STANDARD MODEL

Theoretical Constraints on Higgs Mass

• Large Mh → large self-coupling → blow up at low-energy scale Λ due to renormalization

• Small: renormalization due to t quark drives quartic coupling < 0at some scale Λ→ vacuum unstable

• Vacuum could be stabilized by supersymmetryEspinosa, JE, Giudice, Hoecker, Riotto, arXiv0906.0954

LHC 95%

exclusion

Vacuum Stability vs Metastability

• Dependence on scale up to which Standard Model remains

– Stable

– Metastable at non-zero temperature

– Metastable at zero temperature

What is the probable fate of the SM?Confidence Levels (CL) for different fatesConfidence Levels (CL)

without/with Tevatron exclusion

Blow-up excludedat 99.2% CL

Espinosa, JE, Giudice, Hoecker, Riotto

CL asfunction ofinstabilityScale Λ

The LHC will Tell the Fate of the SM

Espinosa, JE, Giudice, Hoecker, Riotto

Examples with LHC measurement of mH = 120 or 115 GeV

How to Stabilize a Light Higgs Boson?

• Top quark destabilizes potential: introduce introduce stop-like scalar:

• Can delay collapse of potential:• But new coupling must be

fine-tuned to avoid blow-up:• Stabilize with new fermions:

– just like Higgsinos

• Very like Supersymmetry!JE + D. Ross

Favoured values of Mh ~ 119 GeV:

Range consistent with evidence from LHC !

Higgs mass

χ2 price to pay if Mh = 125 GeV is < 2

Buchmueller, JE et al: arXiv:1112.3564

Supersymmetry?

• Would unify matter particles and force particles• Related particles spinning at different rates

0 - ½ - 1 - 3/2 - 2 Higgs - Electron - Photon - Gravitino - Graviton

(Every particle is a ‘ballet dancer’)

• Would help fix particle masses• Would help unify forces• Predicts light Higgs boson• Could provide dark matter for the

astrophysicists and cosmologists

Why Supersymmetry (Susy)?

• Hierarchy problem: why is mW << mP ?

(mP ~ 1019 GeV is scale of gravity)• Alternatively, why is

GF = 1/ mW2 >> GN = 1/mP

2 ?• Or, why is

VCoulomb >> VNewton ? e2 >> G m2 = m2 / mP2

• Set by hand? What about loop corrections?

δmH,W2 = O(α/π) Λ2

• Cancel boson loops fermions• Need | mB

2 – mF2| < 1 TeV2

Loop Corrections to Higgs Mass2

• Consider generic fermion and boson loops:

• Each is quadratically divergent: ∫Λd4k/k2

• Leading divergence cancelled if

Supersymmetry!

2

x 2

Other Reasons to like Susy

It enables the gauge couplings to unify

It predicts mH < 130 GeV

As suggested

by EW data

Astronomers saythat most of thematter in theUniverse isinvisible Dark Matter

Supersymmetric particles ?

We shall look for them with the

LHC

Dark Matter in the Universe

• Particles + spartners

• 2 Higgs doublets, coupling μ, ratio of v.e.v.’s = tan β• Unknown supersymmetry-breaking parameters:

Scalar masses m0, gaugino masses m1/2, trilinear soft couplings Aλ, bilinear soft coupling Bμ

• Often assume universality:Single m0, single m1/2, single Aλ, Bμ: not string?

• Called constrained MSSM = CMSSM• Minimal supergravity also predicts gravitino mass

m3/2 = m0, Bμ = Aλ – m0

Minimal Supersymmetric Extension of Standard Model (MSSM)

Why 2 Higgs Doublets?

• Cancel anomalous Higgsino trianglediagrams

• Superpotential must be analytic function of superfields:– Cannot use QUcH, QDcH*– Must use QUcHu, QDcHd

• Two Higgs fields:– Coupling between them: μHuHd

– Two different vev’s, ratio tan β

• Five physical Higgs bosons: 3 neutrals, H±

~

H

~

H

~

H

Non-Universal Scalar Masses?

• Different sfermions with same quantum #s?e.g., d, s squarks?disfavoured by upper limits on flavour-

changing neutral interactions

• Squarks with different #s, squarks and sleptons?disfavoured in various GUT models

e.g., dR = eL, dL = uL = uR = eR in SU(5), all in SO(10)

• Non-universal susy-breaking masses for Higgses?No reason why not! NUHM

•MSSM: > 100 parametersMinimal Flavour Violation: 13 parameters

(+ 6 violating CP)

SU(5) unification: 7 parameters

NUHM2: 6 parameters

NUHM1 = SO(10): 5 parameters

CMSSM: 4 parameters

mSUGRA:

3 parameters

String?

Lightest Supersymmetric Particle

• Stable in many models because of conservation of R parity:

R = (-1) 2S –L + 3B

where S = spin, L = lepton #, B = baryon #

• Particles have R = +1, sparticles R = -1:Sparticles produced in pairsHeavier sparticles lighter sparticles

• Lightest supersymmetric particle (LSP) stable

Possible Nature of LSP

• No strong or electromagnetic interactionsOtherwise would bind to matterDetectable as anomalous heavy nucleus

• Possible weakly-interacting scandidatesSneutrino

(Excluded by LEP, direct searches)Lightest neutralino χ (partner of Z, H, γ)Gravitino

(nightmare for detection)

Classic Supersymmetric Signature

Missing transverse energy

carried away by dark matter particles

Constraints on Supersymmetry

• Absence of sparticles at LEP, Tevatron

selectron, chargino > 100 GeV

squarks, gluino > 300 GeV

• Indirect constraints

Higgs > 114 GeV, b -> s γ

• Density of dark matter

lightest sparticle χ:

WMAP:

0.094 < Ωχh2 < 0.124

gμ - 2

Quo Vadisgμ - 2?

• Strong discrepancy between BNL experiment and e+e- data:

– now ~ 3.6 σ

• Better agreement between e+e-

experiments

• Increased discrepancy between BNL experiment and μ decay data

– now ~ 2.4 σ

• Convergence between e+e-

experiments and τ decay data

• More credibility?

Impact of LHC on the CMSSM

Excluded because stau LSP

Excluded by b s gamma

Preferred (?) by latest g - 2

Assuming the

lightest sparticle

is a neutralino

WMAP constraint on CDM density

tan β = 10 ✕ gμ - 2

LHC

tan β = 55 ✓ gμ - 2

JE, Olive & Spanos

Supersymmetric Models to Study

• Gravity-mediated:– NUHM2

• as below, mhu ≠ mhd

– NUHM1• as below, common mh ≠ m0

– CMSSM• m0, m1/2, tan β (B0), A0

– VCMSSM• as above, & A0 = B0 + m0

– mSUGRA• as above, & m3/2 = m0

– RPV CMSSM

• Other SUSY ✕ models:– Gauge-mediated

– Anomaly-mediated

– Mixed modulus-anomaly-mediated

– Phenomenological 19-parameter MSSM

– NMSSM

– ….Less studied in global fits

Most studied

in global fits

Also studied

in global fits

Some

Global

fitsIf model has N parameters,

sample 100 values/parameter:

102N points, e.g., 108 in CMSSM

Data

• Electroweak precision observables

• Flavour physics observables

• gμ - 2

• Higgs mass

• Dark matter

• LHCMasterCode: O.Buchmueller, JE et al.

Electroweak Precision Observables

• Inclusion essential for fair comparison with Standard Model

• Some observables may be

significantly different– E.g., mW, Afb(b)

– Advantage for SUSY?

• Some may not be changed

significantly– Should be counted against/for all models

To gμ – 2 or not to gμ – 2 ?

CMSSM NUHM1

Pre-LHC fits:Mild preference for small masses even without gμ – 2 ?

MasterCode: O.Buchmueller, JE et al.

XENON100 Experiment

Aprile et al: arXiv:1104.2549

Supersymmetry Searches in CMS

Jets + missing energy (+ lepton(s))

Supersymmetry Searches in ATLAS

Jets + missing energy + 0 lepton

Limits on Heavy MSSM Higgses

Favoured values of Mh ~ 119 GeV:

Range consistent with evidence from LHC !

Higgs mass

χ2 price to pay if Mh = 125 GeV is < 2

Buchmueller, JE et al: arXiv:1112.3564

….. pre-Higgs___ Higgs @ 125

68% & 95%

CL contours

Buchmueller, JE et al: arXiv:1112.3564

Favoured values of gluino mass significantly

above pre-LHC, > 2 TeV

Gluino mass

--- pre-Higgs___ Higgs @ 125

… H@125, no g-2

Buchmueller, JE et al: arXiv:1112.3564

Favoured values of squark mass significantly

above pre-LHC, > 2 TeV

Buchmueller, JE et al: arXiv:1112.3564

Squark mass

--- pre-Higgs___ Higgs @ 125

… H@125, no g-2

Favoured values of Bs μ+μ-

above Standard Model

Buchmueller, JE et al: arXiv:1112.3564

Bs μ+μ-

--- pre-Higgs___ Higgs @ 125

… H@125, no g-2

Favoured dark matter scattering rate

well below XENON100 limit

Buchmueller, JE et al: arXiv:1112.3564

Spin-independent

Dark matter scattering--- pre-Higgs___ Higgs @ 125

The Stakes in the Higgs Search

• How is gauge symmetry broken?• Is there any elementary scalar field?• Would have caused phase transition in the Universe when

it was about 10-12 seconds old• May have generated then the matter in the Universe:

electroweak baryogenesis• A related inflaton might have expanded the Universe

when it was about 10-35 seconds old • Contributes to today’s dark energy: 1060 too much!

Conversation with Mrs Thatcher: 1982

What do you do?

Think of things for the experiments to look

for, and hope they find something different

Wouldn’t it be better if they

found what

you predicted?

Then we would not learn anything!