Singlet and nonsinglet three-loop massive form factors

We consider quantum chromodynamics with external vector, axial-vector, scalar, and pseudoscalar currents and compute three-loop corrections to the corresponding vertex function taking into account massive quarks. We consider all nonsinglet contributions as well as those singlet contributions where the external current couples to a massive quark loop. We apply a seminumerical method which is based on expansions around singular and regular kinematical points. They are matched at intermediate values of the squared partonic center-of-mass energy s which allows one to cover the whole kinematic range for negative and positive values of s. Our method permits a systematic increase of the precision by varying the expansion depth and the choice of the intermediate matching points. In our current setup we have at least seven significant digits for the finite contribution of all form factors. We present our results as a combination of series expansions and interpolation functions which allows for a straightforward use in practical applications.