Dissecting Soft Radiation with Factorization

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  +jet and H  +jet events is directly sensitive to these effects, and we use 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→Hg  and gq→Zq  , but a negative interference contribution for qq ¯ →Zg  . Hence, measuring these dependencies allows one to separate hadronization, soft ISR, and MPI contributions in the data.