STANDARD MODEL

Theoretical Constraints on Higgs Mass Large M h → large self-coupling → blow up at low-energy scale Λ due to renormalization Small: renormalization due to t quark drives quartic coupling < 0 at some scale Λ → vacuum unstable Vacuum could be stabilized by supersymmetry Espinosa, JE, Giudice, Hoecker, Riotto, arXiv 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 fates Confidence Levels (CL) without/with Tevatron exclusion Blow-up excluded at 99.2% CL Espinosa, JE, Giudice, Hoecker, Riotto CL as function of instability Scale Λ

The LHC will Tell the Fate of the SM Espinosa, JE, Giudice, Hoecker, Riotto Examples with LHC measurement of m H = 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 M h ~ 119 GeV: Range consistent with evidence from LHC ! Higgs mass χ 2 price to pay if M h = 125 GeV is < 2 Buchmueller, JE et al: arXiv:

Supersymmetry? Would unify matter particles and force particles Related particles spinning at different rates 0 - ½ /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 m W << m P ? (m P ~ GeV is scale of gravity) Alternatively, why is G F = 1/ m W 2 >> G N = 1/m P 2 ? Or, why is V Coulomb >> V Newton ? e 2 >> G m 2 = m 2 / m P 2 Set by hand? What about loop corrections? δ m H,W 2 = O( α / π ) Λ 2 Cancel boson loops  fermions Need | m B 2 – m F 2 | < 1 TeV 2

Loop Corrections to Higgs Mass 2 Consider generic fermion and boson loops: Each is quadratically divergent: ∫ Λ d 4 k/k 2 Leading divergence cancelled if Supersymmetry! 2 x 2

Other Reasons to like Susy It enables the gauge couplings to unify It predicts m H < 130 GeV As suggested by EW data

Astronomers say that most of the matter in the Universe is invisible 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 m 0, gaugino masses m 1/2, trilinear soft couplings A λ, bilinear soft coupling B μ Often assume universality: Single m 0, single m 1/2, single A λ, B μ : not string? Called constrained MSSM = CMSSM Minimal supergravity also predicts gravitino mass m 3/2 = m 0, B μ = A λ – m 0 Minimal Supersymmetric Extension of Standard Model (MSSM)

Why 2 Higgs Doublets? Cancel anomalous Higgsino triangle diagrams Superpotential must be analytic function of superfields: –Cannot use QU c H, QD c H* –Must use QU c H u, QD c H d Two Higgs fields: –Coupling between them: μH u H d –Two different vev’s, ratio tan β Five physical Higgs bosons: 3 neutrals, H ± ~H~H ~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., d R = e L, d L = u L = u R = e R in SU(5), all in SO(10) Non-universal susy-breaking masses for Higgses? No reason why not! NUHM

MSSM: > 100 parameters Minimal 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 pairs Heavier sparticles  lighter sparticles Lightest supersymmetric particle (LSP) stable

Possible Nature of LSP No strong or electromagnetic interactions Otherwise would bind to matter Detectable as anomalous heavy nucleus Possible weakly-interacting scandidates Sneutrino (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: < Ω χ h 2 < g μ - 2

Quo Vadis g μ - 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 ✕ g μ - 2 LHC tan β = 55 ✓ g μ - 2 JE, Olive & Spanos

Supersymmetric Models to Study Gravity-mediated: –NUHM2 as below, m hu ≠ m hd –NUHM1 as below, common m h ≠ m 0 –CMSSM m 0, m 1/2, tan β (B 0 ), A 0 –VCMSSM as above, & A 0 = B 0 + m 0 –mSUGRA as above, & m 3/2 = m 0 –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 fits If model has N parameters, sample 100 values/parameter: 10 2N points, e.g., 10 8 in CMSSM

Data Electroweak precision observables Flavour physics observables g μ - 2 Higgs mass Dark matter LHC MasterCode: O.Buchmueller, JE et al.

Electroweak Precision Observables Inclusion essential for fair comparison with Standard Model Some observables may be significantly different –E.g., m W, A fb (b) –Advantage for SUSY? Some may not be changed significantly –Should be counted against/for all models

To g μ – 2 or not to g μ – 2 ? CMSSM NUHM1 Pre-LHC fits: Mild preference for small masses even without g μ – 2 ? MasterCode: O.Buchmueller, JE et al.

X ENON 100 Experiment Aprile et al: arXiv:

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 M h ~ 119 GeV: Range consistent with evidence from LHC ! Higgs mass χ 2 price to pay if M h = 125 GeV is < 2 Buchmueller, JE et al: arXiv:

….. pre-Higgs ___ % & 95% CL contours Buchmueller, JE et al: arXiv:

Favoured values of gluino mass significantly above pre-LHC, > 2 TeV Gluino mass --- pre-Higgs ___ 125 … no g-2 Buchmueller, JE et al: arXiv:

Favoured values of squark mass significantly above pre-LHC, > 2 TeV Buchmueller, JE et al: arXiv: Squark mass --- pre-Higgs ___ 125 … no g-2

Favoured values of B s  μ + μ - above Standard Model Buchmueller, JE et al: arXiv: Bs μ+μ-Bs μ+μ- --- pre-Higgs ___ 125 … no g-2

Favoured dark matter scattering rate well below XENON100 limit Buchmueller, JE et al: arXiv: Spin-independent Dark matter scattering --- pre-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 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 seconds old Contributes to today’s dark energy: 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!