1. The Top Quark and Precision Measurements S. Dawson BNL April, 2005 M.-C. Chen, S. Dawson, and T. Krupovnikas, in preparation M.-C. Chen and S. Dawson, hep-ph/0311032

2. Standard Model Case is Well Known EW sector of SM is SU(2) x U(1) gauge theory –3 inputs needed: g, g’, v, plus fermion/Higgs masses –Trade g, g’, v for precisely measured G , M Z,  –SM has  =M W 2 /(M Z 2 c  2 )=1 at tree level s  is derived quantity –Models with  =1 at tree level include MSSM Models with singlet or doublet Higgs bosons Models with extra fermion families

3. We have a model…. And it works to the 1% level EW Measurements test consistency of SM Consistency of precision measurements at multi-loop level used to constrain models with new physics 2005

4. Models with  1 at tree level are different SM with Higgs Triplet Left-Right Symmetric Models Little Higgs Models …..many more These models need additional input parameter Decoupling is not so obvious beyond tree level As the scale of the new physics becomes large, the SM is not always recovered, violating our intuition Lore: Effects of L NEW become very small as 

5. Muon Decay in the SM At tree level, muon decay related to input parameters: One loop radiative corrections included in parameter  r Z Where:   e e W If  1, there would be 4 input parameters

6. Calculate top quark contribution to  r Z (m t 2 dependence only) Muon decay constant: Vertex and box corrections,  V-B small  neglect Vacuum polarization,  / , has no quadratic top mass dependence Z-boson 2-point function:

7. Calculate top quark contribution to  r Z (continued) Need  s  2 /s  2 From SM relation using on-mass shell definition for s  2 M W and M Z are physical masses  s  2 /s  2 not independent parameter Includes all known corrections Predict M W in terms of input parameters and m t 2005

8. What’s different with a Higgs Triplet? SM: SU(2) x U(1) –Parameters, g, g’, v Add a real triplet, (  +,  0,  -),  0  =v  –Parameters in gauge sector: g, g’, v, v  –v SM 2 =(246 GeV) 2 =v 2 +4v  2 –Real triplet doesn’t contribute to M Z At tree level,  =1+4v  2 /v 2  1 Return to muon decay: Blank & Hollik, hep-ph/9703392

9. Need Four Input Parameters With Higgs Triplet Use effective leptonic mixing angle at Z resonance as 4 th parameter Variation of s  : This is definition of s  : Proportional to m e  neglect Contrast with SM where  s  2 is proportional to m t 2 * Could equally well have used  as 4 th parameter

10. SM with triplet, cont. Putting it all together: Finally, m t 2 dependence cancels  r t triplet depends logarithmically on m t 2 If there is no symmetry which forces v  =0, then no matter how small v  is, you still need 4 input parameters v   0 then   1 Triplet mass, M   gv   Two possible limits: g fixed, then light scalar in spectrum M  fixed, then g  and theory is non-renormalizable

11. SU(2) L x SU(2) R x U(1) B-L Model Minimal model Physical Higgs bosons: 4 H 0, 2A 0, 2H  Count parameters: (g, g’, ,  ’, v R )  (e, M W 1, M W 2, M Z 1, M Z 2 ) Czakon, Zralek, Gluza, hep-ph/9906356  EWSB SU(2) R x U(1) B-L  U(1) Y Assume v L =0 (could be used to generate neutrino masses) Assume g L =g R =g

12. Renormalization of s  in LR Model Expand equations to incorporate one-loop corrections: etc Gauge boson masses after symmetry breaking: +2=2+’2+2=2+’2 Solve for  s  2 using

13. Renormalization of s  in LR Model, cont. Scale set by: At leading order in M W 1 2 /M W 2 2  v 2 /v R 2 : Very different from SM! As M W 2 2 ,  s  2 /s  2  0 The SM is not recovered!

14. Thoughts on Decoupling  Limit M W 2 2 ,  s  2  0  SM is not recovered 4 input parameters in Left-Right model: 3 input parameters in SM No continuous limit from Left-Right model to SM Even if v R is very small, still need 4 input parameters  No continuous limit which takes a theory with  =1 at tree level to  1 at tree level

15. Results on Top Mass Dependence Scale fixed to go through data point Absolute scale arbitrary Plots include only m t dependence

16. Final example: Littlest Higgs Model EW precision constraints in SM require M h light To stabilize M h introduce new states to cancel quadratic dependence on higher scales –Classic model of this type is MSSM Littlest Higgs model: non-linear  model based on SU(5)/SO(5) –Global SU(5)  Global SO(5) with  –Gauged [SU(2) x U(1)] 1 x [SU(2) x U(1)] 2  SU(2) x U(1) SM –  is complex Higgs triplet

17. Littlest Higgs Model, continued Model has complex triplet (  1) at tree level –Requires 4 input parameters Quadratic divergences cancelled at one-loop by new states W, Z, B  W H, Z H, B H t  T H   Cancellation between states with same spin statistics –Naturalness requires f ~ few TeV Just like in SM with triplet, dependence of  r on charge 2/3 quark, T, is logarithmic! TT T Ttb

18. Littlest Higgs Model, continued One loop contributions numerically important –Tree level corrections (higher order terms in chiral perturbation theory)  v 2 /f 2 –One loop radiative corrections  1/16  2 –Large cancellations between tree level and one-loop corrections –Low cutoff with f  2 TeV is still allowed for some parameters. –Contributions grow quadratically with scalar masses Quadratic contributions cancel between these Quadratic contribution remains from mixed diagrams

19. Fine Tuned set of parameters in LH Model  Parameters chosen for large cancellations

20. Models with triplets have Quadratic dependence on Higgs mass M h 0 is lightest neutral Higgs In SM: Quadratic dependence on M h 0 in LR Model: Quadratic dependence also found in little Higgs model Czakon, Zralek J. Gluza, hep-ph/9906356 M.-C. Chen and S. Dawson, hep-ph/0311032

21. Conclusion Models with  1 at tree level require 4 input parameters in gauge sector for consistent renormalization –Cannot write models as one-loop SM contribution plus tree level new physics contribution in general Models with extended gauge symmetries can have very different behaviour of EW quantities from SM beyond tree level –Obvious implications for moose models, little Higgs models, LR models, etc