Post on 14-Jan-2022
Supersymmetry . . . dead or alive?!
National Seminar, Nikhef 30 March 2012
Wim Beenakker
Radboud University NijmegenThe Netherlands
– p.1/36
Contents
1 The Higgs-boson mass and new physics
2 Supersymmetry
3 The Higgs-boson mass and supersymmetry
4 Probing the supersymmetry-breaking sector
5 Conclusions
W. Beenakker National Seminar , 30/03/2012 – p.2/36
1 The Higgs-boson mass and new physics
Naturalness: the mass of a particle is called naturally small if setting the associated
Lagrangian parameter to zero enhances the symmetry of the system
⇒ such a symmetry-breaking mass is protected
against large quantum corrections,
resulting in δm ∝ m
Standard Model (SM): the masses of fermions
and gauge bosons are protected by symmetry,
but not the Higgs-boson mass MH
δMH tends to be governed by the highest mass scale in the theorythat couples (at tree/loop level) to the Higgs boson!
W. Beenakker National Seminar , 30/03/2012 – p.3/36
1 The Higgs-boson mass and new physics
The hierarchy problem: assume the SM to be an effective low-energy theory,
originating from a theory that emerges at energies ΛNP ≫ Λew = O(100 GeV)
⇒ if the new-physics particles couple to the SM particles,
then there is a stability problem for the Higgs-boson mass
M2H(Λew) = M2
H(ΛNP ) + CΛ2NP (quadratic divergences)
For example: ∝ − f2F
M2F for MF = O(ΛNP )
H HF̄
FfF
fF
⇒ • M2H(Λew) = O(Λew) requires a tremendous amount of fine-tuning
• a symmetry or theoretical concept is needed to make this plausible
(ΛP lanck ≫/ Λew, no fundamental Higgs bosons, supersymmetry, . . . )
W. Beenakker National Seminar , 30/03/2012 – p.4/36
1 The Higgs-boson mass and new physics
Theoretical limits on MH in the SM
Renormalization group scaling for the quartic Higgs self-coupling λ(Q):
16π2 dλ
dt= 12 (λ2 + λf2
t − f4t ) + · · · ≡ β(λ)
t = log(Q/µ) and ft =√
2 mt/v (v = 246 GeV)
Initial condition λ(v) = M2H/v2 ≡ λ0
• Small λ0: coupling to top-quark causes λ(Q) to decrease with Q
⇒ λ(Q) becomes negative below ΛP lanck = O(1019 GeV)
⇒ vacuum unstable, can collapse into much deeper minimum
• Large λ0: Higgs self coupling causes λ(Q) to grow with Q
⇒ evolution becomes non-perturbative below ΛP lanck
W. Beenakker National Seminar , 30/03/2012 – p.5/36
1 The Higgs-boson mass and new physics
Before the LHC Ellis et al.
GeV) / Λ(10
log4 6 8 10 12 14 16 18
[G
eV]
HM
100
150
200
250
300
350
LEP exclusionat >95% CL
Tevatron exclusion at >95% CL
Perturbativity bound Stability bound Finite-T metastability bound Zero-T metastability bound
error bands, w/o theoretical errorsσShown are 1
π = 2λπ = λ
GeV) / Λ(10
log4 6 8 10 12 14 16 18
[G
eV]
HM
100
150
200
250
300
350
SM can be extended up to the Planck scale if MH ≈ 135 – 170 GeV
W. Beenakker National Seminar , 30/03/2012 – p.6/36
1 The Higgs-boson mass and new physics
The Higgs mass after 2 years of LHC operation: excess observed around 125 GeV
ATLAS-CONF-2012-019 CMS-PAS-HIG-12-008
[GeV]Hm110 115 120 125 130 135 140 145 150
SM
σ/σ
95%
CL L
imit
on
-110
1
10 Obs.Exp.
σ1 ±σ2 ± = 7 TeVs
-1 Ldt = 4.6-4.9 fb∫ATLAS Preliminary 2011 Data
CLs Limits
ATLAS exclusion @ 95% CL: 110 –117.5 , 118.5 –122.5 , 129 – 539 GeV
CMS exclusion @ 95% CL: 127.5 – 600 GeV
W. Beenakker National Seminar , 30/03/2012 – p.7/36
1 The Higgs-boson mass and new physics
Zooming in after 2 years of LHC operation Ellis et al.
GeV) / Λ(10
log4 6 8 10 12 14 16 18
[G
eV]
HM
100
105
110
115
120
125
130
135
140
145
150
LEP exclusionat >95% CL
Stability bound Finite-T metastability bound Zero-T metastability bound
error bands, not including theoretical errorsσShown are 1
GeV) / Λ(10
log4 6 8 10 12 14 16 18
[G
eV]
HM
100
105
110
115
120
125
130
135
140
145
150
125 GeV
A first glimpse of new physics ⇒ hierarchy problem?
W. Beenakker National Seminar , 30/03/2012 – p.8/36
2 Supersymmetry
The SM has been a great success, but many open questions remain
• Do particle masses derive from the Higgs mechanism?
• What is behind the family structure, charge quantization and mass hierarchy ofthe matter fermions?
• Is there a relation between the three Standard Model gauge couplings( g′: hypercharge, g: weak, gs: strong) and do they unify at high energies?
• What is causing the left–right asymmetry?
• What is the origin of the Standard-Model parameters?
• Why does the universe consist of matter rather than a matter–antimatter mixture(matter–antimatter asymmetry)?
• What is the cold dark matter of the universe?
• Where does gravity fit in?
• Why is Λew = O(100 GeV)≪ ΛP lanck = O(1019 GeV)?
• ?? Inflation, cosmological constant, dark energy ??
W. Beenakker National Seminar , 30/03/2012 – p.9/36
2 Supersymmetry
Theoretical motivations for supersymmetry (SUSY):
• Most general symmetry of the S-matrix:⋆ Poincaré invariance and gauge symmetry⋆ on top of that SUSY links particles of different spins
⇒ superfields: supermultiplets of fermions and bosons
• Local SUSY theories require introduction of gravity
⇒ connection between SUSY versions of the SM and gravity
• Many problems in string theory/string field theory can be solved by means ofSUSY (e.g. the stability of the string vacuum)
• The lightest SUSY particle might be a prime dark-matter candidate
• SUSY solves the hierarchy problem by linking fermionic and bosonic loop effects
H HF̄
FfF
fF
+H H
hF
F̃1,2 hF
=f2F
no quadratic divergences
W. Beenakker National Seminar , 30/03/2012 – p.10/36
2 Supersymmetry
A minimal SUSY extension of the SM (MSSM) can be made experimentallycompatible with theories of Grand Unification (GUTs):
• the hypercharge, weak and strong couplings come together at a singlehigh-energy scale Λ ≈ 2× 1016 GeV (unification of running gauge couplings)
α1(Q) = 5g′2(Q)/12π
α2(Q) = g2(Q)/4π
α3(Q) = g2s(Q)/4π
Martin
2 4 6 8 10 12 14 16 18Log10(Q/GeV)
0
10
20
30
40
50
60
α-1
U(1)
SU(2)
SU(3)
SM
MSSM
W. Beenakker National Seminar , 30/03/2012 – p.11/36
2 Supersymmetry
Properties of the minimal SUSY extension of the SM (MSSM):
• Each fermionic/bosonic d.o.f. in the SM has exactly one correspondingbosonic/fermionic superpartner d.o.f. with the same gauge quantum numbers
Squarks
Gauginos
Higgsinos
Sleptons
• Contains two Higgs doublets (because of analyticity and anomaly cancellation)⇒ after symmetry breaking 5 physical Higgs states remain (H±, A, H, h )
W. Beenakker National Seminar , 30/03/2012 – p.12/36
2 Supersymmetry
• R-parity is conserved:
R = (−1)3(B−L)+2S =
8
<
:
+1 for Standard Model particles/Higgses
−1 for superpartners
B = baryon number , L = lepton number , S = spin
⋆ Supported by large classes of theories
⋆ Prevents rapid proton-decay
⋆ Very special SUSY signatures:
− superpartners are produced in pairs at collider experiments
− each superpartner decays into an odd number of other superpartners
− the lightest superpartner (LSP) is stable!
⇒ • escapes as missing energy in collider experiments
• candidate for cold dark matter if colourless, neutral and
preferably fermionic ⇒ neutralino (gaugino – Higgsino mixture)
W. Beenakker National Seminar , 30/03/2012 – p.13/36
2 Supersymmetry
• No superpartners have been observed yet, so SUSY has to be broken at Λew
⇒ soft SUSY breaking:
⋆ good SUSY properties maintained ⇒ no quadratic divergences
⋆ superpartners get masses m̃ = O(TeV)
⋆ necessary for Higgs mechanism
• ∼ 100 parameters . . . how to deal with this?
⋆ Resort to specific (gravity/string-inspired) models of SUSY breaking
⇒ constrained models: handful of (unification) parameters,
highly correlated mass spectra,
highly model-dependent signatures
Example: constrained MSSM (CMSSM, “mSUGRA”),1 sign and 4 parameters (i.e. m0 , m1/2 , tan β , A0)
⋆ Use flavour and CP constraints to reduce the number of parameters
⇒ phenomenological MSSM (pMSSM):
effectively 19 parameters, much less model-dependent
W. Beenakker National Seminar , 30/03/2012 – p.14/36
2 Supersymmetry
• the electroweak Higgs mechanism can be generated radiatively through runningmasses, starting from a unified mass at the unification scale
Renormalization group evolution in the CMSSM
2 4 6 8 10 12 14 16 18Log10(Q/1 GeV)
0
500
1000
1500M
ass
[GeV
]
m0
m1/2
(µ2+m0
2)1/2
squarks
sleptons
M1
M2
M3
Hd
Hu
W. Beenakker National Seminar , 30/03/2012 – p.15/36
2 Supersymmetry
What to look for at the LHC:
• Coloured superpartners (squarks, gluinos) couple to gluons and shouldtherefore be produced abundantly at the LHC. Characteristic signatures:
⋆ missing transverse energy (LSP or neutrinos)⋆ energetic jets (general)⋆ charged leptons (superpartner decay cascades, model-dependent)
⋆ like-charge dileptons l+l+ or l−l− (gluino decays, model-dependent)⋆ LHC can probe the coloured SUSY sector up to m̃ ≈ 2 – 3 TeV
At present we have reached ∼ 1.3 TeV (model-dependent)
• Electroweak superpartners can be light (especially in GUTs)
• Finding the underlying unified theory is tough at hadron colliders, since theenergy is not tunable (many particles produced at the same time). But . . .
• SUSY predicts the existence of a light scalar Higgs boson, since the quartic
Higgs couplings are fixed by gauge couplings
⇒ MSSM : Mh ≈ 100 – 135 GeV , general SUSY : Mh ≤ 180 GeV
W. Beenakker National Seminar , 30/03/2012 – p.16/36
3 The Higgs-boson mass and supersymmetry
The Higgs-boson mass in the MSSM
• In the SM MH is essentially a “free” parameter
• In the MSSM the quartic Higgs couplings are fixed by gauge couplings
⇒ mass of lightest CP-even Higgs boson h is bounded from above
M2h ≈ M2
Z cos2(2β) +3m2
t
2π2v2
»
log“M2
S
m2t
”
+X2
t
M2S
“
1− X2t
12M2S
”
–
tree level top/stop loops
in the decoupling regime MA ≫MZ
Relevant parameters
tan β = ratio of the Higgs vevs
MA = mass of the CP-odd Higgs boson
MS ≡ √mt̃1mt̃2
= “SUSY-breaking mass”
Xt ≡ At − µ cotβ = mixing parameter in stop sector
W. Beenakker National Seminar , 30/03/2012 – p.17/36
3 The Higgs-boson mass and supersymmetry
• The maximum value Mmaxh is obtained for
⋆ the decoupling regime MA ≫MZ
⋆ tanβ relatively large, i.e. roughly tan β ≥ 10
⋆ heavy stop(s), i.e. large MS
⋆ “maximal mixing”, i.e. Xt =√
6 MS
• Experimental constraints on Mh strongly affect the allowed MSSM
parameter space through the MSSM quantum corrections
⇒ measurement of Mh = indirect SUSY search!
W. Beenakker National Seminar , 30/03/2012 – p.18/36
3 The Higgs-boson mass and supersymmetry
Implications of a 125 GeV Higgs on the pMSSMArbey et al.
No-stop-mixing scenario Xt = 0 excluded for MS < 1 TeV
A lot of pMSSM parameter space left, small stop masses still allowed
W. Beenakker National Seminar , 30/03/2012 – p.19/36
3 The Higgs-boson mass and supersymmetry
Implications of a 125 GeV Higgs on constrained models
Arbey et al.
model AMSB GMSB mSUGRA no-scale cNMSSM VCMSSM NUHM
Mmaxh 121.0 121.5 128.0 123.0 123.5 124.5 128.5
Minimal models are being excluded!
W. Beenakker National Seminar , 30/03/2012 – p.20/36
3 The Higgs-boson mass and supersymmetry
Implications of a 125 GeV Higgs on high-scale SUSY modelsArbey et al.
High-scale SUSY models on the ropes: Mh is too large!
W. Beenakker National Seminar , 30/03/2012 – p.21/36
3 The Higgs-boson mass and supersymmetry
Just beyond CMSSM: non-universal gaugino masses in a SU(5) GUTCaron et al.Mass-generating terms for the gauginos λ:
Lgaugino mass ∼ 〈Fab〉λaλb + c.c.
Gauginos are in the adjoint 24-dimensional representation of SU(5)
⇒ Fab is in a representation appearing in (24⊗ 24)Symm = 1⊕ 24⊕ 75⊕ 200
tree-level @ ΛGUT 1-loop @ Λew
rep M1 M2 M3 MEW1 MEW
2 MEW3
1 1 1 1 0.14 0.29 124 -0.5 -1.5 1 -0.07 -0.43 175 -5 3 1 -0.72 0.87 1200 10 2 1 1.44 0.58 1
← CMSSM
Non-singlet representations: non-CMSSM tree-level mass relations at ΛGUT
⇒ important for SUSY phenomenology (LSP, decay cascades)
W. Beenakker National Seminar , 30/03/2012 – p.22/36
3 The Higgs-boson mass and supersymmetry
direct searches(at face value)
W. Beenakker National Seminar , 30/03/2012 – p.25/36
3 The Higgs-boson mass and supersymmetry
Actual impact of direct searches on the 200 representationCaron et al.
MSUSY = minimum of gluino mass and light-flavour squark masses
450 GeV gluinos still allowed due to small mass splitting with LSP
⇒ dedicated search required to exclude this!
W. Beenakker National Seminar , 30/03/2012 – p.26/36
4 Probing the supersymmetry-breaking sector
An effective field theory (EFT)
Consider the exchange of an unknown heavy X particle
G G
Q
X
G2
Q2−M2
X
Q≪MX
effective interaction
−
G2
M2
X
[
1 +Q2
M2
X
+ · · ·
]
The coupling G is dimensionless, but the effective coupling G2/M2X is dimensionful
Q≪MX : the interaction appears weak
Q = O(MX): the dynamics related to the X particle shows up
⇒ a form factor replaces the effective coupling,
resulting in a proper energy dependence of the reaction
W. Beenakker National Seminar , 30/03/2012 – p.27/36
4 Probing the supersymmetry-breaking sector
Travelling along the EFT chain using the renormalization group (RG)
6
?
?
µ
µ = MΦ
high-energy EFT
L(φi) + L(φi,Φ)
low-energy EFT
L(φi) + δL(φi)
fields φi,Φ
fields φi
matching
RG
RG
L(φi) contains the same operators in the high- and low-energy EFT,
but the couplings/masses can be different due to the matching conditions
δL(φi) encodes the information on the heavy field Φ (effective interactions)
W. Beenakker National Seminar , 30/03/2012 – p.28/36
4 Probing the supersymmetry-breaking sector
EFT for radiative SUSY breaking
• Spontaneous SUSY breaking in hidden sector
• Transferred to visible (MSSM) sector by gravity, gauge interactions, . . .
• Scale hierarchy possible: MS ∝ Λ2
SUSY
ΛP lanck≪ ΛSUSY
W. Beenakker National Seminar , 30/03/2012 – p.29/36
4 Probing the supersymmetry-breaking sector
Studying physics beyond experimental access (bottom-up approach)
6µ
new physicsthreshold
evolvedparameters
compare theorywith experiment
-�RG boundary conditions
from matching
more fundamental theory
low-energy EFT
experimentally accessible regime����
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6RG
Drawbacks: • numerical RG evolution ⇒ experimental uncertainties might increase
• the threshold of new physics has to be guessed ⇒ error-prone
• in general all running parameters need to be known
W. Beenakker National Seminar , 30/03/2012 – p.30/36
4 Probing the supersymmetry-breaking sector
2 4 6 8 10 12 14 16 18Log10(Q/1 GeV)
0
500
1000
1500M
ass
[GeV
]
m0
m1/2
(µ2+m0
2)1/2
squarks
sleptons
M1
M2
M3
Hd
Hu
W. Beenakker National Seminar , 30/03/2012 – p.31/36
4 Probing the supersymmetry-breaking sector
A new approach: use RG invariants and sum rules
Construct combinations of parameters that remain constant under RG evolution:
the MSSM has 16 of these RG invariants (D.A. Demir; Carena et al.)
Advantages: • less input, no numerical RG evolution, purely algebraic
• we do not need to know the threshold of new physics
• fast diagnostic tool for probing high-energy matching conditions
Task: find appropriate sum rules to directly test specific high-scale models/concepts
• Carena et al.; W.B. and J. Hetzel: sum rules for specific SUSY-breaking models(model-dependent approach)
• W.B. and J. Hetzel: sum rules for testing flavour-universality, unification andmultiple unification (model-independent approach)
The true power of these sum rules is their falsifying power
Assumption: no new physics between electroweak and SUSY-breaking scale
Tough task: determine all soft masses and gauge couplings at the same energy scale
W. Beenakker National Seminar , 30/03/2012 – p.32/36
4 Probing the supersymmetry-breaking sector
An example: gauge-coupling unification revisited
g21(Q) =
5
3g′2(Q) , g2
2(Q) = g2(Q) , g23(Q) = g2
s(Q)
16π2 dga
dt= bag3
a (a = 1, 2, 3) with t = log(Q/µ)
Sum rule for gauge-coupling unification:
Ig =b2 − b3
g21
+b3 − b1
g22
+b1 − b2
g23
= 0
SM: ba = (41/10 ,−19/6 ,−7)
Ig = − 3.25± 0.03
MSSM: ba = (33/5 , 1 ,−3)
Ig = − 0.06± 0.032 4 6 8 10 12 14 16 18
Log10(Q/GeV)
0
10
20
30
40
50
60
α-1
U(1)
SU(2)
SU(3)
The MSSM is compatible with unification, the SM is not!
W. Beenakker National Seminar , 30/03/2012 – p.33/36
5 Conclusions
Upshot after 2 years of LHC operation:
• Search for SUSY: presently dominated by the Higgs-boson mass
• Constrained SUSY-breaking models:⋆ great for benchmarking⋆ too restrictive in mass spectrum and phenomenology⋆ already strongly constrained by data, especially minimal models
• pMSSM:⋆ much richer features, (compressed) mass spectra and phenomenology⋆ a lot less constrained by data
⇒ SUSY is not dead, we need dedicated search strategies
• New development in probing high-scale physics: RG invariants and sum rules
My personal opinion . . .
W. Beenakker National Seminar , 30/03/2012 – p.35/36