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Author Info

  • Katy Hartling
  • Kunal Kumar
  • Heather E. Logan

Model Description and Implementation

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The Georgi-Machacek (GM) model was proposed in 1985 [1] as a plausible scenario for EWSB with interesting collider signatures. In this model, the scalar sector of the Standard Model (SM) is extended by the addition of one complex and one real SU(2) triplet. The hypercharge assignments of the triplets allows for a custodial SU(2) symmetry to be imposed upon the scalar potential, so that rho=1 is preserved at tree level. This is desirable for SM extensions in light of constraints from electroweak precision data. The model has the following salient features that make it phenomenologically interesting:

  • the hVV (and hhVV) coupling can be enhanced compared to the SM
  • the presence of additional scalars (including doubly charged ones)

The GM model can thus be a useful benchmark for the study of Higgs properties as well as searches for additional scalars.

The doublet vev v\phi and the triplet vevs v_chi are constrained by v_phi2 + 8 v_chi2 = v_SM2 to ensure the model generates the measured W and Z boson masses. We parametrize the relative size of the vevs by tan \theta_H = 2\sqrt{2} v_chi/v_phi.

The scalars (apart form Goldstone bosons) in this model can be classified as two custodial SU(2) singlets, a triplet and a fiveplet. The two custodial singlets mix by an angle alpha to give eigenstates h and H, one of which is the 125 GeV Higgs.

We follow Ref. [2] to implement the most general scalar potential that conserves custodial SU(2). It is automatically CP-conserving. The parameters of the potential are denoted by mu2sq, mu3sq, lam1, lam2, lam3, lam4, lam5, M1coeff and M2coeff in the .fr file. We trade three of these to obtain the set of 9 external parameters (mh, Gf, tanth, lam2, lam3, lam4, lam5, M1coeff, M2coeff) in the .fr file that define the scalar potential.

The GM Lagrangian implementation is based on the SM implementation (SM. fr v 1.3). In addition to the scalar potential, we modify all the relevant SM Lagrangian terms that change in the GM model (e.g.: Scalar Kinetic Terms, Yukawa couplings).

We also provide the CalcHEP and MG5 model folders generated from the .fr file. In the case of MG5, event generation can be simplified by using the program GMCALC to generate a param_card.dat file. (Note that the widths of t, W+, h and additional scalars should be updated in MG5 using the compute_widths option.)


  1. H. Georgi and M. Machacek, Nucl. Phys. B 262, 463 (1985)
  2. K. Hartling, K. Kumar and H. E. Logan, Phys. Rev. D 90, 015007 (2014) [hep-ph].

Model files


Additional Files

UFO Folder, CalcHEP Folder

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