Implementation Author

• Kunal Kumar (to be contacted for any queries regarding this model implementation)
  • kkumar -at- physics.carleton.ca, Carleton University

In collaboration with

• Katy Hartling
  • khally -at- physics.carleton.ca, Carleton University
• Heather E. Logan
  • logan -at- physics.carleton.ca, Carleton University

Model Description and Implementation

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_{\phi}^2 + 8 v_{\chi}^2 = v_{SM}^2 $

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 MadGraph5 model folders generated from the .fr file (feynman gauge was chosen for generating both these model folders). In the case of MG5, event generation can be simplified by using the program GMCALC (description below) to generate a param_card.dat file. (Note that the widths of t, W+, h and additional scalars should be updated in MadGraph5 using the compute_widths option.)

References

1. H. Georgi and M. Machacek, Nucl. Phys. B 262, 463 (1985) ​http://www.sciencedirect.com/science/article/pii/0550321385903256.
2. K. Hartling, K. Kumar and H. E. Logan, Phys. Rev. D 90, 015007 (2014) ​[hep-ph].

Model files
GM.tar.gz​ : Contains, the .fr file, restriction files, a mathematica notebook to check the model and a package to generate model folders for CalcHEP and MadGraph5.

Interfaces
The .fr file can be used to generate model folders to be used in MadGraph5 and CalcHEP.

GM_UFO.tar.gz​ : Model folder for MadGraph5
(Note : Using this folder with the current (v2.2.2) of MadGraph5 may result in the following bug ​https://bugs.launchpad.net/mg5amcnlo/+bug/1395215. The link provides a description and resolution of the bug. This bug is not present in earlier versions of MadGraph5 and will be fixed in the next release of MadGraph5.

GM-CH.tar.gz​ : Model folder for CalcHEP

Validation
The feynman rules generated were checked by comparing with calculations done by hand (​arXiv:1404.2640). Decay widths have been checked against those calculated by GMCALC.

GMCALC
A calculator for the Georgi-Machacek model. ​http://people.physics.carleton.ca/~logan/gmcalc/

Change Log

• v1.2
  • Modified the antiparticle names of some scalars for clarity
  • Changed name of EXT. variable th --> tanth for clarity
  • Modified the labels used for some terms of the Lagrangian
  • Modified default values of certain EXT. parameters
  • Added the field "TeX-->" for EXT. parameters lam2-lam5