The elliptic dilogarithm for the sunset 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

We present the result for the finite part of the two-loop sunrise integral with unequal masses in four space-time dimensions in terms of the O(e0)-part and the O(e1)-part of the sunrise integral around two space-time dimensions. The latter two integrals are given in terms of elliptic generalisations of Clausen and Glaisher functions. Interesting aspects of the result for the O(e1)-part of the sunrise integral around two space-time dimensions are the occurrence of depth two elliptic objects and the weights of the individual terms.

The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case

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

Simple one-dimensional integral representations for two-loop self-energies: the master diagram

The scalar two-loop self-energy master diagram is studied in the case of arbitrary masses. Analytical results in terms of Lauricella- and Appell-functions are presented for the imaginary part. By using the dispersion relation a one-dimensional integral representation is derived. This representation uses only elementary functions and is thus well suited for a numerical calculation of the master diagram.

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.

S. Bauberger

Papers

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

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

Simple one-dimensional integral representations for two-loop self-energies: the master diagram

Simple one-dimensional integral representations for two-loop self-energies: the master diagram

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