Issues with the model

[andrey-popov]

There are several issues with the MadGraph model. They should be fixed for the second publication.

Lagrangian

1. In this model the Hgg form-factors are defined only for q² > 2m_t despite the fact that they are known also below the threshold. Because of this, there is no tail in m_tt < 2m_t (for the interference, for instance). This is a minor issue.
2. Sign of the coupling of the CP-odd state is not standard: m_t / v (g_H tt̄ - ig_A tγ₅t̄) Φ, while usually g_A is used with the opposite sign. Though the sign is not visible unless couplings to other particles are considered.

Model parameters

1. Widths of the top quark and W boson written to the param_card by default, which are defined here, are not consistent with their default masses. This leads to wrong cross sections when these particles are decayed. See discussion in these slides.
2. It is not possible to let MadGraph compute widths of the top quark and the W boson by setting them to auto as this leads to an error:

   compute_widths 24 6 --precision_channel=0.01 --body_decay=4.0025 --path=/gridgroup/cms/popov/Analyses/HToTT/2017.08.23_Analytical-results/MadGraph/PROC_Massive_Higgs_UFO_4/Cards/param_card.dat --output=/gridgroup/cms/popov/Analyses/HToTT/2017.08.23_Analytical-results/MadGraph/PROC_Massive_Higgs_UFO_4/Cards/param_card.dat
   Please note that the automatic computation of the width is
       only valid in narrow-width approximation and at tree-level.
   INFO: Get two body decay from FeynRules formula
   Results written to /gridgroup/cms/popov/Analyses/HToTT/2017.08.23_Analytical-results/MadGraph/PROC_Massive_Higgs_UFO_4/Cards/param_card.dat
   INFO: get decay diagram for w+
   Vertexlist of this model has not been searched.Automatically run the model.find_vertexlist()
   Found 1 stable particles
   Command "generate_events run_03" interrupted in sub-command:
   "set max_npoint_for_channel 0" with error:
   NameError : name 'ggH0' is not defined
   

   An apparently similar problem was discussed here, but I haven't investigated.
3. Values chosen for m_Z, G_F, and α_em give the W boson a mass of around 79.8 GeV. Since the signal process involves W bosons but is not sensitive to the fine-structure constant, should better change the input value of α_em(m_Z) from its measurement (approximately 1/127.9) to an effective value that gives m_W ≈ 80.4 GeV (would be about 1/132.5).
4. Should consider switching to massless leptons and light-flavour quarks and a diagonal CKM matrix in the model. It simplifies definition of exclusive final states and equalizes decays of W bosons. Not strictly needed though.
5. Should update other theory parameters to values that are actually used for event generation, e.g. m_t = 172.5 GeV, so that the need for manual changes is minimized.