Related papers: Iterative and Iterative-Noniterative Integral Solu…
Three-loop vacuum integrals are an important building block for the calculation of a wide range of three-loop corrections. Until now, only results for integrals with one and two independent mass scales are known, but in the electroweak…
We calculate the complete three-loop O(alpha_s^3) anomalous dimension matrix for the dimension-five dipole operators that arise in the Standard Model after integrating out the top quark and the heavy electroweak bosons. Our computation…
We derive the structure of three-loop anomalous dimensions governing infrared singularities of QCD amplitudes with one massive and an arbitrary number of massless external partons. The contributions of tripole and quadrupole correlations…
We present the analytic calculation of all master integrals for 3-, 4-, and 5-particle semi-inclusive cuts of four-loop massless propagators by means of differential equations. We fix the integration constants by reducing the semi-inclusive…
Based on the Simplified Differential Equations approach, we present results for the two-loop non-planar hexa-box families of master integrals. We introduce a new approach to obtain the boundary terms and establish a one-dimensional integral…
Explicit formulas for the solutions of the recurrence relations for 3--loop vacuum integrals are suggested. This formulas can be used for direct calculations and demonstrate a high efficiency. They also produce a new type of recurrence…
We compute the three loop MSbar anomalous dimension for the 3-quark operator corresponding to the proton. This requires the treatment of gamma^5 within dimensional regularization as well as evanescent operators generated through the…
We have computed the next-to-next-to-leading-order (NNLO) contributions to the evolution of unpolarized parton distributions in perturbative QCD. In this talk, we briefly recall why this huge computation was necessary and outline how it was…
The general structure of infrared divergences in the scattering of massive particles is captured by the soft anomalous dimension matrix. The latter can be computed from a correlation function of multiple Wilson lines. The state-of-the-art…
We describe the analytic calculation of the master integrals required to compute the two-mass three-loop corrections to the $\rho$ parameter. In particular, we present the calculation of the master integrals for which the corresponding…
We describe birational representations of discrete groups generated by involutions, having their origin in the theory of exactly solvable vertex-models in lattice statistical mechanics. These involutions correspond respectively to two kinds…
We report on the recent completion of the three-loop calculation of the soft anomalous dimension in massless gauge-theory scattering amplitudes. This brings the state-of-the-art knowledge of long-distance singularities in multi-leg QCD…
In this paper, we present several formulas for both the discrete and fractional iterates of an invertible power series $f$, using a new unifying approach based on umbral calculus. Known formulas are extended, and their proofs simplified,…
Single-scale quantities, like the QCD anomalous dimensions and Wilson coefficients, obey difference equations. Therefore their analytic form can be determined from a finite number of moments. We demonstrate this in an explicit calculation…
In this paper we show that certain Feynman integrals can be expressed as linear combinations of iterated integrals of modular forms to all orders in the dimensional regularisation parameter $\varepsilon$ . We discuss explicitly the equal…
The three loop anomalous dimension for the gauge invariant, renormalizable, non-local mass operator for a gluon is computed in the MSbar scheme. In addition the anomalous dimensions of the associated localizing ghost fields are also deduced…
We present a system of canonical differential equations satisfied by the three-loop banana integrals with four distinct non-zero masses in $D = 2-2\eps$ dimensions. Together with the initial condition in the small-mass limit, this provides…
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,…
Three loop ladder and $V$-topology diagrams contributing to the massive operator matrix element $A_{Qg}$ are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable…
We calculate the four-loop massless QCD corrections with three closed quark lines to quark and gluon form factors. We apply a novel integration by parts algorithm based on modular arithmetic and compute all relevant master integrals for…