## 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. [3]. More details on the implementation in VBFNLO can be found in Refs. [4,5,6].

For comparisons with programs that use the definition from [3] (for example MadGraph5 [7] with the UFO file written by Eboli et al. [8], you should note that our definition of the field strength tensors is slightly different than the one of [3]. 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.

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

[2] 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.

[3] 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 .

[4] 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 .

[5] 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 .

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

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

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