A disturbance in the (strong) Force: Alien operators for precision QCD
by
Next-generation collider experiments, such as the high-luminosity phase of the LHC and the upcoming electron-ion collider, are expected to push the precision of many QCD-related measurements to the 1% level. As such, it is important for theory predictions to reach the same level of precision. Particularly important for processes involving initial-state hadrons are the perturbative corrections to the QCD splitting functions. The latter determine the scale dependence of the parton distribution functions through the DGLAP equation. It is well-known that the Mellin moments of the splitting functions correspond to the anomalous dimensions of leading-twist gauge-invariant operators of spin N. The most convenient way to compute these anomalous dimensions is through the renormalization of the off-shell operator matrix elements. A major obstacle in this approach is the mixing with non-gauge-invariant (alien) operators, whose structure becomes increasingly complicated at higher spin. In this talk, we will discuss the systematic study of these alien operators at arbitrary spin. In particular, using generalized BRST symmetry relations, we derive the functional form of the aliens which are necessary to perform the renormalization of the physical operators to four loops in QCD. This marks an important step towards the determination of the full four-loop splitting functions, which will be vital for high-precision phenomenology.