Presentation is loading. Please wait.

Presentation is loading. Please wait.

Radiative Corrections to the Standard Model S. Dawson TASI06, Lecture 3.

Similar presentations

Presentation on theme: "Radiative Corrections to the Standard Model S. Dawson TASI06, Lecture 3."— Presentation transcript:

1 Radiative Corrections to the Standard Model S. Dawson TASI06, Lecture 3

2 Radiative Corrections Good References: –Jim Wells, TASI05, hep-ph/ –K. Matchev, TASI04, hep-ph/ –M. Peskin and T. Takeuchi, Phys. Rev. D46, (1992) 381 –W. Hollik, TASI96, hep-ph/

3 Basics SM is SU(2) x U(1) theory –Two gauge couplings: g and g’ Higgs potential is V=-  2  2 +  4 –Two free parameters Four free parameters in gauge-Higgs sector –Conventionally chosen to be  =1/ (61) G F = (1) x GeV -2 M Z =  GeV M H –Express everything else in terms of these parameters

4 Example:  parameter At tree level, Many possible definitions of  ; use At tree level G CC =G NC =G F

5  parameter (#2) Top quark contributes to W and Z 2-point functions q  q piece of propagator connects to massless fermions, and doesn’t contribute here

6 Top Corrections to  parameter (Example) 2-point function of Z Shift momentum, k’=k + px N c =number of colors n=4-2  dimensions

7 Top Corrections to  parameter (#2) Shift momenta, keep symmetric pieces Only need g  pieces

8 Top Corrections to  parameter (#3) Only need answer at p 2 =0 Dimensional regularization gives:

9 Top Corrections to  parameter (#4) 2-point function of W, Z L t =1-4s W 2 /3 R t =-4s W 2 /3

10 Top quark doesn’t decouple Longitudinal component of W couples to top mass-- eg, tbW coupling: Decoupling theorem doesn’t apply to particles which couple to mass For longitudinal W’s:

11 Why doesn’t the top quark decouple? In QED, running of  at scale  not affected by heavy particles with M >>  Decoupling theorem: diagrams with heavy virtual particles don’t contribute at scales  << M if –Couplings don’t grow with M –Gauge theory with heavy quark removed is still renormalizable Spontaneously broken SU(2) x U(1) theory violates both conditions –Longitudinal modes of gauge bosons grow with mass –Theory without top quark is not renormalizable Effects from top quark grow with m t 2 Expect m t to have large effect on precision observables

12 Modification of tree level relations   r is a physical quantity which incorporates 1- loop corrections

13 Corrections to G F G F defined in terms of muon lifetime Consider 4-point interaction,with QED corrections Gives precise value: Angular spectrum of decay electrons tests V-A properties

14 G F at one loop Vertex and box corrections are small (but 1/  poles don’t cancel without them)

15 Renormalizing Masses Propagator corrections form geometric series

16 Running of , 1  (0)=1/ (61)  (p 2 )=  (0)[1+  ]

17 Running of , 2   p k k+p Photon is massless:   (0)=0 Calculate in n=4-2  dimensions

18 Running of , 3 Contributions of heavy fermions decouple: Contributions of light fermions:

19 Running of , 4 From leptons:  lept (M Z )= Light quarks require   at low p 2 Strong interactions not perturbative Optical theorem plus dispersion relation:

20 Have we seen  run? Langacker, Fermilab Academic Series, 2005

21 Final Ingredient is  s W 2 s W is not an independent parameter

22 Predict M W Use on-shell scheme:  r incorporates the 1-loop radiative corrections and is a function of ,  s, M h, m t,…

23 Data prefer light Higgs Low Q 2 data not included –Doesn’t include atomic parity violation in cesium, parity violation in Moller scattering, & neutrino-nucleon scattering (NuTeV) –Higgs fit not sensitive to low Q 2 data M h < 207 GeV –1-side 95% c.l. upper limit, including direct search limit Direct search limit from e + e -  Zh

24 Logarithmic sensitivity to M h Data prefer a light Higgs 2006

25 Understanding Higgs Limit M W (experiment)=  0.030

26 Light Higgs and Supersymmetry? Adding the extra particles of a SUSY model changes the fit, but a light Higgs is still preferred

27 How to define sin 2  W At tree level, equivalent expressions Can use these as definitions for renormalized sin 2  W They will all be different at the one-loop level On-shell Z-mass Effective s W (eff)

28 sin 2  w depends on scale Moller scattering, e - e -  e - e -  -nucleon scattering Atomic parity violation in Cesium

29 S,T,U formalism Suppose “new physics” contributes primarily to gauge boson 2 point functions –cf  r where vertex and box corrections are small Also assume “new physics” is at scale M>>M Z Two point functions for  , WW, ZZ,  Z

30 S,T,U, (#2) Taylor expand 2-point functions Keep first two terms Remember that QED Ward identity requires any amplitude involving EM current vanish at q 2 =0

31 S,T,U (#3) Use J Z =J 3 -s W 2 J Q Normalization of J Z differs by -1/2 from Lecture 2 here

32 S,T,U (#4) To O(q 2 ), there are 6 coefficients: Three combinations of parameters absorbed in , G F, M Z In general, 3 independent coefficients which can be extracted from data

33 S,T,U, (#5) Advantages: Easy to calculate Valid for many models Experimentalists can give you model independent fits SM contributions in , G F, and M Z

34 Limits on S & T A model with a heavy Higgs requires a source of large (positive)  T Fit assumes M h =150 GeV

35 Higgs can be heavy in models with new physics Specific examples of heavy Higgs bosons in Little Higgs and Triplet Models M h  GeV allowed with large isospin violation (  T=  ) and higher dimension operators We don’t know what the model is which produces the operators which generate large  T

36 Compute S,T, U from Heavy Higgs SM values of S, T, U are defined for a reference M h0

37 Using S,T, & U Assume new physics only contributes to gauge boson 2-point functions (Oblique corrections) Calculate observables in terms of SM contribution and S, T, and U

38 Conclusion Radiative corrections necessary to fit LEP and Tevatron data Radiative corrections strongly limit new models

Download ppt "Radiative Corrections to the Standard Model S. Dawson TASI06, Lecture 3."

Similar presentations

Ads by Google