Supersymmetric Higgs bosons and beyond Jos Francisco Zurita (ITP, - - PowerPoint PPT Presentation
Supersymmetric Higgs bosons and beyond Jos Francisco Zurita (ITP, Univ. Zrich) Phys.Rev.D81:015001, 2010 (and work in progress)* * in collaboration with: Marcela Carena, Kyoungchul Kong, Eduardo Pontn Thursday, March 4, 2010 Outline
* in collaboration with: Marcela Carena, Kyoungchul Kong, Eduardo Pontón
José Francisco Zurita (ITP, Univ. Zürich)
Phys.Rev.D81:015001, 2010 (and work in progress)*
Thursday, March 4, 2010
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mh > 90 GeV mh < 130 GeV
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V = µ2φ∗φ + λ(φ∗φ)2 = µ2 2 (φ2
1 + φ2 2) + λ
4 (φ2
1 + φ2 2)2
φ = 1 √ 2[v + h(x)]
V has minima at Expand
L = (Dµφ)†Dµφ − 1 4Fµ νF µ ν − V
Yukawa couplings g
¯ ψLφ
fermion masses
ghf ¯
f = mf/v
ghV V = 2m2
V /v2
A single unknown parameter: mh
h3, h4, hA2, h2A2
m2
A = g2v2
m2
h = λv2
⊕ ⊕
|φ| =
One gets
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g (c) W, Z (d) (a) (b) g Q H ¯ Q W, Z W, Z H H W, Z H
!(pp"H+X) !pb" #s = 14 TeV Mt = 175 GeV CTEQ4M gg"H qq"Hqq qq
_’"HWgg,qq
_"Htt _gg,qq
_"Hbb _MH !GeV" 200 400 600 800 1000 10
10
10
10
1 10 10 2
114.4 GeV < mh < 1 TeV
Exclusion (Tevatron, Jan. 2010)
162 GeV < mh < 166 GeV
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numbers, and same mass.
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Since no scalar particle with the electron mass and charge has been detected... SUSY is broken
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Soft terms come in two kinds:
L = LSUSY + Lsoft
breaks SUSY explicitly.
LMSSM
soft
= −1 2
g g + M2 W W + M1 B B + c.c
QHu − d ad QHd − e ae LHd + c.c
Q† m2
e Q Q −
L† m2
e L
L − u m2
u
u† − d m2
d d† −
e m2
e
e† − m2
HuH∗ uHu − m2 HdH∗ dHd − (bHuHd + c.c) .
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xµ xµ, θ, ¯ θ The 4D spacetime is extended to the superspace Fields become superfields:
Φ(xµ, θ, ¯ θ) = φ + √ 2θψ + θ2F + i∂µφθσµ¯ θ − i √ 2θ2∂µψσµ¯ θ − 1 4∂µ∂µφθ2¯ θ2
L =
θ K +
K: Kähler potential (kin. terms and gauge int.) W: Super potencial (Yukawa-like interactions) : scalar : fermion : auxiliary
φ ψ
F
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α
tan β = vu/vd mA Tree level: , , mixing betweenh y H
V = m2
11H† uHu + m2 22H† dHd − [bHuHd + c.c]
+ 1 2λ1(H†
dHd)2 + 1
2λ2(H†
uHu)2 + λ3(H† uHu)(H† dHd) + λ4(HuHd)(H† uH† d)
+ 1 2λ5(HuHd)2 +
dHd) + λ7(H† uHu)
Hu, Hd → h, H, A, H± v2 = v2
u + v2 d
scalars pseudoscalar
Φ Φ¯ uu Φ ¯ dd ΦV V h0 cos α/senβ −senα/ cos β sen(β − α) H0 senα/senβ cos α/ cos β cos(β − α) A0 1/ tan β tan β
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MSSM:
λ1 = λ2 = (g2
1 + g2 2)/4,
λ3 = (g2
2 − g2 1)/4,
λ4 = −g2
2/4,
λ5 = λ6 = λ7 = 0
2-loops: Tree level:
mS, At, Ab
1 10 20 40 60 80 100 120 140 1 10 LEP 88-209 GeV Preliminary
mh° (GeV/c2) tan!
Excluded by LEP Theoretically Inaccessible mh°-max
1 10 100 200 300 400 500 1 10 LEP 88-209 GeV Preliminary
mA° (GeV/c2) tan!
Excluded by LEP mh°-max
MSUSY=1 TeV M2=200 GeV µ=-200 GeV mgluino=800 GeV Stop mix: Xt=2MSUSY
mh < 130 GeV
m(0)
h
≤ mZ|cos(2β)|
m(0)
h
≈ 0, tan β ≈ 1 m(0)
h
≈ mZ, tan β > 10
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114.4 GeV < mh < 135 GeV
MSSM
BMSSM can manifest in the Higgs sector
Starting point: Effective theory (valid below scale M)
W = µHuHd + ω1 2M (1 + α1X)(HuHd)2
O(1/M) ≡ Dim5
∆λ5 = α1ω1 mS M ∆λ6 = ∆λ7 = ω1 µ M
Only 2 parameters: ω1, α1 ∼ O(1)
X = mS θ2
Spurion:
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Huber, Seniuch (’05), Delaunay, Grojean, Wells (’08), Noble, Perelstein (’08), Grinstein, Trott (’08)
EWSB takes place in the supersymmetric limit (different from the MSSM!).
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K = H†
deV Hd + H† ueV Hu
+ c1 M 2 (1 + γ1(X + X†) + β1XX†)(H†
deV Hd)2
+ c2 M 2 (1 + γ2(X + X†) + β2XX†)(H†
ueV Hu)2
+ c3 M 2 (1 + γ3(X + X†) + β3XX†)(H†
ueV Hu)(H† deV Hd)
+ c4 M 2 (1 + γ4(X + X†) + β4XX†)(HuHd)(HuHd)† + {[ c6 M 2 (1 + β6XX† + γ6X + δ6X†)H†
deV Hd
+ c7 M 2 (1 + β7XX† + γ7X + δ7X†)H†
ueV Hu](HuHd) + h.c} ,
: 20 extra free parameters.
O(1/M 2)
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Vnon−ren. ⊃ 1 M 2 |HuHd|2 (λ8H†
dHd + λ′ 8H† uHu)
λ(0)
1,4 ∼ g2
λ(0)
5,7 = 0
∆λ(5)
5,7 = 0
Dimension 6 analysis is needed !
∆λ(5)
1,4 = 0
O(v2/M 2)
Lkin mix ⊃ − 2c3 M 2 {(DµHd)†Hd
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m2
h = (m2 h)MSSM + (∆m2 h)5d + . . .
(∆m2
h)5d
ω1 2 v2(4µ − α1ms M )
tan β ≈ 1 tan β > 10
Μ ms 200 GeV M 1 TeV tan Β 2 max mh for pars 1 MSSM
100 200 300 400 50 100 150 200 250 300
mA GeV mh GeV
Μ ms 200 GeV M 1 TeV tan Β 20 max mh for pars 1 MSSM
100 200 300 400 50 100 150 200 250 300
mA GeV mh GeV
MSSM vacua sEWSB vacua
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h0 H0
Μ ms 200 GeV M 1 TeV tan Β 2 MSSM MSSM
100 200 300 400 1.0 0.5 0.0 0.5 1.0
mA GeV ghVVghVV
SM
and gHVVghVV
SM
h0 H0
Μ ms 200 GeV M 1 TeV tan Β 20 MSSM MSSM
100 200 300 400 1.0 0.5 0.0 0.5 1.0
mA GeV ghVVghVV
SM
and gHVVghVV
SM
hV V = 1 + O(x2, y2) x = m2
Z/m2 A,
y = µ/M, ms/M
HV V = A1x + A2y
A1, A2 ∼ O(1)
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h0 H0
Μ ms 200 GeV M 1 TeV tan Β 2 MSSM
100 200 300 400 2 1 1 2
mA GeV ghbbghbb
SM and gHbbghbb SM
h0 H0
Μ ms 200 GeV M 1 TeV tan Β 20 MSSM
100 200 300 400 10 5 5 10 15 20
mA GeV ghbbghbb
SM and gHbbghbb SM
hb¯ b = 1 + (A1x + A2y)/ tan β + O(x2, y2)
Hb¯ b = − tan β(1 + (A1x + A2y)/ tan β) + O(x2, y2)
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λi = λ(0)
i
+ ∆λ(5)
i
+ ∆λ(6)
i
+ ∆λ(1−loop)
i
* includes LEP bound h to jets
+ LEP charged Higgs + latest Tevatron data
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Excluded by LEP Excluded by Tevatron Tevatron upgrade Allowed
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Excluded by LEP Excluded by Tevatron Tevatron upgrade Allowed
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Excluded by LEP Excluded by Tevatron Tevatron upgrade Allowed
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σmodel(gg → h) σSM(gg → h) ≃
ggh
gSM
ggh
2 ≡ Γmodel
h→gg
ΓSM
h→gg
Excluded by LEP Excluded by Tevatron Tevatron upgrade Allowed
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σmodel(gg → h) σSM(gg → h) ≃
ggh
gSM
ggh
2 ≡ Γmodel
h→gg
ΓSM
h→gg
Excluded by LEP Excluded by Tevatron Tevatron upgrade Allowed
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B R i n t
b
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Excluded by LEP Excluded by Tevatron Tevatron upgrade Allowed
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Excluded by LEP Excluded by Tevatron Tevatron upgrade Allowed
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E x
i c d e c a y s
H±
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approach up to the second order in the 1/M expansion.
MSSM.
low tangent beta (relax the MSSM tension).
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In the end, SUSY is not that messy...
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In the end, SUSY is not that messy... and is not that Messi either!
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C S x B R i n t
W
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Excluded by LEP Excluded by Tevatron Tevatron upgrade Allowed
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Excluded by LEP Excluded by Tevatron Tevatron upgrade Allowed
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Excluded by LEP Excluded by Tevatron Tevatron upgrade Allowed
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Solve (with fixed params) for . Keep if and .
∼ 0.2
δv/v < 10%
|ω1|, |c1|, |c2|, |c3|, |c4|, |c6|, |c7| ∈ [0, 1]. |α1|, |βi|, |γi|, |δ6|, |δ7| ∈ [1/3, 1] for i = 1, 2, 3, 4, 6, 7.
λi → λi ± 2 Max {|ω1|, |c1|, |c2|, |c3|, |c4|, |c6|, |c7|} µ M 3 , i = 1, . . . 7 ,
−0.2 < T tree + T Higgs + T SUSY < 0.3
Medina, Shah, Wagner (’09)
v, tan β
1.5(15) < tan β < 2.5(25)
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No decoupling scenario:
203 237 183 200
mh mH mA
mH±
g2
hZZ/SM = 0.23
g2
HZZ/SM = 0.75
H SM-like Charged Higgs observable in the top-bottom channel : LHC reach in the four lepton channel (ZZ)
0.73 0.25 1.2 0.70 0.3 0.5
φ
h H
φ → WW φ → ZZ
σ(gg → φ) × BR(φ → ZZ)
h/H
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Unusual hierarchy scenario:
164 193 102 158
mh mH mA
mH±
g2
HZZ/SM = 0.87
g2
hZZ/SM = 0.13
H SM-like h can be excluded/found at the future Tevatron run:
BR(h → WW) = 0.77 σ(gg → h) × BR(h → WW)/SM = 0.9
H can be excluded/found at the LHC, 4 lepton-channel
σ(gg → H) × BR(H → ZZ)/SM = 0.66 BR(H → ZZ) = 0.24
BR(H± → W ±A) = 0.23
BR(A → bb/ττ) = 0.89/0.1
A/H±:
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