# 2022_March9_Bluemlein.txt

2022_March9_Bluemlein.txt — 1.8 KB

## File contents

Algorithmic Combinatorics Seminar Title: The unpolarized and polarized 3-loop anomalous dimensions from off-shell operator matrix elements Speaker: Prof. Dr. Johannes Blümlein (Deutsches Elektronen-Synchrotron, Germany) Time and Location: Wednesday, March 9, 2022, 2 p.m. Zoom presentation Abstract: We report on recent analytic massless 3-loop computations of so-called (differential) operator matrix elements in Quantum Chromodynamics (QCD). These quantities allow, in the off-shell case, to calculate essential quantities of QCD, the anomalous dimensions. They rule the evolution equations of particle physics, namely the change of quark and the gluon densities inside nucleons as a function of x in [0,1], when going from long distances to short distances, i.e. from small to high energies. By their application to experimental data, the strong coupling constant, a fundamental parameter in physics, can be measured at an unprecedented precision. This calculation method is a rather direct one. We have now a fully automated chain of codes to perform such a calculation, including computer algebra at the physics side and at the combinatoric side. In this case the result can be thoroughly written in terms of nested harmonic sums (or harmonic polylogarithms), unlike in the massive case, where many more function spaces contribute. Furthermore, all recurrences factorize at first order. The present program shall be extended to more quantities, e.g. the 3-loop Wilson coefficients, also needed to describe physical processes. Finally, the method will allow also to calculate anomalous dimensions at the 4-loop level, being a much larger problem. We have the computing facilities to perform such a calculation and expect further algorithmic improvements to be carried out to achieve this goal in the future.