== W' Effective model ==

=== Authors ===

 * [http://fuks.web.cern.ch/fuks/ Benjamin Fuks]
   * IPHC Strasbourg / University of Strasbourg
   * fuks@… 
 * Julien Donini
   * LPC Clermont / University of Clermont-Ferrand
   * julien.donini@cern.ch (cern.ch)

=== Description of the model ===

This model is an extension of the SM, including additional interaction of fermions to a W' boson following the lowest-order effective Lagrangian
described in Refs. [#point1 [1]] [#point2 [2]]:

{{{
#!latex
$\mathcal{L} = \frac{V'_{ij}}{2\sqrt{2}} \bar{f}_{i} \gamma_{\mu} \left( g'_{R_{i,j}} (1+\gamma^5 ) +g'_{L_{i,j}} (1-\gamma^5 ) \right) W'^{\mu} f_j + h.c.$
}}}
where g',,R,L,, are the right-handed (left-handed) W'-boson gauge couplings to fermions f,,i,, and f,,j,,, and V',,ij,, is either the CKM matrix or a diagonal matrix,
for quarks and leptons respectively.

=== Model files ===

   * [http://feynrules.irmp.ucl.ac.be/wiki/Wprime/weff.fr weff.fr]: the main model file.
   * [http://feynrules.irmp.ucl.ac.be/wiki/Wprime/WEff.nb WEff.nb]: example of Mathematica notebook that loads the model, calculates the Feynman rules and extract the model files within the UFO format.
   * [http://feynrules.irmp.ucl.ac.be/wiki/Wprime/weff.ufo.tgz weff.ufo.tgz]: The model files in UFO format (for !MadGraph 5).

Notes:
   * The W'-boson mass and width are set using the parameters MWp and WWp, respectively
   * The left-handed (right-handed) W'-boson couplings to quarks and leptons are given by the matrices CLq and CLl (CRq and CRl) respectively. \\
     By default CLq and CRq are set to the CKM values and CLl and CRl are set to identity.
   * The left-handed and right-handed W'-boson coupling constants are set by the parameters gL and gR. \\
     By default these values are set at 0.1.

=== Validation ===

The W' model was validated using !MadGraph in the context of W' -> tb searches at the LHC [#point3 [3]]:

   * Several kinematical distributions of the W' decay products (including from top-quark decay) were checked, at the parton level or after showering (using Pythia). [[BR]] 
     Variables sensitive to the W' chirality were studied (such as cos(theta*): the angle between the lepton in the top-quark rest frame and the top direction in the CM frame).
     
   * The cross-sections calculated with this model were compared to theoretical values from [#point2 [2]]. Results for left- and right-handed W' were shown [[BR]]  
     to be in very good agreement with LO calculations over all tested mass range (0.5 to 3.0 TeV).


=== References ===

[=#point1] [1] Z. Sullivan, Fully differential W production and decay at next-to-leading order in QCD, Phys. Rev.
(2002) 075011, arXiv:hep-ph/0207290 [hep-ph].

[=#point2] [2] D. Duffty and Z. Sullivan, Model independent reach for W-prime bosons at the LHC, Phys. Rev.
D86 (2012) 075018, arXiv:1208.4858 [hep-ph].

[=#point3] [3] ATLAS Collaboration: [https://cds.cern.ch/record/1547566 ATLAS-CONF-2013-050]