Radiative Corrections in Quantum Field Theory

Transcription

1 p. 1/47 Radiative Corrections in Quantum Field Theory Martinus Veltman 80th birthday J. Iliopoulos Amsterdam, June 24, 2011

2 Happy Birthday, Tini p. 2/47

3 p. 3/47 Radiative Corrections in Quantum Field Theory

4 p. 4/47 Radiative Corrections in Quantum Field Theory Because of Tini s contributions

5 p. 5/47 Radiative Corrections in Quantum Field Theory Because of Tini s contributions Because they are at the basis of all successes of Q.F.T.

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9 p. 9/47 These papers, gave us to-day THE STANDARD MODEL

10 p. 10/47 THE STANDARD MODEL HAS BEEN ENORMOUSLY SUCCESSFUL

11 p. 11/47 Observable Mesure Ajustement α (5) had (m Z ) ± m Z [GeV] ± Γ Z [GeV] ± σ 0 had [nb] ± R l ± A 0,l fb ± A l (P τ ) ± R b ± R c ± A 0,b fb ± A 0,c fb ± A b ± A c ± A l (SLD) ± sin 2 θ lept eff (Q fb ) ± m W [GeV] ± Γ W [GeV] ± m t [GeV] ± O mes. - Oajust. σ mes

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14 p. 14/47 ǫ 1 = 3G Fm 2 t 8 2π 2 3G Fm 2 W 4 2π 2 tan2 θ W ln m H m Z +... (1) ǫ 3 = G Fm 2 W 12 2π 2 ln m H m Z G Fm 2 W 6 2π 2 ln m t m Z +... (2)

15 6 5 incertitude théorique α α(5) had = ± χ % CL 1 0 région exclue p. 15/47

16 What we have learnt p. 16/47

17 p. 17/47 What we have learnt Perturbation theory is remarkably reliable

18 p. 18/47 What we have learnt Perturbation theory is remarkably reliable Outside the region of strong interactions

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20 -We know of no reason for this remarkable validity p. 20/47

21 p. 21/47 Dyson s argument: A n α n (2n 1)!! Perturbation theory breaks down when A n A n+1 2n + 1 α 1 For QED n >> 1 ; For QCD???

22 I want to exploit this experimental fact and argue that the available precision tests of the Standard Model allow us to claim with reasonable confidence that new physics will be unravelled at the LHC. 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. p. 22/47

23 p. 23/47 Precision measurements at one energy scale allow us to guess New Physics at the next scale

24 p. 24/47 EXAMPLES: 1) Yukawa s prediction of the π meson. The Physics was accurate, the details were not

25 p. 25/47 EXAMPLES: 1) Yukawa s prediction of the π meson. The Physics was accurate, the details were not 2) Tini s work of the 60 s gave us: -The neutral currents -The W bosons -...

26 In the same way New Physics may be predicted for LHC p. 26/47

27 p. 27/47 Major task of Tevatron and LHC Study the Higgs sector of the theory. m 2 H λ g 2 m 2 W 0 < λ < 1

28 p. 28/47 Major task of Tevatron and LHC Study the Higgs sector of the theory. Limits on the Standard Model Higgs mass: 1) m H 114 GeV (Exp.) 2) m H 200 GeV (From global fit) 3) m H O(1TeV) (Validity of perturbation) 4) m H O(130GeV) (Vacuum stability)

29 p. 29/47 m 2 H λ dλ dt = 3 4π 2 [λ 2 + 3λh 2 t 9h 4 t +...]

30 p. 30/47 Validity of perturbation The Landau pole does not occur up to Λ

31 p. 31/47 Validity of perturbation The Landau pole does not occur up to Λ Λ 1TeV m H 0.8TeV

32 p. 32/47 Validity of perturbation The Landau pole does not occur up to Λ Λ 1TeV m H 0.8TeV Λ GeV m H 180GeV

33 p. 33/47 Vacuum stability λ > 0 for Λ GeV m H 130GeV

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35 p. 35/47 Can we predict the value of the Higgs mass in the Standard Model? (No New Physics assumed!) m Z /m H = C (3) C = m Z m H = g g2 2 8λ (4)

36 p. 36/47 16π 2 β g1 = g π 2 β g2 = g π 2 β λ = 12λ g2 1λ 9g 2 2λ g g2 1g g4 2 (5)

37 p. 37/47 β z = β η1 + β η2 = = λw [( 27 16π 2 ρz 100 ρ ρ + 9 ) 4 +12(ρ + 1) 2] z 2 ( 2ρ ρ 16 3 ) z η 1 = g2 1 λ ; η 2 = g2 2 λ ; z = η 1 + η 2 ; ρ = η 1 η 2 ; w = η 1 η 2 β z has no zeroes for z > 0

38 Possible (Predictable) LHC Results p. 38/47

39 p. 39/47 Possible (Predictable) LHC Results 1) A Light Higgs is found

40 p. 40/47 Possible (Predictable) LHC Results 1) A Light Higgs is found The Standard Model is complete

41 p. 41/47 Possible (Predictable) LHC Results 1) A Light Higgs is found The Standard Model is complete No new Strong Interactions Perturbation theory is reliable

42 p. 42/47 Possible (Predictable) LHC Results 1) A Light Higgs is found The Standard Model is complete No new Strong Interactions Perturbation theory is reliable m 2 H αm2 Hierarchy, or Fine tuning

43 p. 43/47 Possible (Predictable) LHC Results 2) A Light Higgs is NOT found

44 p. 44/47 Possible (Predictable) LHC Results 2) A Light Higgs is NOT found Perturbation theory breaks down New Strong Interactions

45 p. 45/47 Possible (Predictable) LHC Results THE ABSENCE OF A LIGHT HIGGS IMPLIES NEW PHYSICS BUT A LIGHT HIGGS IS UNSTABLE WITHOUT NEW PHYSICS

46 p. 46/47 CONCLUSIONS THE TIME FOR SPECULATIONS WILL BE SOON OVER! L.H.C. IS WORKING

47 p. 47/47 CONCLUSIONS THE TIME FOR SPECULATIONS WILL BE SOON OVER! L.H.C. IS WORKING THE COMPUTATION OF THE RADIATIVE CORRECTIONS IS THE MOST URGENT THEORETICAL TASK

48 p. 48/47 CONCLUSIONS THE TIME FOR SPECULATIONS WILL BE SOON OVER! L.H.C. IS WORKING THE COMPUTATION OF THE RADIATIVE CORRECTIONS IS THE MOST URGENT THEORETICAL TASK

49 p. 49/47 CONCLUSIONS TINI CANNOT RETIRE NEVER BEFORE AN EXPERIMENTAL FACILITY WAS LOADED WITH SO GREAT EXPECTATIONS