The ridge-like structure found in two-particle correlation from proton-proton collisions is one of the hot topics in high-energy heavy-ion physics. Because the scale of pp collisions is not large enough to generate a high-temperature and high-density medium called QGP, this phenomenon cannot be suitably understood through hydrodynamics, unlike in nucleus-nucleus collision.
In a meanwhile, jet particles lose considerable energy while moving through the collisions with partons in the medium. The momentum transferred from jets to medium partons is in the direction of jets' motion, which might produce the collective motion of the medium, such as the ridge. In this sense, the momentum kick model has been tested in the nucleus-nucleus and pp collisions at various energies.

For its validity we try to apply this model to the correlation observable and we need the initial parton distribution of the medium. We have adopted several distribution functions: Maxwell-Boltzmann(MB), Juttner-Synge(JS), and phenomenological parton distribution functions from the soft scattering model (phPDs) and from the hard scattering model (phPDh). However, the MB and JS can not explain the parton momentum distribution over a wide range of pseudo-rapidity and phPDs does not describe the lightcone variable distribution. Therefore we proceed to use phPDh relatively in detail.

In this study, we find the optimal values of model parameters by fitting to the simulated data for pp collisions at $\sqrt{s_{NN}} = 2.76 \,\rm{TeV}$ from PYTHIA8. We compare not only the the transverse momentum and rapidity distribution but also the lightcone variable distribution. Using these settings, we calculate the two-particle correlations and compare them to the experimental results.