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The Top Quark and Precision Measurements

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. Standard Model Case is Well Known. EW sector of SM is SU(2) x U(1) gauge theory

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The Top Quark and Precision Measurements

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  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, MZ,  • SM has =MW2/(MZ2c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. EW Measurements test consistency of SM 2005 We have a model…. And it works to the 1% level Consistency of precision measurements at multi-loop level used to constrain models with new physics

  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 Lore: Effects of LNEW become very small as  As the scale of the new physics becomes large, the SM is not always recovered, violating our intuition

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

  6. Calculate top quark contribution to rZ(mt2 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 rZ(continued) • Need s2/s2 • From SM relation using on-mass shell definition for s2 MW and MZ are physical masses s2/s2 not independent parameter 2005 Predict MW in terms of input parameters and mt Includes all known corrections

  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 • vSM2=(246 GeV)2=v2+4v2 • Real triplet doesn’t contribute to MZ • At tree level, =1+4v2/v2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 4th parameter • Variation of s: This is definition of s: Proportional to meneglect Contrast with SM where s2 is proportional to mt2 * Could equally well have used  as 4th parameter

  10. SM with triplet, cont. • Finally, mt2 dependence cancels • Putting it all together: mt2 dependence cancels rttriplet depends logarithmically on mt2 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 H0, 2A0, 2H • Count parameters: (g, g’, , ’, vR) (e , MW1, MW2, MZ1, MZ2) Assume gL=gR=g  EWSB Assume vL=0 (could be used to generate neutrino masses) SU(2)R x U(1)B-LU(1)Y Czakon, Zralek, Gluza, hep-ph/9906356

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

  13. Renormalization of s in LR Model, cont. • Scale set by: • At leading order in MW12/MW22  v2/vR2: Very different from SM! • As MW22, s2/s2 0 • The SM is not recovered!

  14. Thoughts on Decoupling • Limit MW22, 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 vR 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 mt dependence

  16. Final example: Littlest Higgs Model • EW precision constraints in SM require Mh light • To stabilize Mh 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  WH, ZH, BH • 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! b T t T T T

  18. Littlest Higgs Model, continued • One loop contributions numerically important • Tree level corrections (higher order terms in chiral perturbation theory)  v2/f2 • 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 • Mh0is lightest neutral Higgs • In SM: • Quadratic dependence on Mh0in 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

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