28 | | Together with the new fermion fields definitions, the following interactions are added to the SM Lagrangian |
| 29 | Together with the new fermion fields definitions, the following interactions are added to the SM Lagrangian: |
| 30 | [[Image(Lagrangian.png)]] |
| 31 | |
| 32 | 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' and ZQQ' interactions between top partners have not been included. For convenience, mixings with eventual heavier particles have been neglected as well. |
| 33 | |
| 34 | The new user-defined parameters, summarised in [attachment:Parameters.pdf], consist of: |
| 35 | * the KAPPA block : the top partners coupling strengths (set to 1 by default), |
| 36 | * the MASS block : the corresponding quark masses (set to 600 GeV by default), |
| 37 | * the DECAY block : the corresponding total widths (see the note below), |
| 38 | * the XI block : the corresponding branching ratios into W, Z, and Higgs bosons, |
| 39 | * the ZETA block : all top partners couplings to the three SM quark generations. |
| 40 | |
| 41 | |
| 42 | All the above parameter classes are combined internally in FeynRules to match the model-independent prescription presented in [1]. The default MadGraph parameter cards use the standard values for the SM input parameters as given in [attachment:Parameters.pdf]. 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. |
| 43 | |
| 44 | '''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. |
| 45 | |
| 46 | |
| 47 | === Validation === |
| 48 | |
| 49 | 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 \texttt{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]. |
| 50 | |
| 51 | 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. |
| 52 | |
| 53 | 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. 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 |
| 54 | 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. |
| 55 | |
| 56 | === Files === |
| 57 | |
| 58 | 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. |
| 59 | |
| 60 | To import the model into MadGraph, it is enough to copy the UFO directory into the models subdirectory of MadGraph, and load the model using the "import model VLQ\_UFO" command. |
| 61 | |
| 62 | |
| 63 | \item VLQ.fr{} FeynRules main file |
| 64 | |
| 65 | \item VLQ.nb Mathematica notebook used to load VLQ.fr{} |
| 66 | |
| 67 | \item Massless.rst\qquad Model restriction file.\ By default, all the |
| 68 | fermion masses are put to zero, except for the top, bottom and tau lepton. |
| 69 | |
| 70 | \item VLQ\_UFO.tar\qquad Model files for MadGraph5 |
| 71 | |
| 72 | \item VLQ\_FA.tar\qquad Model files for FeynArts.\ The tarball also includes |
| 73 | a Mathematica notebook used to validate the FeynArts output. |
| 74 | |
| 75 | \item Parameters.pdf\qquad SM\ \& VLQ\ input parameters description |
| 76 | |
| 77 | |
| 78 | === References === |
| 79 | |
| 80 | [1] M. Buchkremer, G. Cacciapaglia, A. Deandrea, L. Panizzi, ?? Model Independent searches of top partners ?? [arXiv:hep-ph/13XX.XXXX] |
| 81 | |
| 82 | [2] http://pdg.lbl.gov/2012/reviews/rpp2012-rev-ckm-matrix.pdf |
| 83 | |
| 84 | [3] J. Alwall, R. Frederix, J.-M. G\'{e}rard, A. Giammanco, M. Herquet, and others, Is $V_{tb}=1?$, Eur.Phys.J.C49 (2007) 791-801 [arXiv:hep-ph/0607115] |
| 85 | |
| 86 | [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] |
| 87 | |
| 88 | [5] P. Meade and M. Reece, BRIDGE: Branching ratio inquiry decay generated} [arXiv:hep-ph/0703031] |
| 89 | |
| 90 | [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] |