== VLQ Model ==
=== Authors ===
* Mathieu Buchkremer
* Université catholique de Louvain (CP3)
* mathieu.buchkremer_at_uclouvain.be
* Giacomo Cacciapaglia
* Université de Lyon (CNRS/IN2P3)
* g.cacciapaglia_at_ipnl.in2p3.fr
* Aldo Deandrea
* Université de Lyon (CNRS/IN2P3)
* deandrea_at_ipnl.in2p3.fr
* Luca Panizzi
* University of Southampton (School of Physics and Astronomy)
* l.panizzi_at_soton.ac.uk
=== Description ===
This model is an extension of the Standard Model (SM) with new top partners, intended for model-independent searches of Vector-Like quarks. The corresponding FeynRules implementation is based on a minimal effective Lagrangian description, which provides a direct connection between experimental observables and the new quark couplings. All fields and parameters are defined accordingly to the parameterisation detailed in [1]. The particle content, Feynman rules and parameters of the model are summarized in [attachment:Parameters.pdf].
=== Model Implementation ===
As a generic framework, the four Vector-Like states X (Q=5/3), T (2/3), B (-1/3) and Y (-4/3) are introduced as new spin 1/2 class members. Each class defines a specific top partner with a fixed electric charge, without any assumption on the other quantum numbers. The model file [attachment:VLQ.fr], loaded in Mathematica with [attachment:VLQ.nb], is designed to allow for a straightforward extension to additional vector-like fermions, simply by adding the new particles to the corresponding class (F(5), F(6), F(7) and F(8) for X-, T-, B- and Y-type quarks, respectively). Particles embedded in larger SU(2) representations may also be introduced under new classes, following the same model-independent prescription.
Together with the new fermion fields definitions, the following interactions are added to the SM Lagrangian:
[[Image(Lagrangian.png)]]
The X, T, B and Y electromagnetic and strong currents, as well as the associated kinetic and mass terms, are also implemented for all four quark species. The model-dependent, off-diagonal WQQ', ZQQ' and HQQ' interactions between two heavy partners have not been included. For convenience, mixings with eventual heavier particles have been neglected as well.
The new user-defined parameters, summarised in [attachment:Parameters.pdf], consist of:
* the KAPPA block : the top partners coupling strengths (set to 1 by default),
* the MASS block : the corresponding quark masses (set to 600 GeV by default),
* the DECAY block : the corresponding total widths (see the note below),
* the XI block : the corresponding branching ratios into W, Z, and Higgs bosons,
* the ZETA block : all top partners couplings to the three SM quark generations.
'''Important''': for consistency reasons, the "XI" and "ZETA" blocks described in [attachment:Parameters.pdf] should always be defined in agreement with [[Image(Branching.png)]]
All the above parameter classes are combined internally in the FeynRules model file [attachment:VLQ.fr] to match the model-independent prescription presented above [1]. The default parameter cards use the standard MadGraph values for the SM input parameters, as given in [attachment:Parameters.pdf]. The default configuration assumes a vector-like T singlet, mixing exclusively with the third generation. For consistency, all light quarks included in the proton definition are restricted to be massless (5F scheme) using the restriction file [attachment:Massless.rst] when loading the FeynRules model, except for the top, bottom and tau lepton masses. The default model loads the real 3X3 CKM matrix given in [attachment:Parameters.pdf] [2] as an external parameter. In general, the presence of new top partners induce model-dependent corrections to the mixings between the novel heavy fermions and the lighter quark families, and the SM electroweak couplings must be modified accordingly.
'''Extension''': In addition to the above parameterisation, an extension including chromomagnetic couplings between VL and Standard Model quarks is provided in the file VLQ_Chromomagnetic.fr. The new couplings (typically generated at loop level in minimal SM extensions) are implemented in terms of the dimension 6 operator:
[[Image(LagrangianChromo.png)]]
where G denotes the field strength tensor of the gluon, v is the Higgs field vacuum expectation value and gs is the QCD coupling. The KAPPA block is complemented with the additional parameter kappa_g (set to 1 by default), specifying the strength of the new corresponding strong coupling. The new GLUON block includes the new Tqg(g) and Bqg(g) couplings to the three SM quark families, together with the energy scale Lambda (set to 10 TeV by default). These parameters can be adjusted independently from the others described above.
'''Note''': the top partners widths are set to 1 GeV by default, but the actual values must be adjusted manually by the user. The total widths can be evaluated explicitly in MadGraph (specifying all the corresponding decay channels), for a fixed choice of the parameters defined in the KAPPA, MASS, XI and ZETA blocks.
=== Validation ===
Performing the usual FeynRules sanity checks (Version: 1.6.11), the various components of the above effective Lagrangian have been checked to be hermitian, correctly normalized and diagonal. The vertices and analytical expressions for the partial decay rates of all top partners have been cross-checked using the FR$PartialWidth option in the current development version of FeynRules (Version: 1.7.159). The partial decay rates and branching ratios have been computed numerically for various benchmark points with MadGraph (Version: 1.5.7), and are in excellent agreement with the results of [3] for a T singlet and [4] for a (X,T) doublet. The three-body decay widths and branching ratios have been evaluated with BRIDGE (Version: 2.24) [5].
In order to provide an exhaustive test of all the top partners couplings, the cross-sections for a selection of processes of direct phenomenological interest for the model applications have been tested systematically. The detailed simulation of the signals has been performed using Madgraph5 (Version: 1.5.7) for event generation at the partonic level, interfaced with PYTHIA (Version: 2.1.20) for parton showering. The QCD pair-production cross-sections have been computed in the VLQ model and match the leading order predictions at the % level for top pair production when setting M = mt at 7, 8 and 14 TeV LHC running energies.
As for electroweak production, the t-channel, s-channel and WT associated production cross-sections have been compared to the results in [3] for unity mixings (|Vtb|²=1), and are consistent with the SM predictions for M equal to the top mass. All the simulations have been performed independently in CalcHep, MadGraph4 (Usermod) and MadGraph5 (FeynRules) for various benchmark points (M = 600,800 and 1000 GeV) at leading order (CTEQ6L1). The cross-sections for Vector-Like quarks and anti-quarks have been compared for pp > Qt, Qj, QW, QZ and QH between the three built-in implementations, and the results are in agreement at the % level, except for pp > Qj which may allow for deviations as large as 10% in the W- and Z- mediated channels. Please note that the use of the MadGraph implementation is here restricted to 2>2 processes. Finally, the model results have been compared to the cross-sections presented in [6], assuming exclusive mixing with the first generation for all four Vector-Like quark types. The ratios of the cross-sections for electroweak single production of X, T, B and Y quarks have been compared with MadGraph for M = 900 (1800) GeV
at the LHC for 7(14) TeV, N=50000 events and MZ-fixed factorization and renormalization scales (CTEQ6L1). The results are found to be consistent at the 5% level.
=== Files ===
Below we provide the tarballs containing the main model files and outputs. The model implementation is also known to work with the CalcHEP/CompHEP interfaces, which can be generated from the [attachment:VLQ.nb] Mathematica notebook. Although FeynRules now supports exclusively the version 5 of MadGraph (UFO format, in the unitary gauge), the MadGraph4 model files can be provided on demand.
To import the model into MadGraph, it is enough to untar the UFO directory into the models subdirectory of MadGraph, and load the model using the "import model VLQ_UFO" command. '''Note''': by default, the model files assume a vector-like T singlet mixing exclusively with the third generation, as described in [attachment:Parameters.pdf].
* [attachment:VLQ.fr] : FeynRules main file.
* [attachment:VLQ.nb] : Mathematica notebook used to load [attachment:VLQ.fr].
* [attachment:Massless.rst] : Model restriction file. By default, all the fermion masses are put to zero, except for the top, bottom and tau lepton.
* [attachment:VLQ_UFO.tar] : Model files for MadGraph5.
* [attachment:VLQ_FA.tar] : Model files for FeynArts.
* [attachment:Parameters.pdf] : Input parameters description.
* [attachment:VLQ_Chromomagnetic.fr] : FeynRules model extension for the chromomagnetic coupling.
* [attachment:VLQ_Chromomagnetic_UFO.tar] : Model files for MadGraph5 with the chromomagnetic coupling.
Dedicated Les Houches' models for specific representations can be found at :
- [http://feynrules.irmp.ucl.ac.be/wiki/VLQ_tsingletvl Singlet T model]
- [http://feynrules.irmp.ucl.ac.be/wiki/VLQ_tbdoubletvl Standard doublet (T,B) model]
- [http://feynrules.irmp.ucl.ac.be/wiki/VLQ_xtdoubletvl Exotic doublet (X,T) model]
Dedicated model for a bottom partner can be found at :
- [http://feynrules.irmp.ucl.ac.be/wiki/VLQ_bsingletvl Singlet B model]
=== References ===
[1] M. Buchkremer, G. Cacciapaglia, A. Deandrea, L. Panizzi, Model Independent Framework for Searches of Top Partners, [arXiv:hep-ph/1305.4172].
[2] http://pdg.lbl.gov/2012/reviews/rpp2012-rev-ckm-matrix.pdf
[3] J. Alwall, R. Frederix, J.-M. Gérard, A. Giammanco, M. Herquet, and others, Is $V_{tb}=1?$, Eur.Phys.J.C49 (2007) 791-801 [arXiv:hep-ph/0607115]
[4] G. Cacciapaglia, A. Deandrea, L. Panizzi, S. Perries and V. Sordini, Heavy Vector-like quark with charge 5/3 at the LHC, JHEP 1303 (2013) 004 [arXiv:hep-ph/1211.4034]
[5] P. Meade and M. Reece, BRIDGE: Branching ratio inquiry decay generated} [arXiv:hep-ph/0703031]
[6] A. Atre, G. Azuelos, M. Carena, T. Han, E. Ozcan, J. Santiago and G. Unel, Model-Independent Searches for New Quarks at the LHC, JHEP 1108 (2011) 080 [arXiv:hep-ph/1102.1987]