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Article Dans Une Revue Journal of High Energy Physics Année : 2011

The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM

Résumé

We provide an analytic formula for the (rescaled) one-loop scalar hexagon integral $\tilde\Phi_6$ with all external legs massless, in terms of classical polylogarithms. We show that this integral is closely connected to two integrals appearing in one- and two-loop amplitudes in planar $\cN=4$ super-Yang-Mills theory, $\Omega^{(1)}$ and $\Omega^{(2)}$. The derivative of $\Omega^{(2)}$ with respect to one of the conformal invariants yields $\tilde\Phi_6$, while another first-order differential operator applied to $\tilde\Phi_6$ yields $\Omega^{(1)}$. We also introduce some kinematic variables that rationalize the arguments of the polylogarithms, making it easy to verify the latter differential equation. We also give a further example of a six-dimensional integral relevant for amplitudes in $\cN=4$ super-Yang-Mills.

Dates et versions

hal-00613050 , version 1 (02-08-2011)

Identifiants

Citer

Lance J. Dixon, James M. Drummond, Johannes M. Henn. The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM. Journal of High Energy Physics, 2011, 2011 (6), pp.100. ⟨10.1007/JHEP06(2011)100⟩. ⟨hal-00613050⟩
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