A complete top-quark EFT implementation

Under the umbrella of the LHC TOP WG, common standards and prescriptions were established for the EFT interpretation of top-quark measurements at the LHC. They are summarized in the note at ​https://arxiv.org/abs/1802.07237. Details concerning the present UFO model implementation are provided in Appendix B.1.

EFT degrees of freedom that are natural for the description of top-quark processes were defined as linear combinations of Warsaw basis operator coefficients. They match the interference structure of the EFT with SM amplitudes and give a direct parametrization of the top-quark couplings to physical W and Z gauge bosons (see Appendices C, D, and E of the note for degrees of freedom definitions).

The CKM matrix is approximated as a unit matrix. Masses and Yukawa couplings of all fermions except for the top and bottom quarks are neglected by default. A U(2)q+u+d flavour symmetry is imposed on the first two generations of quarks (see Section 4 of the note for details). All operators of the Warsaw basis involving a top quark and satisfying this flavour assumption are included (four-quark, two-quark, and two-quark-two-lepton operators). Baryon and lepton number violating operators are not included. In total the model includes O(90) flavour-conserving degrees of freedom which have a DIM6=1 coupling order.

Enhancing the U(2)q+u+d flavour symmetry to U(2)q×U(2)u×U(2)d (the baseline scenario considered as prescription) is done by neglecting the 10+10 CPV supplementary degrees of freedom. A further restriction to the top-philic can also be obtained following the constraints given in the note.

Top-quark FCNCs are also included by allowing one quark bilinear in each operator to break the U(2)q×U(2)u×U(2)d baseline flavour symmetry requirement and couple the third generation with either the first or the second. Operators with one light and one heavy quark, one light quark one heavy quark and two leptons, one light quark and three heavy quarks, three light and one heavy quark are included. The O(300) degrees of freedom are assigned a FCNC=1 coupling order. Requiring FCNC=0 at the generation level is required to not consider them.

Two versions of the models are provided dim6top_LO_UFO and dim6top_LO_UFO_each_coupling_order. In the second one, each degree of freedom is assigned with an individual coupling order, like DIM6_ctZ, DIM6_cQQ1, or FCNC_cqq11x3331. This allows for the selection of individual degrees of freedom interferences at the generation level in MG5_aMC@NLO. The syntax:

> generate p p > t t~ FCNC=0 DIM6^2==1 DIM6_ctZ^2==1
> generate p p > t t~ FCNC=0 DIM6^2==2 DIM6_ctZ^2==1 DIM6_ctW^2==1

would for instance respectively retain only the interference between SM and ctZ amplitudes, and the interferences between ctZ and ctW amplitudes, in top pair production.

Only tree-level simulation in the unitary gauge is possible. Loop induced couplings of the Higgs boson to pairs of gluons, photons, or Zγ are not included.

A positive QED=n coupling order is also assigned to operators involving n Higgs doublet fields in the unbroken phase to compensate for the QED=-1 coupling order of the Higgs vev which appears in the broken phase.

The bottom quark is massive by default. Switching to the five-flavour factorization scheme can be achieve by using a restriction card in which MB is set to 0, or by redefining

> define p = p b b~
> define j = p

before process generation and setting MB to 0 in the param_card (setting ymb to 0 may also be desired, for consistency).

Benchmark results for the linear and quadratic dimension-six EFT dependences of total rates are provided in Tables 10-21 of the note, for processes like pp→tt̅, tt̅bb̅, tt̅tt̅, tt̅e⁺ν, tt̅e⁺e⁻, tt̅γ, tt̅h and pp→tj, te⁻ν, tje⁺e⁻, tjγ, tjh.

Please refer to ​https://arxiv.org/abs/1802.07237 for further details and when using this model.

Contact persons are Gauthier Durieux and Cen Zhang.

Feynrule files: dim6top.m​, dim6top.fr​, dim6top_each_coupling_order.fr​

UFO model files: dim6top_LO_UFO.tar.gz​, dim6top_LO_UFO_each_coupling_order.tar.gz​

Changelog:

• 2018-06-06: corrected the Lorentz structures of the operators relative to cbtud1 and cbtud8 coefficients from scalar to vector (thanks to Céline Degrande)
• 2018-05-28: moved the definition of 'ctA' below that of 'sw' and 'cw' in parameters.py, to avoid "MadGraph5Error : Unable to evaluate mdl_ctA = (mdl_ctW-mdl_cw*mdl_ctZ)/mdl_sw: raise error: name 'mdl_cw' is not defined" (thanks to Marcel Vos)
• 2018-05-21: corrected the Lorentz structure of Oledq operator from tensor to scalar (thanks to Ken Mimasu)