Iliopoulos - Radiative Corrections in Quantum Field Theory

7/28/2019 Iliopoulos - Radiative Corrections in Quantum Field Theory

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Radiative Corrections

in Quantum Field Theory

Martinus Veltman 80th birthday

J. Iliopoulos

Amsterdam, June 24, 2011

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Happy Birthday, Tini

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Because of Tinis contributions

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These papers, gave us to-day

THE STANDARD MODEL

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THE STANDARD MODEL

HAS BEEN ENORMOUSLYSUCCESSFUL

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0 1 2 3

had(mZ)(5)

0.02761 0.00036 0.02768

mZ[GeV]mZ[GeV] 91.1875 0.0021 91.1873

Z[GeV]Z[GeV] 2.4952 0.0023 2.4965

had

[nb]0

41.540 0.037 41.481

Rl

Rl

20.767 0.025 20.739

Afb

A0,l

0.01714 0.00095 0.01642

Al

(P)A

l

(P) 0.1465 0.0032 0.1480

RbRb 0.21638 0.00066 0.21566

Rc

Rc

0.1720 0.0030 0.1723

AfbA0,b

0.0997 0.0016 0.1037

Afb

A0,c

0.0706 0.0035 0.0742

Ab

Ab

0.925 0.020 0.935

Ac

Ac

0.670 0.026 0.668

Al(SLD)Al(SLD) 0.1513 0.0021 0.1480

sin2effsin2lept(Qfb) 0.2324 0.0012 0.2314

mW

[GeV]mW[GeV] 80.425 0.034 80.398

W[GeV]W[GeV] 2.133 0.069 2.094

mt[GeV]mt[GeV] 178.0 4.3 178.1

Mesure AjustementObservableO - Omes. ajust.

mes.

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1 = 3GFm

2t

8

22 3GFm

2W

4

22tan2 W ln m

H

mZ+ ... (1)

3 =GFm

2W

12

22ln

mHmZ

GFm2W

6

22ln

mtmZ

+ ... (2)

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0

1

2

3

4

5

6

10020 400

2

rgion exclue

had=

(5)0.027610.00036

incertitude thorique

260

95% CL

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What we have learnt

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What we have learnt

Perturbation theory is remarkably reliable

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What we have learnt

Perturbation theory is remarkably reliable

Outside the region of strong interactions

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-We know of no reason for this remarkable validity

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Dysons argument:

An n(2n 1)!!

Perturbation theory breaks down when An An+1

2n + 1 1

For QED n >> 1 ; For QCD ???

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I want to exploit this experimental fact and argue that the

available precision tests of the Standard Model allow us toclaim with reasonable confidence that new physics will beunravelled at the LHC.The argument assumes the validity of perturbation theoryand it will fail if the latter fails. But, as we just saw,

perturbation theory breaks down only when stronginteractions become important. But new strong interactionsimply new physics.

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Precision measurements at one energy scale

allow us to guess New Physics at the next scale

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EXAMPLES:

1) Yukawas prediction of the meson.

The Physics was accurate, the details were not

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EXAMPLES:

1) Yukawas prediction of the meson.

The Physics was accurate, the details were not

2) Tinis work of the 60s gave us:-The neutral currents-The W bosons-.......

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In the same way New Physics may be

predicted for LHC

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M j k f T d LHC


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Major task of Tevatron and LHC

Study the Higgs sector of the theory.

m2H g2 m2W

0 < < 1

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M j k f T d LHC


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Major task of Tevatron and LHC

Study the Higgs sector of the theory.

Limits on the Standard Model Higgs mass:

1) mH 114 GeV (Exp.)2) mH 200 GeV (From global fit)

3) mH O(1TeV) (Validity of perturbation)

4) mH O(130GeV) (Vacuum stability)

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m2

H

ddt =

342

[2 + 3h2t 9h4t + ...]

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V lidit f t b ti


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Validity of perturbation

The Landau pole does not occur up to

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V lidit f t b ti


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1T eV mH 0.8T eV

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V lidit f t b ti


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1T eV mH 0.8T eV

1016GeV mH 180GeV

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V t bilit


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Vacuum stability

> 0

for 1016GeV

mH 130GeV

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Can we predict the value of the Higgs mass in the Standard

Model?(No New Physics assumed!)

mZ/mH = C (3)

C = mZmH

=g2

1 +g22

8(4)

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162g1 = g31 110

162g2 = g3243

6

162 = 122

9

5

g21

9g22 +27

100

g41 +9

10

g21g22 +

9

4

g42

(5)

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z = 1 + 2 =

=w

162z

27

1002 +

9

10 +

9

4

z2

22 +

54

5 16

3

z

+12( + 1)2

1 =g21

; 2 =g22

; z = 1 + 2 ; =1

2; w = 12

z has no zeroes for z > 0

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P ibl (P di t bl ) LHC R lt


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Possible (Predictable) LHC Results

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1) A Light Higgs is found

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The Standard Model is complete

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No new Strong Interactions

Perturbation theory is reliable

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No new Strong Interactions

Perturbation theory is reliable

m2H M2

Hierarchy, or Fine tuning

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2) A Light Higgs is NOT found

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2) A Light Higgs is NOT found

Perturbation theory breaks down

New Strong Interactions

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THE ABSENCE OF A LIGHT HIGGS

IMPLIES NEW PHYSICS

BUT A LIGHT HIGGS IS UNSTABLE

WITHOUT NEW PHYSICS

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CONCLUSIONS


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CONCLUSIONS

THE TIME FOR SPECULATIONS WILL BE SOON OVER!

L.H.C. IS WORKING

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CONCLUSIONS


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CONCLUSIONS


L.H.C. IS WORKING

THE COMPUTATION OF THE RADIATIVE CORRECTIONS

IS THE MOST URGENT THEORETICAL TASK

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CONCLUSIONS


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CONCLUSIONS


L.H.C. IS WORKING

THE COMPUTATION OF THE RADIATIVE CORRECTIONS

IS THE MOST URGENT THEORETICAL TASK

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CONCLUSIONS


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CONCLUSIONS

TINI CANNOT RETIRE

NEVER BEFORE AN EXPERIMENTAL FACILITY WASLOADED WITH SO GREAT EXPECTATIONS

Iliopoulos - Radiative Corrections in Quantum Field Theory

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