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!
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