A soft-hard framework with exact four momentum conservation for small systems

A new framework, called x-scape, for the combined study of both hard and soft transverse momentum sectors in high energy proton-proton ($p$-$p$) and proton-nucleus ($p$-$A$) collisions is set up. A dynamical initial state is set up using the 3d-Glauber model with transverse locations of hotspots within each incoming nucleon. A hard scattering that emanates from two colliding hotspots is carried out using the Pythia generator. Initial state radiation from the incoming hard partons is carried out in a new module called I-matter, which includes the longitudinal location of initial splits. The energy-momentum of both the initial hard partons and their associated beam remnants is removed from the hot spots, depleting the energy-momentum available for the formation of the bulk medium. Outgoing showers are simulated using the matter generator, and results are presented for both cases, allowing for and not allowing for energy loss. First comparisons between this hard-soft model and single inclusive hadron and jet data from $p$-$p$ and minimum bias $p$-$Pb$ collisions are presented. Single hadron spectra in $p$-$p$ are used to carry out a limited (in number of parameters) Bayesian calibration of the model. Fair comparisons with data are indicative of the utility of this new framework. Theoretical studies of the correlation between jet $p_T$ and event activity at mid and forward rapidity are carried out.