On the Cutoff Dependence of the Quark Mass Parameter in Angular Ordered Parton Showers

We show that the presence of an infrared cutoff $Q_0$ in the parton shower (PS) evolution for massive quarks implies that the generator quark mass corresponds to a $Q_0$-dependent short-distance mass scheme and is therefore not the pole mass. Our analysis considers an angular ordered parton shower based on the coherent branching formalism for quasi-collinear stable heavy quarks and splitting functions at next-to-leading logarithmic (NLL) order, and it is based on the analysis of the peak of hemisphere jet mass distributions. We show that NLL shower evolution is sufficient to describe the peak jet mass at full next-to-leading order (NLO). We determine the relation of this short-distance mass to the pole mass at NLO. We also show that the shower cut $Q_0$ affects soft radiation in a universal way for massless and quasi-collinear massive quark production. The basis of our analysis is (i) an analytic solution of the PS evolution based on the coherent branching formalism, (ii) an implementation of the infrared cut $Q_0$ of the angular ordered shower into factorized analytic calculations in the framework of Soft-Collinear-Effective-Theory (SCET) and (iii) the dependence of the peak of the jet mass distribution on the shower cut. Numerical comparisons to simulations with the HERWIG 7 event generator confirm our findings. Our analysis provides an important step towards a full understanding concerning the interpretation of top quark mass measurements based on direct reconstruction.