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The Top Quark and Precision Measurements

Explore precision measurements testing the Standard Model (SM) in the electroweak sector using top quark contributions and models like MSSM, Higgs Triplets, and Little Higgs. Understand implications on new physics and constraints. Investigate muon decay, Higgs Triplets, and Left-Right Models in depth.

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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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