The elliptic dilogarithm for the sunset graph

Analytic treatment of the two loop equal mass sunrise graph

We present the Higgs boson production cross section at Hadron colliders in the gluon fusion production mode through N3LO in perturbative QCD. Specifically, we work in an effective theory where the top quark is assumed to be infinitely heavy and all other quarks are considered to be massless. Our result is the first exact formula for a partonic hadron collider cross section at N3LO in perturbative QCD. Furthermore, our result is an analytic computation of a hadron collider cross section involving elliptic integrals. We derive numerical predictions for the Higgs boson cross section at the LHC. Previously this result was approximated by an expansion of the cross section around the production threshold of the Higgs boson and we compare our findings. Finally, we study the impact of our new result on the state of the art prediction for the Higgs boson cross section at the LHC.

/pdf/arxiv-higgs-boson-production-at-hadron-colliders-at-n-3-lo-jsydg46hzb.pdf

arXiv : Higgs Boson Production at Hadron Colliders at N$^3$LO in QCD

Generalized Recurrence Relations for Two-loop Propagator Integrals with Arbitrary Masses

New results for the ε-expansion of certain one-, two- and three-loop Feynman diagrams

https://pure.uva.nl/ws/files/2930731/1362_13591y.pdf

Analytical and numerical methods for massive two-loop self-energy diagrams

Motivated by the precision results in the electroweak theory studies of two-loopFeynman diagrams are performed. Specifically this paper gives a contribution to the knowledge of massive two-loop self-energy diagrams in arbitrary and especially four dimensions.This is done in three respects firstly results in terms of generalized, multivariable hypergeometric functions are presented giving explicit series for small and large momenta. Secondly the imaginary parts of these integrals are expressed as complete elliptic integrals.Finally one-dimensional integral representations with elementary functions are derived.They are very well suited for the numerical evaluations.

/pdf/analytical-and-numerical-methods-for-massive-two-loop-self-45a26pnn0v.pdf

In this paper the class ofN loop massive scalar self-energy diagrams withN+1 propagators is studied in an arbitrary number of dimensions. As it is known these integrals cannot be expressed in terms of polylogarithms. Here it is shown, however, that they can be described by generalized hypergeometric functions of several variables, namely Laricella functions. These results represent previous small and large momentum expansions in closed form. Numerical comparisons for the finite part in four dimensions with a two-dimensional integral representation show good agreement.

/pdf/closed-expressions-for-specific-massive-multiloop-self-sxsw7gacrf.pdf

Closed expressions for specific massive multiloop self-energy integrals

Motivated by the results of the electroweak precision experiments, studies of two-loop self-energy Feynman diagrams are performed. An algebraic method for the reduction of all two-loop self-energies to a set of standard scalar integrals is presented. The gauge dependence of the self-energies is discussed and an extension of the pinch technique to the two-loop level is worked out. It is shown to yield a special case of the background-field method which provides a general framework for deriving Green functions with desirable theoretical properties. The massive scalar integrals of self-energy type are expressed in terms of generalized multivariable hypergeometric functions. The imaginary parts of these integrals yield complete elliptic integrals. Finally, one-dimensional integral representations with elementary integrands are derived which are well suited for numerical evaluation.

M. Buza

Papers

Analytical and numerical methods for massive two-loop self-energy diagrams

Analytical and numerical methods for massive two-loop self-energy diagrams

Closed expressions for specific massive multiloop self-energy integrals

Calculation of two-loop self-energies in the electroweak Standard Model

Calculation of two-loop self-energies in the electroweak Standard Model