We compute the six-dimensional hexagon integral with three non-adjacent external masses analytically. After a simple rescaling, it is given by a function of six dual conformally invariant cross-ratios. The result can be expressed as a sum of 24 terms
involving only one basic function, which is a simple linear combination of logarithms, dilogarithms, and trilogarithms of uniform degree three transcendentality. Our method uses differential equations to determine the symbol of the function, and an algorithm to reconstruct the latter from its symbol. It is known that six-dimensional hexagon integrals are closely related to scattering amplitudes in N=4 super Yang-Mills theory, and we therefore expect our result to be helpful for understanding the structure of scattering amplitudes in this theory, in particular at two loops.
We describe a framework to develop, implement and validate any perturbative Lagrangian-based particle physics model for further theoretical, phenomenological and experimental studies. The starting point is FeynRules, a Mathematica package that allows
to generate Feynman rules for any Lagrangian and then, through dedicated interfaces, automatically pass the corresponding relevant information to any supported Monte Carlo event generator. We prove the power, robustness and flexibility of this approach by presenting a few examples of new physics models (the Hidden Abelian Higgs Model, the general Two-Higgs-Doublet Model, the most general Minimal Supersymmetric Standard Model, the Minimal Higgsless Model, Universal and Large Extra Dimensions, and QCD-inspired effective Lagrangians) and their implementation/validation in FeynArts/FormCalc, CalcHep, MadGraph/MadEvent, and Sherpa.
