Related papers: Master Integrals for Four-Loop Massless Propagator…
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…
In this paper we calculate at high-precision the Laurent expansions in e=(4-D)/2 of the 17 master integrals which appeared in the analytical calculation of 3-loop QED contribution to the electron g-2, using difference and differential…
We compute the two-loop master integrals for non-leptonic heavy-to-heavy decays analytically in a recently-proposed canonical basis. For this genuine two-loop, two-scale problem we first derive a basis for the master integrals that…
We present a complete reevaluation of the irreducible two-loop vacuum-polarization correction to the photon propagator in quantum electrodynamics, i.e. with an electron-positron pair in the fermion propagators. The integration is carried…
We analytically calculate one-loop five-point Master Integrals, \textit{pentagon integrals}, with up to one off-shell leg to arbitrary order in the dimensional regulator in $d=4-2\epsilon$ space-time dimensions. A pure basis of Master…
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…
We evaluate analytically all previously unknown nonplanar master integrals for massless five-particle scattering at two loops, using the differential equations method. A canonical form of the differential equations is obtained by…
The inclusive four-particle phase space integral of any $1\to 4$ matrix element in massless QCD contains divergences due to the soft and collinear emission of up to two particles in the final state. We show that any term appearing in this…
The massless one-loop box integral with arbitrary indices in arbitrary space-time dimension $d$ is shown to reduce to a sum over three generalised hypergeometric functions. This result follows from the solution to the third order…
We extend the ${\cal O}(\alpha_s^5)$ result of the analytic calculation of the quark mass anomalous dimension in pQCD [1] to the case of a generic gauge group. We present explicit formulas which express the relevant renormalization…
We study multi-propagator angular integrals, a class of phase-space integrals relevant to processes with multiple observed final states and a test-bed for transferring loop-integral technology to phase space integrals without reversed…
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 paper we calculate at high-precision the expansions in e=(4-D)/2 of the master integrals of 4-loop vacuum bubble diagrams with equal masses, using a method based on the solution of systems of difference equations. We also show that…
At variance with fully inclusive quantities, which have been computed already at the two- or three-loop level, most exclusive observables are still known only at one loop, as further progress was hampered up to very recently by the greater…
We present analytic results of the two-loop master integrals for hadronic $tW$ production that contain two massive propagators. For the planar integral family, we succeed in constructing the canonical basis, so the results are written in…
We show that all Feynman integrals in two Euclidean dimensions with massless propagators and arbitrary non-integer propagator powers can be expressed in terms of single-valued analogues of Aomoto-Gelfand hypergeometric functions. The latter…
We compute the master integrals for massless two-loop vertex graphs with three off-shell legs. These master integrals are relevant for the QCD corrections to H to V*V* (where V = W, Z) and for two-loop studies of the triple gluon (and…
We present analytic results for the two tennis-court integral families relevant to $2\to2$ scattering processes involving one massive external particle and massless propagators in terms of Goncharov polylogarithms of up to transcendental…
Loop calculations involve the evaluation of divergent integrals. Usually [1] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers…
We present a new FORM program for analytically evaluating four-loop massless propagator-type Feynman integrals in an efficient way. Our program Forcer implements parametric reductions of the aforementioned class of Feynman integrals into a…