T uhin S. R oz Tata Institute of Fundamental Research A rough - - PowerPoint PPT Presentation
Supersymmetry wi ! an Inhomo " ne # s T uhin S. R oz Tata Institute of Fundamental Research A rough outline of the talk Why Supersymmetry? What is the S -term and why is it important? What do we need to turn the S-term
T uhin S. Roz
Tata Institute of Fundamental Research
v2
ew ∼ m2 w
g2
How do you generate this scale? Even after you generate this — how do you make it radiatively stable?
v2
ew ∼ m2 w
g2 = fn
t , . . . , ˜
m2
i , M 2 a, . . .
superpartner masses In electroweak scale supersymmetry, you control electroweak scale by controlling superpartner masses
Control superpartner masses SUSY rotates chirality into scalar sector — gives full control of radiative corrections on superpartner masses How do we generate small (electroweak scale) superpartner masses?
˜ m2 ∼ F 2 M 2
parameter of mass dimension 2 parametrizes susy breaking scale mediation scale For Planck mediation:
M = MPl
F ∼ 1010−11 GeV
˜ m2 ∼ F 2 M 2
Smallness of electroweak scale or smallness of superpartner masses raises the question how do you generate
p F, M ⌧ MPl if M ⌧ MPl p F ⌧ M if M ⇠ MPl
parameter of mass dimension 2 parametrizes susy breaking scale mediation scale
p F MPl ⌧ 1
We know how nature does it with QCD
g2
⌧ 1
Smallness of electroweak scale or smallness of superpartner masses raises the question how do you generate
Skeleton of a complete SUSY model
Dynamical SUSY breaking in a hidden sector messenger mechanism gravity, gauge, gaugino, anomaly etc etc
qcd gauge coupling becomes strong
chiral symmetry is broken
energy scale
~ few GeVs
take qcd
hidden sector gauge coupling becomes strong
supersymmetry is broken
energy scale
Planck scale TeV
intermediate scale
just like qcd
Before I understand this question let’s visit the question of predictability in softly broken supersymmetric theories: How much can you predict the IR if you have a model of UV More importantly: How well do you know UV if you know IR very well
M
Mint
1 TeV Only MSSM fields are dynamic
SUSY breaking fields are also dynamic
renormalization is due to hidden + MSSM interactions renormalization is due to MSSM interactions
Cohen, Roy, Schmaltz
[hep-ph/0612100]
Meade, Seiberg, Shih
[0801.3278]
Consider the first generation particles: with MSSM interactions only
d dt ⇥ m2
Q =
1 16π2
3
qa g2
a M 2 a
Q =
m2
0 + 4.5 M 2 1/2
2 unknowns
qa ≡ {32 3 , 6, 2 5}
d dt ⇥ m2
Q =
1 16π2
3
qa g2
a M 2 a G + γ ⇥
m2
Q
⇥ m2
Q = N0 + 3
qa Na
4 unknowns
Consider the first generation particles: with MSSM + hidden interactions
RGE for the S-term is homogeneous with/without hidden sector dynamics 풮 = Tr (Yϕm2
ϕ) =
˜ m2
Hu − ˜
m2
Hd + Tr ( ˜
m2
q − ˜
m2
l − 2 ˜
m2
u + ˜
m2
d + ˜
m2
e)
16π2 d dt풮 = (γ + 66 5 g2
1) 풮
d dt 풮 = (⋯) × 풮
풮
μ=1 TeV
≠ 0 ⟹ 풮
μ=Mint
≠ 0 ⟹ 풮
μ=M
≠ 0
You can show that Irrespective of any hidden sector dynamics
A theory with a non zero S-term + no FI for Hypercharge A theory with a zero S-term + FI for Hypercharge V → V + #풮 θ2¯ θ2 Consider a toy model with SQED and softly broken supersymmetry and no hidden sector FI only runs because of gauge coupling running
d dt ( 풮 g2 ) = 0
Consider a toy model with SQED and softly broken supersymmetry and no hidden sector This argument will break down if more operators exist that explicitly involve V Can’t probably be a superpotential operator A theory with a non zero S-term + no FI for Hypercharge A theory with a zero S-term + FI for Hypercharge V → V + #풮 θ2¯ θ2
Consider a toy model with SQED and softly broken supersymmetry and no hidden sector ∫ d4θ f1 (ϕ⋯)
† eqV f2 (ϕ⋯)
f1, f2 are chiral functions of fields φ with charge q
∫ d4θ × (#θ2¯ θ2 풮) × f1 (ϕ⋯)
† f2 (ϕ⋯)
A theory with a non zero S-term + no FI for Hypercharge A theory with a zero S-term + FI for Hypercharge V → V + #풮 θ2¯ θ2
generates You break the theorem above C-terms
ℒsoft ⊃ Cu h†
d ˜
q Yu ˜ u ∫ d4θ k Λ H†
d eV/2 (QU)
In the MSSM, the operator with lowest dimension would be, for example Equivalently, you can start with a soft operator (rotating k to superspace): You are guaranteed to get an Inhomogeneous S-term
Simplify:
ℒsoft ⊃ Ctyt h†
d ˜
q3 ˜ u3 C-terms Corrections at RGEs one loop order will be confined to soft masses for Hd , q3, and u3
16π2 d dt ˜ m2
q3 = 2Xt − 32
3 g2
3
M3
2 − 6g2 2
M2
2 − 2
15 g2
1
M1
2 + 1
5 g2
1풮
16π2 d dt ˜ m2
u3 = 4Xt − 32
3 g2
3
M3
2 − 32
15 g2
1
M1
2 − 4
5 g2
1풮
16π2 d dt ˜ m2
hd = − 6g2 2
M2
2 − 6
5 g2
1
M1
2 − 3
5 g2
1풮
Xt ≡ yt
2
( ˜ m2
q3 + ˜
m2
u3 + ˜
m2
hu + At 2
)
RGEs for soft mass-squareds for Hd , q3, and u3
˜ q, ˜ u, hd ˜ q, ˜ u, hd e q, e u
e q, e u
Y Y ∗ ξuY ∗ ξ∗
uY
˜ q, ˜ u, hd ˜ q, ˜ u, hd
˜ Hu
q, u
Y (Ct + μ)
Y† (Ct + μ)
†
X X
Y†
˜ H
You can guess that the effects of these diagram will be proportional to yt
2
( Ct + μ
2 − μ 2
)
16π2 d dt ˜ m2
q3 = 2Xt − 32
3 g2
3
M3
2 − 6g2 2
M2
2 − 2
15 g2
1
M1
2 + 1
5 g2
1풮
+ 2ξt 16π2 d dt ˜ m2
u3 = 4Xt − 32
3 g2
3
M3
2 − 32
15 g2
1
M1
2 − 4
5 g2
1풮
+ 4ξt 16π2 d dt ˜ m2
hd = − 6g2 2
M2
2 − 6
5 g2
1
M1
2 − 3
5 g2
1풮
+ 6ξt Xt ≡ yt
2
( ˜ m2
q3 + ˜
m2
u3 + ˜
m2
hu + At 2
) ξt ≡ yt
2
( Ct + μ
2 − μ 2
)
16π2 d dt 풮 = 66 5 g2
1풮 − 12 ξt
풮
μ=1 TeV
≠ 0 ⟹ 풮
μ=Mint
≠ 0
All scalars including scalar Higgses are massless
gauginos and Higgsinos are massive
The spectrum is independent of details of messenger model and hidden sector model
scalar sequestering
is characterized by the spectrum at the intermediate scale
Perez, Roy, Schmaltz,
Phys.Rev. D79 (2009) 095016
Mediation scale Intermediate scale Electroweak scale
Dominated by (superconformal) dynamics in hidden sector
μ ∼ Ma ˜ m2
ϕ = 0
˜ m2
Hu =
˜ m2
Hd = −
μ
2
Bμ = 0
˜ m2
e (μ) =
6M2
1 (μ)
5b1 1 − {1 − b1g2
1 (μ)
8π2 log ( Mint μ )}
2
16π2 d dt ˜ m2
e = − 24
5 g2
1
M1
2
Mint ≳ μ × exp 8π2 b1g1 (μ)
2
1 − 6 6 + 5b1 ≳ 3.9 × 1018 GeV ( μ 1 TeV ) ˜ m2
e (μ) ≳ M2 1 (μ)
Implies: Initial condition: ˜ m2
ϕ = 0
Same as in gaugino mediation
Consider RH slepton mass at the EW scale
16π2 d dt ˜ m2
e = − 24
5 g2
1
M1
2 + 6
5 g2 풮 16π2 d dt풮 = 66 5 g2
1풮 − 12 yt 2
( Ct + μ
2 − μ 2
)
Consider RH slepton mass at the EW scale Take: Ct = − μ = 1 TeV M1 = 100 GeV
Λint (GeV)
20 40 60 80 100 120 140 160 180 103 104 105 106 107 108 109 1010 1011
˜ me3,tanβ = 2.5 ˜ me1,2,tanβ = 2.5 ˜ me3,tanβ = 25 ˜ me1,2,tanβ = 2520 40 60 80 100 120 140 160 180 103 104 105 106 107 108 109 1010 1011
˜ me (GeV)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 5 10 15 20 25 30 35 40 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 5 10 15 20 25 30 35 40
tan β
˜ me3 − ˜ me1 ˜ me1
˜ m2
e3 >
˜ m2
e1,2
because of the initial condition
˜ m2
H = − |μ|2
Consider RH slepton mass at the EW scale
Detailed phenomenological questions:
For answers to some of these questions look for the forthcoming Chakraborty, Roy (Feb, 2019)