HIGH ENERGY PHYSICS at the dawn of the L.H.C. era J. Iliopoulos, - PowerPoint PPT Presentation

HIGH ENERGY PHYSICS at the dawn of the L.H.C. era J. Iliopoulos, ENS, Paris Les Houches Summer School August 2011

• The long awaited experimental results are coming close. • The last year of theoretical speculations. • We feel quite confident that fundamental discoveries are ahead. • A most exciting period to enter High Energy Physics.

• We often say that revolutions in Physics come because an unexpected experimental result forces physicists to change their theoretical paradigms. • This has often been the case in the past. • But the revolution which linked permanently Physics and Geometry had a theoretical, even an aesthetic, motivation. • It led to the formulation of the STANDARD MODEL in Particle Physics. • It is a gauge theory based on the group SU ( 3 ) × SU ( 2 ) × U ( 1 ) spontaneously broken to SU ( 3 ) × U ( 1 ) em .

THE STANDARD MODEL HAS BEEN ENORMOUSLY SUCCESSFUL

O - O ajust. Observable Mesure Ajustement mes. σ mes. ∆α (5) ∆α had (m Z ) 0.02761 ± 0.00036 0.02768 m Z [ GeV ] m Z [ GeV ] 91.1875 ± 0.0021 91.1873 Γ Z [ GeV ] Γ Z [ GeV ] 2.4952 ± 0.0023 2.4965 σ had [ nb ] σ 0 41.540 ± 0.037 41.481 20.767 ± 0.025 R l R l 20.739 A 0,l 0.01714 ± 0.00095 A fb 0.01642 0.1465 ± 0.0032 A l (P τ ) A l (P τ ) 0.1480 0.21638 ± 0.00066 R b R b 0.21566 0.1720 ± 0.0030 R c R c 0.1723 A 0,b 0.0997 ± 0.0016 A fb 0.1037 A 0,c 0.0706 ± 0.0035 A fb 0.0742 0.925 ± 0.020 A b A b 0.935 0.670 ± 0.026 A c A c 0.668 0.1513 ± 0.0021 A l (SLD) A l (SLD) 0.1480 sin 2 θ eff sin 2 θ lept (Q fb ) 0.2324 ± 0.0012 0.2314 m W [ GeV ] m W [ GeV ] 80.425 ± 0.034 80.398 Γ W [ GeV ] Γ W [ GeV ] 2.133 ± 0.069 2.094 m t [ GeV ] m t [ GeV ] 178.0 ± 4.3 178.1 0 1 2 3

ǫ 1 = 3 G F m 2 2 π 2 − 3 G F m 2 2 π 2 tan 2 θ W ln m H t W √ √ + ... (1) m Z 8 4 ǫ 3 = G F m 2 − G F m 2 2 π 2 ln m H 2 π 2 ln m t W W √ √ + ... (2) m Z m Z 12 6

• All but one of the parameters of the Standard Model have been quite accurately determined by experiment. • The precision of the measurements often led to successful predictions of new Physics. (Ex. Neutral currents, Charmed Particles, Gauge bosons, New quarks, etc) • The last remaining parameter is the Higgs boson mass. • Through the radiative corrections it enters into the determination of other physical quantities, but the dependence is only logarithmic. (Screening Theorem).

6 incertitude théorique ∆α 5 ∆α (5) 0.02761 ± 0.00036 had = 4 ∆χ 2 3 95% CL 2 1 région exclue 0 260 20 100 400 m H [ GeV ]

SM CMS Preliminary, CMS Preliminary, s s = 7 TeV = 7 TeV CL CL CL Observed Observed Observed S S S σ -1 -1 Combined, L Combined, L = 1.1 fb = 1.1 fb CL CL CL Expected Expected Expected 1 1 1 ± ± ± σ σ σ / 95% S S S int int CL CL CL Expected Expected Expected 2 2 2 ± ± ± σ σ σ 10 S S S σ Bayesian Observed Bayesian Observed Bayesian Observed Limit 1 100 200 300 400 500 600 2 Higgs boson mass (GeV/c )

Limits on the Standard Model Higgs mass : 1) 160 GeV ≥ m H ≥ 114 GeV (Exp.) 2) m H = 85 + 39 − 28 GeV (From global fit) 3) m H ≤ O (1TeV) (Validity of perturbation) 4) m H ≥ O (130GeV) (Vacuum stability)

m 2 H ∼ λ 4 π 2 [ λ 2 + 3 λ h 2 d λ 3 t − 9 h 4 dt = t + ... ]

Validity of perturbation The Landau pole does not occur up to Λ Λ ∼ 1 TeV → m H ≤ 0 . 8 TeV Λ ∼ 10 16 GeV → m H ≤ 180 GeV

Vacuum stability λ > 0 for Λ ∼ 10 16 GeV m H ≥ 110 − 120 GeV

Can we “predict” the value of the Higgs mass ? m Z / m H = C (3) � g 2 1 + g 2 C = m Z 2 = √ (4) m H 8 λ

1 16 π 2 β g 1 = g 3 1 10 43 16 π 2 β g 2 = − g 3 (5) 2 6 16 π 2 β λ = 12 λ 2 − 9 2 λ + 27 1 + 9 2 + 9 5 g 2 1 λ − 9 g 2 100 g 4 10 g 2 1 g 2 4 g 4 2

β z = β η 1 + β η 2 = �� 27 � � � − λ w 100 ρ 2 + 9 10 ρ + 9 2 ρ 2 + 54 5 ρ − 16 z 2 − = z 16 π 2 ρ z 4 3 + 12 ( ρ + 1 ) 2 � (6) η 1 = g 2 η 2 = g 2 ρ = η 1 1 2 ; ; z = η 1 + η 2 ; ; w = η 1 η 2 (7) λ λ η 2

What we have learnt Perturbation theory is remarkably reliable Outside the region of strong interactions

Why ? -We do not really understand why. Simple argument : A n ∼ α n ( 2 n − 1 )!! Perturbation theory breaks down when A n ∼ A n + 1 2 n + 1 ∼ α − 1 For QED n >> 1 ; For QCD ? ? ?

General rule : Precision measurements at a given energy scale allow to guess new Physics at the next energy scale

Example : Yukawa’s prediction of the π meson in 1934 The range of nuclear forces is of order 1 fermi ( ∼ 10 − 13 cm). The Physics was correct, the details were not ! ! Example : The prediction for charmed particles in 1969 The absence, with very high accuracy, of certain weak decays

• Three decades of intense experimental effort, mainly at L.E.P., but also at the Tevatron, B -factories, ν -physics etc, have brought the agreement between the Standard Model and experiment to an impressive degree of accuracy. • I want to exploit this experimental fact and argue that the available precision tests of the Standard Model allow us to claim with confidence that new physics is present at the TeV scale and the LHC can, probably, discover it. • The argument assumes the validity of perturbation theory and it will fail if the latter fails. But, as we just saw, perturbation theory breaks down only when strong interactions become important. But new strong interactions imply new physics.

First task of LHC Study the Higgs sector of the theory.

Possible (Predictable) LHC Results 1) A Light Higgs is found The Standard Model is complete No new Strong Interactions ⇒ Perturbation theory is reliable ⇒ H ∼ α M 2 ⇒ Hierarchy m 2

Possible Answers : • Supersymmetry • Possible solution of the dark matter problem • Gauge coupling unification

60 −1 50 � 1 40 −1 � 30 −1 � 2 20 10 −1 � 3 0 2 4 6 8 10 12 14 16 18 Log 10 (Q/1 GeV)

• Theoretically very attractive • Fermion-Boson connection • Higgs-Gauge boson connection • Non-renormalisation theorems • Possible connection with Gravity • BUT...The precise supersymmetry breaking mechanism is still unknown

Other answers to the hierarchy problem : • Large extra dimensions • Connection with Gravity • More spectacular, less probable ? ?

Possible (Predictable) LHC Results 2) A Light Higgs is NOT found • Seems unlikely, but... • Perturbation theory breaks down • ⇒ New Strong Interactions

Possible Answers : • Technicolor The Higgs boson is a bound state of new, heavy fermions • Little Higgs The Higgs boson is a pseudo-Goldstone boson of a new symmetry

THE ABSENCE OF A LIGHT HIGGS IMPLIES NEW PHYSICS BUT A LIGHT HIGGS IS UNSTABLE WITHOUT NEW PHYSICS

CONCLUSIONS THE TIME FOR SPECULATIONS WILL BE SOON OVER ! L.H.C. IS WORKING NEVER BEFORE AN EXPERIMENTAL FACILITY WAS LOADED WITH SO GREAT EXPECTATIONS