su 11

Dilepton signal: LH1 LH1: ms = 40 GeV, (δ1, δ2)=(100,100) GeV Signal: pp SA SSZ SSl + l, l=e,µ Two isolated opposite charge e or µ with missing ET, no hard jets. 1/σ d σ/ d Mll ( &!! &!!& M ll W + W ZZ/γ t t W + Z/γ W + t SA ) &!!" S. &!!' Su ) 12! "! #! $! %! &!! &"! &#! &$! M ll

Dilepton signal: LH1 LH1: ms = 40 GeV, (δ1, δ2)=(100,100) GeV Signal: pp SA SSZ SSl + l, l=e,µ Two isolated opposite charge e or µ with missing ET, no hard jets. 1/σ d σ/ d Mll ( &!! &!!& M ll W + W ZZ/γ t t W + Z/γ W + t SA ) &!!" S. &!!' Su ) 12! "! #! $! %! &!! &"! &#! &$! M ll

Dilepton signal: LH1 LH1: ms = 40 GeV, (δ1, δ2)=(100,100) GeV I+II I+II+III Cuts PT l >15 GeV, ηl <2.5 ΔR(ll)>0.4 no jets with PT i >20 GeV, ηj <3 MET >100 GeV HT >200 GeV 80 GeV < Mll < 100 GeV S (fb) SA 6.550 3.68 B (fb) H + H 0.496 0.040 WW 345.1 12.41 ZZ /γ 82.69 39.86 tt 91.20 7.37 WZ 104.35 37.55 Wt 68.68 15.00 total 102.18 L=100 fb 1 S/B 0.04 s/ (B) 3.64 S. Su 13

Low mass region: LH4 LH4: ms = 73 GeV, (δ1, δ2)=(10,50) GeV Signal: pp SA SSZ* SSl + l, l=e,µ Two isolated opposite charge e or µ with large missing ET, no hard jets. 1/σ d σ/ d Mll &!! &!!& M ll W + W ZZ/γ t t W + Z/γ W + t SA ) &!!" S. Su 14 &!!' )! "! #! $! %! &!! &"! &#! &$! M ll

Low mass region: LH4 LH4: ms = 73 GeV, (δ1, δ2)=(10,50) GeV Signal: pp SA SSZ* SSl + l, l=e,µ Two isolated opposite charge e or µ with large missing ET, no hard jets. 1/σ d σ/ d Mll &!! &!!& M ll W + W ZZ/γ t t W + Z/γ W + t SA ) &!!" S. Su 14 &!!' )! "! #! $! %! &!! &"! &#! &$! M ll

Low mass region: LH4 LH4: ms = 73 GeV, (δ1, δ2)=(10,50) GeV Signal: pp SA SSZ* SSl + l, l=e,µ Two isolated opposite charge e or µ with large missing ET, no hard jets. 1/σ d σ/ d Mll &!! &!!& M ll W + W ZZ/γ t t W + Z/γ W + t SA ) &!!" S. Su 14 &!!' )! "! #! $! %! &!! &"! &#! &$! M ll

Low mass region: LH4 LH4: ms = 73 GeV, (δ1, δ2)=(10,50) GeV Signal: pp SA SSZ* SSl + l, l=e,µ Two isolated opposite charge e or µ with large missing ET, no hard jets.!" " Cos( φ ll ) * 1/σ d σ/ d cos ΔΦll!"!!!"!' W + W ZZ/γ t t W + Z/γ W + t S. Su 15 SA!"!( *!!!"#$!"#%!"#&!"#' " "#' "#& "#% "#$! Cos( φ ll )

Low mass region: LH4 LH4: ms = 73 GeV, (δ1, δ2)=(10,50) GeV Signal: pp SA SSZ* SSl + l, l=e,µ Two isolated opposite charge e or µ with large missing ET, no hard jets.!" " Cos( φ ll ) * 1/σ d σ/ d cos ΔΦll!"!!!"!' W + W ZZ/γ t t W + Z/γ W + t S. Su 15 SA!"!( *!!!"#$!"#%!"#&!"#' " "#' "#& "#% "#$! Cos( φ ll )

Low mass region: LH4 LH4: ms = 73 GeV, (δ1, δ2)=(10,50) GeV I+II I+II+III Cuts PT l >15 GeV, ηl <2.5 ΔR(ll)>0.4 no jets with PT i >20 GeV, ηj <3 MET >90 GeV HT >200 GeV 20 GeV< Mll < 50 GeV cos(ϕll)>0.7 ΔR(ll)<0.8 S (fb) SA 2.48 0.22 B (fb) H + H <0.0001 <0.001 WW 345.14 0.04 ZZ /γ 82.69 0.16 tt 91.20 0.09 WZ 104.35 0.07 Wt 68.68 0.09 total 0.47 L=100 fb 1 S/B 0.47 s/ (B) 3.23 S. Su 16

Low mass region: LH2 LH2: m S = 40 GeV, (δ1, δ2)=(70,70) GeV I+II I+II+III Cuts PT l >15 GeV, ηl <2.5 ΔR(ll)>0.4 no jets with PT i >20 GeV, ηj <3 MET >50 GeV HT >150 GeV Mll < 70 GeV cos(ϕll)>0.7 ΔR(ll)<1.2 S (fb) SA 7.392 0.97 B (fb) H + H 0.568 <0.001 WW 345.1 0.09 ZZ /γ 82.69 0.28 tt 91.20 0.23 WZ 104.35 0.14 Wt 68.68 0.13 total 0.88 L=100 fb 1 S/B 1.11 s/ (B) 10.37 S. Su 17

Dilepton signal: LH5 LH5: ms = 79 GeV, (δ1, δ2)=(50,10) GeV Signal: pp SA SSZ* SSl + l, l=e,µ Soft leptons. Difficult. S. Su 18

Collider reach @ LHC pp SA SSZ (*) SSl + l ms (δ1, δ2) S B S/B S/ (B) GeV GeV fb fb L=100 fb 1 LH1 40 (100,100) 3.68 102.18 0.04 3.64 LH2 40 (70,70) 0.97 0.88 1.11 10.37 LH3 82 (50,50) 0.19 0.47 0.40 2.75 LH4 73 (10,50) 0.22 0.47 0.47 3.23 LH5 79 (50,10) 0.33 0.30 0.09 0.52 HH1 76 (250,100) 0.69 27.17 0.03 1.33 HH2 76 (200,30) 1.22 27.65 0.04 2.32 S. Su 19

Collider reach @ LHC pp SA SSZ (*) SSl + l ms (δ1, δ2) S B S/B S/ (B) GeV GeV fb fb L=100 fb 1 LH1 40 (100,100) 3.68 102.18 0.04 3.64 LH2 40 (70,70) 0.97 0.88 1.11 10.37 LH3 82 (50,50) 0.19 0.47 0.40 2.75 LH4 73 (10,50) 0.22 0.47 0.47 3.23 LH5 79 (50,10) 0.33 0.30 0.09 0.52 HH1 76 (250,100) 0.69 27.17 0.03 1.33 HH2 76 (200,30) 1.22 27.65 0.04 2.32 S. Su 19

Collider reach @ LHC pp SA SSZ (*) SSl + l ms (δ1, δ2) S B S/B S/ (B) GeV GeV fb fb L=100 fb 1 LH1 40 (100,100) 3.68 102.18 0.04 3.64 LH2 40 (70,70) 0.97 0.88 1.11 10.37 LH3 82 (50,50) 0.19 0.47 0.40 2.75 LH4 73 (10,50) 0.22 0.47 0.47 3.23 LH5 79 (50,10) 0.33 0.30 0.09 0.52 HH1 76 (250,100) 0.69 27.17 0.03 1.33 HH2 76 (200,30) 1.22 27.65 0.04 2.32 S. Su 19

Conclusions IDM: provide a scalar WIMP dark matter candidate Viable regions of parameter spaces provide correct relic density DM SM h ms δ1, δ2 λl (I) low ms low mh 30 60 GeV 50 90 GeV 0.2 to 0 (II) 60 80 GeV at least one is large (III) high mh 50 75 GeV large δ1 δ2 < 8 GeV 0.2 to 0.2 1 to 3 (IV) 75 GeV large δ1, δ2 1 to 3 (V) high ms low mh 500 1000 GeV small δ1, δ2 0.2 to 0.3 Rich collider phenomenology dilepton signal (from SA) observable for not too small δ2. S. Su 20