On a two-loop crossed six-line master integral with two massive lines

@article{Huber2009OnAT,
  title={On a two-loop crossed six-line master integral with two massive lines},
  author={Tobias Huber},
  journal={Journal of High Energy Physics},
  year={2009},
  volume={2009},
  pages={024-024}
}
  • T. Huber
  • Published 14 January 2009
  • Mathematics
  • Journal of High Energy Physics
We compute the two-loop crossed six-line vertex master integral with two massive lines in dimensional regularisation, and give the result up to the finite part in D−4. We apply the differential equation technique, and focus in particular on the purely analytical calculation of the boundary condition which we derive from a three-fold Mellin-Barnes representation. We also describe how the computation of the boundary condition is used to derive three non-trivial relations among harmonic… 
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References

SHOWING 1-10 OF 109 REFERENCES
The two loop crossed ladder vertex diagram with two massive exchanges
FEYNMAN DIAGRAMS AND DIFFERENTIAL EQUATIONS
We review in a pedagogical way the method of differential equations for the evaluation of D-dimensionally regulated Feynman integrals. After dealing with the general features of the technique, we…
Vertex diagrams for the QED form factors at the 2-loop level
Dimensional regularization of mass and infrared singularities in two-loop on-shell vertex functions
New results for the ε-expansion of certain one-, two- and three-loop Feynman diagrams
The Master differential equations for the two loop sunrise selfmass amplitudes
The master differential equations in the external square momentum p^2 for the master integrals of the two-loop sunrise graph, in n-continuous dimensions and for arbitrary values of the internal…
Numerical evaluation of loop integrals
We present a new method for the numerical evaluation of arbitrary loop integrals in dimensional regularization. We first derive Mellin-Barnes integral representations and apply an algorithmic…
Integrals for two‐loop calculations in massless QCD
Tools that have been developed for the extension of the Sterman–Weinberg formula in two‐loop order are presented. They are the essential ingredients for any perturbative two‐loop calculation in a…
Master integrals with one massive propagator for the two-loop electroweak form factor
Two-loop quark and gluon form factors in dimensional regularisation
...
...