Dissecting Soft Radiation with Factorization

Abstract

An essential part of high-energy hadronic collisions is the soft hadronic activity that underlies the primary hard interaction. It includes soft radiation from the primary hard partons, secondary multiple parton interactions (MPI), and factorization-violating effects. The invariant mass spectrum of the leading jet in $Z+\mathrm{jet}$ and $H+\mathrm{jet}$ events is directly sensitive to these effects, and we use here a QCD factorization theorem to predict its dependence on the jet radius $R$, jet ${p}_{T}$, jet rapidity, and partonic process for both the perturbative and nonperturbative components of primary soft radiation. We prove that the nonperturbative contributions involve only odd powers of $R$, and the linear $R$ term is universal for quark and gluon jets. The hadronization model in Pythia8 agrees well with these properties. The perturbative soft initial state radiation (ISR) has a contribution that depends on the jet area in the same way as the underlying event, but this degeneracy is broken by dependence on the jet ${p}_{T}$. The size of this soft ISR contribution is proportional to the color state of the initial partons, yielding the same positive contribution for $gg{\rightarrow}Hg$ and $gq{\rightarrow}Zq$, but a negative interference contribution for $q\overline{q}{\rightarrow}Zg$. Hence, measuring these dependencies allows one to separate hadronization, soft ISR, and MPI contributions in the data.