'''Anomalous quartic electroweak gauge-boson interactions'''

'''Authors:'''

* O.J.P.  Eboli (eboli AT fma.if.usp.br)

* M.C. Gonzalez-Garcia (concha AT max2.physics.sunysb.edu) 

'''Description of the models:'''

We concentrate on anomalous quartic interaction among the electroweak gauge bosons that do not have a triple vertex associated to it. We describe these interactions using
dimension eight effective operators assuming that the recently observed Higgs boson belongs to a SU(2),,L,, doublet; see the file 
[http://feynrules.irmp.ucl.ac.be/attachment/wiki/AnomalousGaugeCoupling/quartic.pdf quartic.pdf]  for further details. This model
is an extension of the Standard Model (SM) implemented at [http://feynrules.irmp.ucl.ac.be/wiki/StandardModel]; for further details see this link.

The model labeled SM_LS0_LS1 contains the standard model interactions supplemented by the dimension eight operators L,,S,0,, and L,,S,1,, defined in the file [http://feynrules.irmp.ucl.ac.be/attachment/wiki/AnomalousGaugeCoupling/quartic.pdf quartic.pdf]. These dimension eight effective operators modify the vertices WWWW, WWZZ, and WWZZ that can be a simple re-scaling of the SM quartic interaction for a suitable choice of couplings. 

The model labeled SM_LT012 contains the standard model interactions supplemented by the dimension eight operators L,,T,0,, , L,,T,1,, and L,,T,2,, defined in the file [http://feynrules.irmp.ucl.ac.be/attachment/wiki/AnomalousGaugeCoupling/quartic.pdf quartic.pdf]. These dimension eight effective operators give rise to anomalous WWWW, WWZZ, WWAZ, WWAA, AAAA, AAAZ, AAZZ, AZZZ, and ZZZZ vertices. 

The model labeled SM_LM0123 contains the standard model interactions supplemented by the dimension eight operators L,,M,0,, , L,,M,1,, , L,,M,2,, and L,,M,3,, defined in the file [http://feynrules.irmp.ucl.ac.be/attachment/wiki/AnomalousGaugeCoupling/quartic.pdf quartic.pdf]. These dimension eight effective operators give rise to anomalous WWWW, WWZZ, WWAZ, WWAA, AAZZ, AZZZ, and ZZZZ vertices. 


The model labeled SM_LT8_LT9 contains the standard model interactions supplemented by the dimension eight operators L,,T,8,, and L,,T,9,, defined in the file [http://feynrules.irmp.ucl.ac.be/attachment/wiki/AnomalousGaugeCoupling/quartic.pdf quartic.pdf]. These dimension eight effective operators give rise to anomalous AAAA, AAAZ, AAZZ, AZZZ, and ZZZZ vertices. 




'''References'''

* ''Strongly interacting vector bosons at the CERN LHC: Quartic anomalous couplings'' , A.S. Belyaev et al, Phys.Rev. D59 (1999) 015022 [http://arXiv.org/pdf/hep-ph/9805229.pdf (hep-ph/9805229)]

* ''p p ---> j j e+- mu+- nu nu and j j e+- mu-+ nu nu at order ... for the study of the quartic electroweak gauge boson vertex at CERN LHC'',  O.J.P. Eboli, M.C. Gonzalez-Garcia , and J.K. Mizukoshi, Phys.Rev. D74 (2006) 073005  [http://arXiv.org/pdf/hep-ph/0606118.pdf (hep-ph/0606118 ] the dimension eight operators are from this reference)

* ''Anomalous quartic gauge boson couplings at hadron colliders'', Oscar J.P. Eboli, M.C. Gonzalez-Garcia, S.M. Lietti, and S.F. Novaes., Phys.Rev. D63 (2001) 075008 [http://arXiv.org/pdf/hep-ph/0009262.pdf hep-ph/0009262)]

* ''Bosonic quartic couplings at CERN LHC'', O.J.P. Eboli, M.C. Gonzalez-Garcia, and S.M. Lietti, Phys.Rev. D69 (2004) 095005 [http://arXiv.org/pdf/hep-ph/0310141.pdf (hep-ph/0310141)]

* "Classifying the bosonic quartic couplings ",  O.J.P. Eboli and  M.C. Gonzalez-Garcia, Phys.Rev. D93 (2016) 093013 [https://arxiv.org/pdf/1604.03555.pdf (arXiv:1604.03555)] 

'''Instructions'''

The model files include the quartic and SM vertices in the unitary gauge.  To generate models with any of the other dimension eight operators use the notebooks [http://feynrules.irmp.ucl.ac.be/attachment/wiki/AnomalousGaugeCoupling/quartic_ls01.nb quartic_ls01.nb]  or   [http://feynrules.irmp.ucl.ac.be/attachment/wiki/AnomalousGaugeCoupling/quartic_lt89.nb quartic_lt89.nb]   as examples and include the additional interactions that are already defined in the model file  [http://feynrules.irmp.ucl.ac.be/attachment/wiki/AnomalousGaugeCoupling/quartic.fr quartic.fr]. The anomalous couplings are set to 1 GeV^-4^  by default, thus they should be conveniently chosen before the event generation.


'''2017 version:''' the user must specify the number of anomalous vertices in the scattering amplitude generated by MadGraph. For one vertex use NP=1.

'''June 2019 version:''' contains the operators LS0,1,2 , LM0,1,7 and  LT0,1,2 that can be used simultaneously. Each anomalous interactions has an independent InteractionOrder that is called S0, S1, S2, M0, etc. This version assumes 5 massless quarks.

'''April 2020 version:''' same as the previous one but fixing a bug on LM5 (previously a hermitian conjugate was missing)

'''August 2021 version:''' includes two new operators (T3 and T4) [see  Phys.Rev.D 101 (2020) 11, 113003 • e-Print: 2004.05174]. The UFO files were obtained using on the Cabibbo angle (quartic21.tgz) as well as the full CKM matrix without the CP violating phase (quarticCKM.tgz).