Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-04-14
Physics
High Energy Physics
High Energy Physics - Theory
18 pages, 2 figures
Scientific paper
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.
Dixon Lance J.
Drummond James M.
Henn Johannes M.
No associations
LandOfFree
The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-166873