## Conventions in VBFNLO for Anomalous Quartic Gauge Boson Couplings

VBFNLO allows for calculations including anomalous gauge boson couplings in many processes.

Both dimension-6 and dimension-8 operators are included in the effective Lagrangian which is used for calculations with anomalous gauge boson couplings. They full set of operators can be used in the diboson, triboson and $VVjj$ in VBF production processes. The dimension-6 operators are constructed according to Refs. [1,2] and the dimension-8 operators are taken from Ref. . More details on the implementation in VBFNLO can be found in Refs. [4,5,6].

For comparisons with programs that use the definition from  (for example MadGraph5  with the UFO file written by Eboli et al. , you should note that our definition of the field strength tensors is slightly different than the one of . Therefore you have to rescale the coupling strengths by

\begin{eqnarray*} f_{S,0,1} &=& f_{S,0,1}^\textrm{Éboli} \\ f_{M,0,1} &=& - \frac{1}{g^2} \cdot f_{M,0,1}^\textrm{Éboli} \\ f_{M,2,3} &=& - \frac{4}{g'^2} \cdot f_{M,2,3}^\textrm{Éboli} \\ f_{M,4,5} &=& - \frac{2}{g g'} \cdot f_{M,4,5}^\textrm{Éboli} \\ f_{M,6,7} &=& - \frac{1}{g^2} \cdot f_{M,6,7}^\textrm{Éboli} \\ f_{T,0,1,2} &=& \frac{1}{g^4} \cdot f_{T,0,1,2}^\textrm{Éboli}\\ f_{T,5,6,7} &=& \frac{4}{g^2 g'^2} \cdot f_{T,5,6,7}^\textrm{Éboli}\\ f_{T,8,9} &=& \frac{16}{g'^4} \cdot f_{T,8,9}^\textrm{Éboli} \end{eqnarray*}

where $g$ and $g'$ are the SU(2) and U(1) gauge couplings. The numerical values for $g$ and $g'$ used in the calculation are printed out at the beginning of the VBFNLO run.

 K. Hagiwara, R. Szalapski and D. Zeppenfeld, “Anomalous Higgs boson production and decay”, Phys. Lett. B318 (1993) 155, hep-ph/9308347 .

 K. Hagiwara, S. Ishihara, R. Szalapski and D. Zeppenfeld, “Low-energy effects of new interactions in the electroweak boson sector”, Phys. Rev. D48 (1993) 2182.

 O. J. P. Eboli, M. C. Gonzalez-Garcia and J. K. Mizukoshi, “pp→jje±μ±νν and jje±μ∓νν at O(α6em) and O(α4emα2S) for the study of the quartic electroweak gauge boson vertex at LHC”, Phys. Rev. D74 (2006) 073005, hep-ph/0606118 .

 N. Greiner, “Anomale Kopplungen bei der W-Paar-Produktion in Vektor-Boson-Fusion”, Diploma Thesis, ITP Karlsruhe 2006, https://www.itp.kit.edu/publications/diploma .

 B. Feigl, “Anomale Vier-Vektorboson-Kopplungen bei der Produktion von drei Vektorbosonen am LHC”, Diploma Thesis, ITP Karlsruhe 2009, https://www.itp.kit.edu/publications/diploma .

 O. Schlimpert, “Anomale Kopplungen bei der Streuung schwacher Eichbosonen”, Diploma Thesis, ITP Karlsruhe 2013, https://www.itp.kit.edu/publications/diploma .

 J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer and T. Stelzer, JHEP 1106 (2011) 128 [arXiv:1106.0522 [hep-ph]].

 available from http://feynrules.irmp.ucl.ac.be/wiki/AnomalousGaugeCoupling 