A toolbox for q_{T} and 0-jettiness subtractions at hbox {N}^3hbox {LO}

Abstract

We derive the leading-power singular terms at three loops for both q_T and 0-jettiness, mathcal {T}_0, for generic color-singlet processes. Our results provide the complete set of differential subtraction terms for q_T and mathcal {T}_0 subtractions at hbox {N}^3hbox {LO}, which are an important ingredient for matching hbox {N}^3hbox {LO} calculations with parton showers. We obtain the full three-loop structure of the relevant beam and soft functions, which are necessary ingredients for the resummation of q_T and mathcal {T}_0 at hbox {N}^3hbox {LL}' and hbox {N}^4hbox {LL} order, and which constitute important building blocks in other contexts as well. The nonlogarithmic boundary coefficients of the beam functions, which contribute to the integrated subtraction terms, are not yet fully known at three loops. By exploiting consistency relations between different factorization limits, we derive results for the q_T and mathcal {T}_0 beam function coefficients at hbox {N}^3hbox {LO} in the zrightarrow 1 threshold limit, and we also estimate the size of the unknown terms beyond threshold.