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Beyond the :

• Outline – Why the Standard Model is probably not the final word – One way it might be fixed up: • Supersymmetry • What it is • What is predicts – How can we test it?

A.J. Barr Preface

• Standard Model doing very well – Measurements in agreement with predictions γ – Some very exact: dipole moment to 12 significant figures

• However SM does not include: e e – Dark All QED contributions • Weakly interacting massive particles? to dipole moment with ≤ four loops – calculated • Not in SM at all – Grand • Colour & Electroweak parts of one “Grand Unified” group? – Has a problem with Higgs

ShouldShould expectexpect toto findfind newnew phenomenaphenomena atat highhigh energyenergy mass • Standard Model Higgs boson mass:

114 GeV < mH <~ 1 TeV

Direct searches at “LEP” WW boson partial e+e- collider wave amplitudes > 1

h W e- W

Z0 e+ W W

Experimental search “Probabilities > 1” (compare Fermi model of weak ) More on mH … Fit to lots of data Measured W mass depends on mH (including mW)… H

W W W W emits & absorbs virtual Higgs boson  changes

 changes measured mW: 2 ∆ ∝ m H H mW mW ln 2 mW

 log dependence on mH … mH lighter than about 200 GeV

HiggsHiggs massmass isis samesame orderorder asas W,W, ZZ bosonsbosons Corrections to Higgs Mass?

H The top gets its mass λ by coupling to Higgs t t

t λ λ Similar diagram leads to a change HH_ in the Higgs propagator t  change in mH

Integrate (2) up to loop momentum ~ ΛUV λ2 ∆m2 = − Λ2 H π 2 UV Maximum at which 8 we think existing theory Changes of order ΛUV (SM) is valid Fixing the Higgs mass Problem: t 16 λ λ mGUT ~ 10 GeV mH ~ ΛUV h HH_ c 19 t m = ~ 10 GeV Pl G

mH (true) = mH (bare) + mH loop  needs extraordinary cancellation λ2 ∆ 2 = − Λ2 mH 2 UV  “Fine tuning” of mH (bare) 8π

Fix: Cancel this correction? -0 particle Boson loop  opposite correction: λ λ λ2 2 2 HH ∆m = + Λ H 8π 2 UV NeedNeed newnew partnerpartner ss == ½½ Same coupling as top toto cancelcancel eacheach SMSM particleparticle  New spin-0 particle Supersymmetry • Nature permits only (3) Supersymmetry particular types of •Anti-commuting generators: : = γ µ {Qr ,Qs} 2 rs Pµ (1) Space & time {A,B} ≡ AB + BA • Lorentz transforms • Rotations and •Q changes Fermion into translations Boson and vice-versa:

(2) Gauge symmetry Symbolically:Symbolically: • Such as Standard Model QQ fermion fermion bosonboson symmetries QQ boson boson  fermionfermion

• SU(3) c x SU(2) L x U(1)

EqualEqual numbersnumbers ofof bosonicbosonic && fermionicfermionic degreesdegrees ofof freedomfreedom PreciselyPrecisely whatwhat isis neededneeded toto fixfix HiggsHiggs massmass problemproblem (S)Particles

Standard Supersymmetric Model partners

(L&R) squarks (L&R) Spin-1/2 (L&R) sleptons (L&R) Spin-0 (L&?) sneutrinos (L&?) After Mixing γ B Bino 0 0 0 Spin-1 Z W Wino W± Wino ± 4 x neutral ino glu ino Spin-1/2 glu ino 0 ~ h H0 0 H ~ 2 x charg ino Spin-0 A0 H± ± H (Higgs inos )

Extended higgs sector 2 complex doublets  8-3 = 5 Higgs bosons Two complications

Unrestricted supersymmetry Supersymmetry is a  fast decay broken symmetry u _ _ If exact would have u~s u ~ Proton m(e ) = m(e) d e+ For stable need No partners yet observed conservation of: up to m ~ 100 GeV 3B+L+2S RP = (-1) Expect ~ TeV  fine tuning problem +1 SM particles RP = -1 SUSY particles Do we really need to double the particles?

• Lightest SUSY particle can easily be: – Uncharged – Stable WhyWhy stable?stable? – Massive Visible mass

• Good Invisible mass candidate Bullet cluster

Adding Supersymmetry also helps with - Grand Unification - Electroweak symmetry breaking

SupersymmetrySupersymmetry solvessolves aa lotlot ofof problemsproblems Finding Supersymmetry

• Precision • Direct search experiments E.g. LEP, , LHC E.g. magnetic moment colliders of the : q g q~ γ χ~0 γ + ~ µ µ~ q g ~ χ~0 q χ~0

Currently expt not quite in Produce heavy particles agreement with S.M. which then decay prediction WhyWhy producedproduced inin pairs?pairs? Mass/GeV • Complicated cascade decays – Many intermediates • Typical signal – Jets • Squarks and Gluinos – Leptons • Sleptons and weak gauginos – Missing mmtm • Undetected Lightest SUSY “Typical” SUSY spectrum Particle Simulated SUSY event

Missing transverse momentum Jets Heavy quarks Leptons After finding a Higgs boson…

• Discover Supersymmetry – Backgrounds? • Measure sparticle masses – Probe SUSY breaking mechanism • Measure sparticle spins – Show that they differ by ½ unit from SM • Find the other four Higgs bosons – Supersymmetry requires five Go hunting … More…

• SUSY primer: S.P. Martin http://arxiv.org/abs/hep-ph/9709356