2012/11/12 by Christopher T. Hill, Hill, Christopher T.
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #hep-ph #hep-th
paper · pdf · doi:10.48550/arxiv.1211.2773
30 pages, to appear in Phys. Rev. D
arxiv created 2013/02/06 · arxiv updated 2013/02/07
The top-Higgs system, consisting of top quark (LH doublet, RH singlet), and Higgs boson kinetic terms, with gauge fields set to zero, has an exact (modulo total divergences) symmetry where both fermion and Higgs fields are shifted and mixed in a supersymmetric fashion. The full Higgs-Yukawa interaction and Higgs-potential, including additional 1/Λ2 N JL-like interactions, also has this symmetry to 0(1/Λ4) up to null-operators. Thus the interaction lagrangian can be viewed as a power series in 1/Λ2. The symmetry involves interplay of the Higgs quartic interaction with the Higgs-Yukawa interaction and implies the relationship, λ= \half g2 between the top--Yukawa coupling, g, and Higgs quartic coupling, λ, at a high energy scale Λ= few TeV. We interpret this to be a new physics scale. The top quark is massless in the symmetric phase, satisfying the Nambu-Goldstone theorem. The fermionic shift part of the current is ∝ (1-H^† H/v2), owing to the interplay of λand g, and vanishes in the broken phase. Hence the Nambu-Goldstone theorem is trivially evaded in the broken phase and the top quark becomes heavy (it is not a Goldstino). We have mt=mh,subject to radiative corrections that can in principle pull the Higgs into concordance with experiment.