Wim Beenakker Radboud University Nijmegen The Netherlands

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


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!



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, . . . )



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



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



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



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?


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 ??


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


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


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 )


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)


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


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


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



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



• 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!



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



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!



Implications of a 125 GeV Higgs on high-scale SUSY modelsArbey et al.

High-scale SUSY models on the ropes: Mh is too large!



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)



direct searches(at face value)



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!



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



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)



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



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



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



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



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!


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 . . .


The hunt is still on!


Wim Beenakker Radboud University Nijmegen The Netherlands

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