Multi-Parton Interactions in pp collisions from Machine Learning-based regression

Multi-Parton Interactions (MPI) in pp collisions have attracted the attention of the heavy-ion community since they can help to elucidate the origin of collective-like effects discovered in small collision systems at the LHC. In this work, we report that in PYTHIA 8.244, the charged-particle production in events with a large number of MPI (${\rm N}_{\rm mpi}$) normalized to that obtained in minimum-bias pp collisions shows interesting features. After the normalization to the corresponding $\langle {\rm N}_{\rm mpi} \rangle$, the ratios as a function of $p_{\rm T}$ exhibit a bump at $p_{\rm T}\approx3$ GeV/$c$; and for higher $p_{\rm T}$ ($>8$ GeV/$c$), the ratios are independent of ${\rm N}_{\rm mpi}$. While the size of the bump increases with increasing ${\rm N}_{\rm mpi}$, the behavior at high $p_{\rm T}$ is expected from the "binary scaling" (parton-parton interactions), which holds given the absence of any parton-energy loss mechanism in PYTHIA. The bump at intermediate $p_{\rm T}$ is reminiscent of the Cronin effect observed for the nuclear modification factor in p--Pb collisions. In order to unveil these effects in data, we propose a strategy to construct an event classifier sensitive to MPI using Machine Learning-based regression. The study is conducted using TMVA, and the regression is performed with Boosted Decision Trees (BDT). Event properties like forward charged-particle multiplicity, transverse spherocity and the average transverse momentum ($\langle p_{\rm T} \rangle$) are used for training. The kinematic cuts are defined in accordance with the ALICE detector capabilities. In addition, we also report that if we apply the trained BDT on existing (${\rm INEL}>0$) pp data, i.e. events with at least one primary charged-particle within $|\eta|<1$, the average number of MPI in pp collisions at $\sqrt{s}=5.02$ and 13 TeV are 3.76$\pm1.01$ and 4.65$\pm1.01$, respectively.