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.