Related papers: The massless two-loop two-point function
In the present paper the two and three point functions which occur at the study of the various physical processes are considered. The investigation has dan in the framework of the perturbative theory at the one loop level. The general and…
Recasting the $N$-point one loop scalar integral as a probabilistic problem, allows the derivation of integral recurrence relations as well as exact analytical expressions in the most common cases. $\epsilon$ expansions are derived by…
In this paper, we study the Laurent coefficients of meromorphic modular forms at CM points by giving two approaches of computing them. The first is a generalization of the method of Rodriguez-Villegas and Zagier, which expresses the Laurent…
We study a generalization of the Schramm-Loewner evolution loop measure to pairs of non-intersecting Jordan curves on the Riemann sphere. We also introduce four equivalent definitions for a two-loop Loewner potential: respectively…
Leading (large) logarithms in non-renormalizable theories have been investigated in the recent past. Besides some general considerations, explicit results for the expansion coefficients (in terms of leading logarithms) of partial wave…
An asymptotic expansion of the two-loop two-point ``master'' diagram with two masses $m$ and $M$, on the mass shell $Q^2=M^2$, is presented. The treatment of the non-analytical terms arising in the expansion around the branching point is…
We discuss the two-loop evolution of the flavor-nonsinglet meson distribution amplitude in perturbative QCD. After reviewing previous two-loop computations, we outline the incompatibility of these solutions with the group property of the…
We calculate the two-loop vertex function for the crossed topology, and for arbitrary masses and external momenta. We derive a double integral representation, suitable for a numerical evaluation by a Gaussian quadrature. Real and imaginary…
One-loop functions with loop masses larger than external masses and momenta can always be expanded in terms of external masses and momenta. The precision requested for observables determines the number of the expansion terms retained in the…
We present the general form of the renormalizable four-point interactions of a complex scalar field furnishing an irreducible representation of SU(2), and derive a set of algebraic identities that facilitates the calculation of higher-order…
We prove the following theorems: 1) The Laurent expansions in epsilon of the Gauss hypergeometric functions 2F1(I_1+a*epsilon, I_2+b*epsilon; I_3+p/q + c epsilon; z), 2F1(I_1+p/q+a*epsilon, I_2+p/q+b*epsilon; I_3+ p/q+c*epsilon;z),…
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…
For a large class of two-loop selfenergy- and vertex-type diagrams with only one non-zero mass ($M$) and the vertices also with only one non-zero external momentum squared ($q^2$) the first few expansion coefficients are calculated by the…
We derive an analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms. To obtain this form, we first derive a four-fold, rational (Feynman-)parametric representation…
We compute the master integrals containing 2 and 3 massive propagators entering the planar amplitudes of the 2-loop electroweak form factor. The masses of the $W$, $Z$ and Higgs bosons are assumed to be degenerate. This work is a…
Two representations of the Bessel zeta function are investigated. An incomplete representation is constructed using contour integration and an integral representation due to Hawkins is fully evaluated (analytically continued) to produce two…
We present the analytic calculation of two-loop master integrals that are relevant for $tW$ production at hadron colliders. We focus on the integral families with only one massive propagator. After choosing a canonical basis, the…
In this work, we calculate two-loop six-point planar massless Feynman integrals at higher orders in the dimensional regulator $\epsilon$, corresponding to higher transcendental weights. In previous works, these integrals were calculated up…
In a recent paper we have presented results for a set of massive scalar one-loop master integrals needed in the NNLO parton model description of the hadroproduction of heavy flavors. The one--loop integrals were evaluated in $n=4-2\ep$…
We calculate the two-loop renormalization group (RG) beta-function of a massless scalar field theory from the irreducible version of Polchinski's exact RG flow equation. To obtain the correct two-loop result within this method, it is…