Constraints on new phenomena through Higgs coupling measurements and - - PowerPoint PPT Presentation
Constraints on new phenomena through Higgs coupling measurements and invisible decays with the ATLAS detector G. Carrillo-Montoya on behalf of the ATLAS Collaboration EPS-HEP-2015 Vienna - Austria July 24th - 2015 - CERN, G. Carrillo-Montoya
EPS-HEP-2015 Vienna - Austria July 24th - 2015
EPS - Vienna 2015 1/19
NEW https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/HIGG-2015-03
) µ Signal strength (
1 − 1 2 3
ATLAS
= 7 TeV, 4.5-4.7 fb s
= 8 TeV, 20.3 fb s
= 125.36 GeV
H
m
0.26
+
= 1.17 µ γ γ → H
0.080.34
+
= 1.46 µ ZZ* → H
0.110.21
+
= 1.18 µ WW* → H
0.090.37
+
= 1.44 µ τ τ → H
0.100.37
+
= 0.63 µ b b → H
0.073.7
+
= -0.7 µ µ µ → H
0.44.5
+
= 2.7 µ γ Z → H
0.30.14
+
= 1.18 µ
Combined
0.07Total uncertainty µ
σ 1 ±
(stat.) σ
)
theory sys inc.
(
σ (theory) σ
0.5 1 1.5 2 2.5 3
μttH = 1.81 ± 0.80 μVH = 0.80 ± 0.36 μVBF = 1.23 ± 0.32 μggF = 1.23+0.23
−0.20
Signal strength (μ) ATLAS
√s = 7 TeV, 4.5 − 4.7 fb−1 √s = 8 TeV, 20.3 fb−1
mH = 125.36 GeV
68% CL: 95% CL: ggF+ttH f
µ 2 − 1 − 1 2 3 4 5 6 7
VBF+VH f
µ 2 − 1 − 1 2 3 4 5 6 7 ATLAS
= 7 TeV, 4.5-4.7 fb s
= 8 TeV, 20.3 fb s = 125.36 GeV
Hm WW* → H ZZ* → H bb → H γ γ → H τ τ → H Standard Model Best fit 68% CL 95% CL
arXiv:1507.04548
EPS - Vienna 2015 3/19
Disentangle individual couplings from production and decays Assumptions (LO-inspired benchmark) arxiv:1307.1427): Higgs → single resonance Narrow width approximation σ × BR(i → H → f) = σi ·Γf
ΓH
No modification on the Tensor structure of the couplings (only absolute values are modified) Acceptance unchanged Factors κi such as
σ×BR(gg→H→γγ) (σgg×BR(H→γγ))SM = κ2
g ˙
κ2
γ
κ2
h
V
κ 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
F
κ 4 − 3 − 2 − 1 − 1 2 3 4 ATLAS
= 7 TeV, 4.5-4.7 fb s
= 8 TeV, 20.3 fb s = 125.36 GeV
H
m γ γ → H ZZ* → H WW* → H τ τ → H bb → H Combined SM 68% CL Best fit 95% CL
In this plot, no invisible/undetected decays assumed Note that κ2
g and κ2 γ are loop-induced
depending on (κt, κb and κW).
EPS - Vienna 2015 4/19
Higgs couplings and internal structure Constrains on Multiple Higgs bosons Probing Invisible Higgs boson decays Mass scaling Minimal Composite Higgs Model
1
Higgs couplings and internal structure Mass scaling Minimal Composite Higgs Model
2
Constrains on Multiple Higgs bosons Real Electroweak Singlet 2HDM Simplified MSSM
3
Probing Invisible Higgs boson decays Direct (Invisible) searches Combination of indirect (visible channels) and direct (invisible searches)
EPS - Vienna 2015 5/19
Higgs couplings and internal structure Constrains on Multiple Higgs bosons Probing Invisible Higgs boson decays Mass scaling Minimal Composite Higgs Model
Each coupling in terms of vev (v ≈ 246 GeV) and ǫ (note that SM: ǫ → 0) κf,i = v
mǫ
f,i
M1+ǫ
κV,j = v
m2ǫ
V,j
M1+2ǫ
ε : 0.018 ± 0.039, M : 224+14
−12 GeV Particle mass [GeV]
10 1 10
2
10 v
V
m
V
κ
v
F
m
F
κ
10
10
10 1 Z W t b τ µ ATLAS
= 7 TeV, 4.5-4.7 fb s
= 8 TeV, 20.3 fb s Observed SM Expected
∈ 0.1 − 0.1 0.2 0.3 0.4 M [GeV] 200 220 240 260 280 300
Preliminary ATLAS
= 7 TeV, 4.5-4.7 fb s
= 8 TeV, 20.3 fb s Best fit
SM
arXiv:1507.04548 HIGGS-2015-03
EPS - Vienna 2015 6/19
Higgs couplings and internal structure Constrains on Multiple Higgs bosons Probing Invisible Higgs boson decays Mass scaling Minimal Composite Higgs Model
Scalar Naturalness: Higgs → composite pseudo Nambu-Goldstone boson
95% CL obs (exp): MCHM4:f > 710(510) GeV; MCHM5:f > 780(600) GeV
Higgs couplings modified as function of compositeness scale f ξ = v2/f 2
κ = κV = κF = √1 − ξ
κV = √1 − ξ κF =
1−2ξ
√
1−ξ
SM recovered in the limit ξ → 0, namely f → ∞.
V
κ 0.8 0.9 1 1.1 1.2 1.3
F
κ 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Best fit SM
ATLAS Preliminary
= 7 TeV, 4.5-4.7 fb s
= 8 TeV, 20.3 fb s =0.1 ξ =0.2 ξ =0.3 ξ =0.0 ξ =0.1 ξ =0.2 ξ =0.3 ξ MCHM4 MCHM5
EPS - Vienna 2015 7/19
Higgs couplings and internal structure Constrains on Multiple Higgs bosons Probing Invisible Higgs boson decays Real Electroweak Singlet 2HDM Simplified MSSM
1
Higgs couplings and internal structure Mass scaling Minimal Composite Higgs Model
2
Constrains on Multiple Higgs bosons Real Electroweak Singlet 2HDM Simplified MSSM
3
Probing Invisible Higgs boson decays Direct (Invisible) searches Combination of indirect (visible channels) and direct (invisible searches)
EPS - Vienna 2015 8/19
Higgs couplings and internal structure Constrains on Multiple Higgs bosons Probing Invisible Higgs boson decays Real Electroweak Singlet 2HDM Simplified MSSM
Simplest extension: additional real EW singlet, mH heavier than 125 GeV Couplings → mixing gives: κ2 + κ′2 = 1 Coupling (and signal strength as predicted by heavier SM-like Higgs) modified by allowing new decays BRH,new, like H → hh
2
’ κ
=0.025
H
µ =0.05
H
µ =0.075
H
µ =0.1
H
µ =0.15
H
µ =0.05
H , S M
Γ /
H
Γ =0.15
H , S M
Γ /
H
Γ =0.3
H , S M
Γ /
H
Γ =1.0
H,SM
Γ /
H
Γ
ATLAS Preliminary
= 7 TeV, 4.5-4.7 fb s
= 8 TeV, 20.3 fb s EW singlet
SM <0.12
2
’ κ
<0.23
2
’ κ
0.05 0.1 0.15 0.2 0.25
H,new
BR 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
95%CL: κ′2 < 0.12(0.23)
EPS - Vienna 2015 9/19
Higgs couplings and internal structure Constrains on Multiple Higgs bosons Probing Invisible Higgs boson decays Real Electroweak Singlet 2HDM Simplified MSSM
Two identical complex scalar fields(SU(2)) The 2HDM scalar potential → Z2 broken symmetry In the CP-conserving case, parameters can be reduced to 6: 4 masses mh, mH, mH±, mA, and 2 angles α, β tan β = v1/v2: ratio of vevs (satisfying v2
1 + v2 2 = v2 ≈ (246 GeV)2
α: mixing angle between h and H
Coupling Type I Type II Type III Type IV scale factor (fermiophobic) (MSSM-like) (lep. specific) (flipped) κV sin(β − α) sin(β − α) sin(β − α) sin(β − α) κu cos(α)/ sin(β) cos(α)/ sin(β) cos(α)/ sin(β) cos(α)/ sin(β) κd cos(α)/ sin(β) − sin(α)/ cos(β) cos(α)/ sin(β) − sin(α)/ cos(β) κl cos(α)/ sin(β) − sin(α)/ cos(β) − sin(α)/ cos(β) cos(α)/ sin(β)
Assumptions (for interpretations): 125 GeV is the light higgs, no radiative corrections, only SM decays. Convention: sin(β − α) ≥ 0 SM-like alignment limit retrieved at cos(β − α) = 0
EPS - Vienna 2015 10/19
Higgs couplings and internal structure Constrains on Multiple Higgs bosons Probing Invisible Higgs boson decays Real Electroweak Singlet 2HDM Simplified MSSM
β tan
1 −
10 1 10 ATLAS Preliminary
= 7 TeV, 4.5-4.7 fb s
= 8 TeV, 20.3 fb s
Best fit
SM 2HDM Type I
1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1
) α
cos(
4 3 2 0.4 0.3 0.2
α
β tan
1 −
10 1 10 ATLAS Preliminary
= 7 TeV, 4.5-4.7 fb s
= 8 TeV, 20.3 fb s
Best fit
SM 2HDM Type II
) β
1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1
4 3 2 0.4 0.3 0.2
EPS - Vienna 2015 11/19
Higgs couplings and internal structure Constrains on Multiple Higgs bosons Probing Invisible Higgs boson decays Real Electroweak Singlet 2HDM Simplified MSSM
) α
cos( β tan
1 −
10 1 10 ATLAS Preliminary
= 7 TeV, 4.5-4.7 fb s
= 8 TeV, 20.3 fb s
Best fit
SM 2HDM Lepton-specific
1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1
4 3 2 0.4 0.3 0.2
) α
cos( β tan
1 −
1 10 ATLAS Preliminary
= 7 TeV, 4.5-4.7 fb s
= 8 TeV, 20.3 fb s
Best fit
SM 2HDM Flipped
1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1
10
4 3 2 0.4 0.3 0.2
EPS - Vienna 2015 12/19
Higgs couplings and internal structure Constrains on Multiple Higgs bosons Probing Invisible Higgs boson decays Real Electroweak Singlet 2HDM Simplified MSSM
Assumptions: h production and decay modes as in the SM stops in ggF and γγ not included Same for light staus and charginos Decays to SUSY
Higgs decays not included for tan β > 1: mA > 370 (310) GeV
[GeV]
A
m 200 250 300 350 400 450 500 β tan 1 2 3 4 5 10 20 30 40 Preliminary ATLAS
=7 TeV, 4.5-4.7 fb s
=8 TeV, 19.5-20.3 fb s hMSSM, 95% CL limits
]
d
, k
u
, k
V
Obs., h couplings [k Exp. τ τ → Obs., A/H Exp. bb ν ν ll/ → Zh → Obs., A Exp. ν ν 4l, ll qq/bb/ → ZZ → Obs., H Exp. ν qq/l ν l → WW → Obs., H Exp. ν τ →
+
Obs., H Exp.
EPS - Vienna 2015 13/19
Higgs couplings and internal structure Constrains on Multiple Higgs bosons Probing Invisible Higgs boson decays Direct (Invisible) searches Combination of indirect (visible channels) and direct (invisible searches)
1
Higgs couplings and internal structure Mass scaling Minimal Composite Higgs Model
2
Constrains on Multiple Higgs bosons Real Electroweak Singlet 2HDM Simplified MSSM
3
Probing Invisible Higgs boson decays Direct (Invisible) searches Combination of indirect (visible channels) and direct (invisible searches)
EPS - Vienna 2015 14/19
Higgs couplings and internal structure Constrains on Multiple Higgs bosons Probing Invisible Higgs boson decays Direct (Invisible) searches Combination of indirect (visible channels) and direct (invisible searches)
More details in Philippe Calfayan talk!
ZH → (ℓℓ) INV:
VH → (jj) INV: Submitted to EPJC (2015) VBF H → INV: HIGGS-2015-YY
Results Obs. Exp. VBF h 0.30 0.35 Z(→ ℓℓ)h 0.75 0.62 V(→ jj)h 0.78 0.86 Combined 0.25 0.27
Tag events with large missing energy → use particles produced together with the Higgs Assume productions (& acceptance) as in SM h → ZZ → 4ν: 1.2×10−3 (no sensitivity)
inv
BR 0.05 0.1 0.15 0.2 0.25 0.3 0.35 1-CL
10
10
10 1 Obs. SM exp. ATLAS Preliminary
= 8 TeV, 20.3 fb s
= 7 TeV, 4.5 fb s
EPS - Vienna 2015 15/19
Higgs couplings and internal structure Constrains on Multiple Higgs bosons Probing Invisible Higgs boson decays Direct (Invisible) searches Combination of indirect (visible channels) and direct (invisible searches)
The partial widths for Higgs decays to undetectable (e.g. h → gg) assumed to be negligibly With the visible channels alone (and κV ≤ 1): BRinv < 0.49(0.48) obs (exp) Combination visible channels and invisible searches one can remove restrictions of (κV ≤ 1) Physical boundary BRinv > 0 The most general result with independent parameters:
κW, κZ, κt, κb, κτ, κµ, κg, κγ, κZγ, BRinv
95%CL limit of: 0.23 (0.24) obs (exp)
inv
BR 0.2 − 0.1 − 0.1 0.2 0.3 0.4 0.5 Λ
2 4 6 8 10
Preliminary ATLAS
= 7 TeV, 4.5-4.7 fb s
= 8 TeV, 20.3 fb s Obs.:
EPS - Vienna 2015 16/19
Higgs couplings and internal structure Constrains on Multiple Higgs bosons Probing Invisible Higgs boson decays Direct (Invisible) searches Combination of indirect (visible channels) and direct (invisible searches)
95% CL Observed Expected Assumptions Direct (invisible searches) 0.25 0.27 Productions as SM (κi = 1) Indirect (visible channels) 0.49 0.48 κZ,W ≤ 1 Combination[∗] 0.23 0.24 None[∗∗]
0.23 0.23 κZ,W ≤ 1
0.18 0.24
0.16 0.23
90% CL Observed Expected Assumptions Combination 0.22 0.23 None[∗∗]
[∗] Except VH → (jj)inv, overlapping phase-space [∗∗] Except for undetectable
EPS - Vienna 2015 17/19
Higgs couplings and internal structure Constrains on Multiple Higgs bosons Probing Invisible Higgs boson decays Direct (Invisible) searches Combination of indirect (visible channels) and direct (invisible searches)
Used 90%CL instead of 95% WIMP < mh/2 Higgs only mediator... Higgs Portal → spin dependent! Vector/Fermion(Majorana) are even more EFT dependent...
WIMP mass [GeV] 1 10
2
10
3
10 ]
2
WIMP-nucleon cross section [cm
10
10
10
10
10
10
10
10
10
10
DAMA/LIBRA (99.7% CL) CRESST II (95% CL) CDMS SI (95% CL) CoGeNT (99% CL) CRESST II (90% CL) SuperCDMS (90% CL) XENON100 (90% CL) LUX (90% CL) Scalar WIMP Majorana WIMP Vector WIMP
ATLAS Preliminary
Higgs portal model: ATLAS 90% CL in
= 7 TeV, 4.5-4.7 fb s
= 8 TeV, 20.3 fb s
]
inv
, BR
γ Z
κ ,
γ
κ ,
g
κ ,
µ
κ ,
τ
κ ,
b
κ ,
t
κ ,
Z
κ ,
W
κ [ <0.22 at 90% CL
inv
assumption: BR
W,Z
κ No
EPS - Vienna 2015 18/19
∈
0.02 0.04 0.06 0.08 0.1 0.12 0.14 M [GeV] 220 230 240 250 260 270 280
Simulation Preliminary ATLAS
b , b τ τ , µ µ , γ Z → h Combined , ZZ*, WW* γ γ → Combined h = 14 TeV s
,M] ∈ [
SM : All unc.
Ldt = 300 fb
∫
: No theo.
Ldt = 300 fb
∫
: All unc.
Ldt = 3000 fb
∫
: No theo.
Ldt = 3000 fb
∫
V
κ 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15
F
κ 0.8 0.9 1 1.1 1.2 1.3
: All unc.
Ldt = 300 fb
∫
: All unc.
Ldt = 3000 fb
∫
: No theo.
Ldt = 300 fb
∫
: No theo.
Ldt = 3000 fb
∫
Standard Model
ATLAS Simulation Preliminary = 14 TeV s
Combined , ZZ*, WW* γ γ → h b , b τ τ , µ µ , γ Z → h
=0.1 ξ =0.2 ξ =0.3 ξ =0.0 ξ =0.1 ξ MCHM 4 MCHM 5
H
µ
=0.025
2’ κ =0.05
2’ κ = . 1
2’ κ = . 2
2’ κ =0.3
2’ κ = . 6
2’ κ =1.0
2’ κ =0.05
H,SMΓ /
HΓ =0.1
H , S MΓ /
HΓ =0.2
H , S MΓ /
HΓ = . 5
H,SMΓ /
HΓ =1.0
H , S MΓ /
HΓ =5.0
H , S MΓ /
HΓ =100
H,SMΓ /
HΓ
ATLAS Simulation Preliminary
EW singlet = 14 TeV s
,ZZ*,WW* γ γ → Combined h b ,b τ τ , µ µ , γ Z → h Combined SM : All unc.
Ldt = 300 fb
∫
: No theo.
Ldt = 300 fb
∫
: All unc.
Ldt = 3000 fb
∫
: No theo.
Ldt = 3000 fb
∫ 0.05 0.1 0.15 0.2
H,new
BR 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 [GeV]
A
m 200 400 600 800 1000 1200 β tan 1 2 3 4 5 6 7 8 9 10 Simulation Preliminary ATLAS
b , b τ τ , µ µ , γ Z → h Combined , ZZ*, WW* γ γ → Combined h = 14 TeV s
]
d
κ ,
u
κ ,
V
κ Simplified MSSM [
: all unc.
Ldt = 300 fb
∫
: No theo.
Ldt = 300 fb
∫
: all unc.
Ldt = 3000 fb
∫
: No theo.
Ldt = 3000 fb
∫ ATL-PHYS-PUB-2014-017
) α
cos( β tan 0.1 0.2 0.3 0.4 1 2 3 4 10 0.4 − 0.2 − 0.2 0.4 β tan 0.1 0.2 0.3 0.4 1 2 3 4 10 0.4 − 0.2 − 0.2 0.4 β tan 0.1 0.2 0.3 0.4 1 2 3 4 10 0.4 − 0.2 − 0.2 0.4 β tan 0.1 0.2 0.3 0.4 1 2 3 4 10 0.4 − 0.2 − 0.2 0.4 ATLAS Simulation Preliminary
= 14 TeV s
Combined
,ZZ*,WW* γ γ → h b ,b τ τ , µ µ , γ Z → h SM : All unc.
Ldt = 300 fb
∫
: No theo.
Ldt = 300 fb
∫
: All unc.
Ldt = 3000 fb
∫
: No theo.
Ldt = 3000 fb
∫
2HDM Type I
) α
cos( β tan 0.1 0.2 0.3 0.4 1 2 3 4 10 0.1 − 0.1 β tan 0.1 0.2 0.3 0.4 1 2 3 4 10 0.1 − 0.1 β tan 0.1 0.2 0.3 0.4 1 2 3 4 10 0.1 − 0.1 β tan 0.1 0.2 0.3 0.4 1 2 3 4 10 0.1 − 0.1 ATLAS Simulation Preliminary
= 14 TeV s
Combined
,ZZ*,WW* γ γ → h b ,b τ τ , µ µ , γ Z → h SM : All unc.
Ldt = 300 fb
∫
: No theo.
Ldt = 300 fb
∫
: All unc.
Ldt = 3000 fb
∫
: No theo.
Ldt = 3000 fb
∫
2HDM Type II
ATL-PHYS-PUB-2014-017
Higgs discovery, great achievement of the LHC program... Precise measurements of the Higgs boson couplings let us to constrain new phenomena Understanding of the real nature of the Electroweak Symmetry Breaking → tool to explore new physics!
−12 GeV)
The LHC in Run-I...
NNLO, NNLL, EW corrections, uncertainties inclusive & exclusive PH
T , line-shape, interference, BR, etc... [link]
Nature is very kind... mH = 125.09 GeV → although not easy, many modes to study at the LHC...
√s [TeV] 7 8 13 σpp→H [pb] 17.352 22.097 50.471 σggF [pb] 15.11 (QCD)+7.1%
−7.8 PDF+7.6% −7.1%
19.24 (QCD)+7.2%
−7.8%PDF+7.5% −6.9%
43.87 (QCD)+7.5%
−7.9%PDF+7.1% −6.0%
σVBF [pb] 1.222 (QCD)+0.3%
−0.3%PDF+2.5% −2.1%
1.579 (QCD)+0.2%
−0.2%PDF+2.6% −2.8%
3.744 (QCD)+0.7%
−0.7%PDF+3.2% −3.2%
σVH [pb]* 0.934 (QCD)+0.9%
−0.9%PDF+2.6% −2.6%
1.149 (QCD)+1.0%
−1.0%PDF+2.3% −2.3%
2.350 (QCD)+0.7%
−1.5%PDF+2.2% −2.2%
σttH [pb] 0.0861 (QCD)+3.2%
−9.3%PDF+8.4% −8.4%
0.129 (QCD)+3.8%
−9.3%PDF+8.1% −8.1%
0.507 (QCD)+5.7%
−9.3%PDF+8.8% −8.8%
LHCXSEC WG
MCHM4 MCHM5
ξ 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 Λ
2 4 6 8 10 12 14
Preliminary ATLAS
= 7 TeV, 4.5-4.7 fb s
= 8 TeV, 20.3 fb s MCHM4 Obs. Exp.
ξ 0.5 − 0.4 − 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 Λ
2 4 6 8 10 12 14
Preliminary ATLAS
= 7 TeV, 4.5-4.7 fb s
= 8 TeV, 20.3 fb s MCHM5 Obs. Exp.
Natural path to explore → two identical complex scalar fields(SU(2)) The 2HDM scalar potential is a Z2 broken symmetric 2HDM V(Φ1, Φ2) = m2
1Φ† 1Φ1 + m2 2Φ† 2Φ2 + (m2 12Φ† 1Φ2 + h.c)
+ 1 2λ1(Φ†
1Φ1)2 + 1
2λ2(Φ†
2Φ2)2
+ λ3(Φ†
1Φ1)(Φ† 2Φ2) + λ4(Φ† 1Φ2)(Φ† 2Φ1) + 1
2λ5[(Φ†
1Φ2)2 + h.c]
In the CP-conserving case, parameters can be reduced to: 3 masses mh, mH, mH±, mA,, 2 angles α, β and 1 potential parameter m2
12
For the VV final states → type I and II where there are not FCNC
Mass mixing matrix for the neutral, CP-even Higgs bosons:
M2
S = (m2 Z +δ1)
− cos(β) sin(β) − cos(β) sin(β) sin2(β)
A
− cos(β) sin(β) − cos(β) sin(β) cos2(β)
sin2(β)
The couplings in a simplified MSSM model can be obtained from this mass mixing matrix as follows: The trace of the mass mixing matrix is taken and evaluated at the light Higgs boson mass of mh = 125.09 GeV, allowing the δ1 and δ corrections to be determined as a function of mA and tan β. Neglecting the sub-leading correction δ1, then by substituting for δ the mass mixing matrix is fully determined by mA and tan β. This matrix is diagonalised to find the eigenvectors, and in particular those components of the eigenvector corresponding to the light Higgs boson, su and
κV =
sd (mA,tan β)+tan β su(mA,tan β)
√
1+tan2 β
κu = su(mA, tan β) √
1+tan2 β tan β
κd = sd(mA, tan β)
where the functions su and sd are given by: su =
1
A+m2 Z 2 tan2 β
Z +m2 A tan2 β − m2 h(1+tan2 β) 2
sd =
A + m2 Z
m2 Z + m2 A tan2 β − m2 h(1+tan2 β) su.
ΓMajorana(h → χχ) = λ2 Majorana
hχχ
v 2mh 32πΛ2
2mχ mh 23/2 ΓScalar(h → χχ) =λ2 Scalar
hχχ
v 2 64πmh
2mχ mh 21/2 ΓVector(h → χχ) = λ2 Vector
hχχ
v 2 256πm4
χmh
h − 4m2 χm2 h + 12m4 χ
1 − 2mχ mh 21/2 σMajorana
χN
= λ2 Majorana
hχχ
4πΛ2m4
h
m2
χm4 Nf 2 N
(mχ + mN)2 σScalar
χN
= λ2 Scalar
hχχ
16πm4
h
m4
Nf 2 N
(mχ + mN)2 σVector
χN
= λ2 Vector
hχχ
16πm4
h
m4
Nf 2 N
(mχ + mN)2