Related papers: On one master integral for three-loop on-shell HQE…
We calculate master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy. Our results are expressed in terms of the iterated integrals,…
We present analytical results for all master integrals for massless three-point functions, with one off-shell leg, at four loops. Our solutions were obtained using differential equations and direct integration techniques. We review the…
In this letter we discuss a regularization scheme for the integration of generic on-shell forms. The basic idea is to extend the three-particle amplitudes to the space of unphysical helicities keeping the dimension of the related coupling…
We carry out a systematic investigation of all the 2-loop integrals occurring in the electron vertex in QED in the continuous $D$-dimensional regularization scheme, for on-shell electrons, momentum transfer $t=-Q^2$ and finite squared…
HQET lagrangian up to $1/m^3$ terms is discussed. Consequences of reparameterization invariance are considered. Results for the chromomagnetic interaction coefficient at two loops, and in all orders in the large--$\beta_1$ approximation,…
We present the calculation of massless two-loop Master Integrals relevant to five-point amplitudes with one off-shell external leg and derive the complete set of planar Master Integrals with five on-mass-shell legs, that contribute to many…
The calculation of the two-loop corrections to the three jet production rate and to event shapes in electron-positron annihilation requires the computation of a number of up to now unknown two-loop four-point master integrals with one…
We evaluate three typical four-loop non-planar massless propagator diagrams in a Taylor expansion in dimensional regularization parameter $\epsilon=(4-d)/2$ up to transcendentality weight twelve, using a recently developed method of one of…
We summarize the results for the master integrals of the three-loop quark and gluon form factor in massless QCD. Working in dimensional regularization we extract poles up to 1/epsilon^6. The computational techniques involve, among others,…
We evaluate analytically higher terms of the epsilon-expansion of the three-loop master integrals corresponding to three-loop quark and gluon form factors and to the three-loop master integrals contributing to the electron g-2 in QED up to…
The $\epsilon$-expansion of several two-loop self-energy diagrams with different thresholds and one mass are calculated. On-shell results are reduced to multiple binomial sums which values are presented in analytical form.
In this work we compute the most general massive one-loop off-shell three-point vertex in D-dimensions, where the masses, external momenta, and exponents of propagators are arbitrary. This follows our previous paper in which we have…
After a brief introduction to Heavy Quark Effective Theory, we discuss $\alpha$ representation in HQET and methods of calculation of some kinds of HQET diagrams up to three loops.
We evaluate analytically the one-loop one-mass hexagon in six dimensions. The result is given in terms of standard polylogarithms of uniform transcendental weight three.
The three-loop form factors in massless QCD can be expressed as a linear combination of master integrals. Besides a number of master integrals which factorise into products of one-loop and two-loop integrals, one finds 16 genuine three-loop…
We compute the (three) master integrals for the crossed ladder diagram with two exchanged quanta of equal mass. The differential equations obeyed by the master integrals are used to generate power series expansions centered around all the…
The state-of-the-art in current two-loop QCD amplitude calculations is at five-particle scattering. Computing two-loop six-particle processes requires knowledge of the corresponding one-loop amplitudes to higher orders in the dimensional…
We discuss a practical approach to compute master integrals entering physical quantities which depend on one parameter. As an example we consider four-loop QCD corrections to the relation between a heavy quark mass defined in the…
We provide high-energy approximations for all one-loop scalar 3- and 4-point functions and the corresponding tensor integrals that appear in scattering processes with four external on-shell particles. Our expressions are valid if all…
In this paper we continue the work begun in 2002 on the identification of the analytical expressions of Feynman integrals which require the evaluation of multiple elliptic integrals. We rewrite and simplify the analytical expression of the…