Multiparton interactions in $pp$ collisions from machine learning-based regression

Multiparton interactions (MPI) in $pp$ collisions have attracted the attention of the heavy-ion community since they can help to elucidate the origin of collectivelike effects discovered in small collision systems at the LHC. In this work, we report that in pythia8.244, the charged-particle production in events with a large number of MPI (${\mathrm{N}}_{\mathrm{mpi}}$) normalized to that obtained in minimum-bias $pp$ collisions shows interesting features. After the normalization to the corresponding $⟨{\mathrm{N}}_{\mathrm{mpi}}⟩$, the ratios as a function of $p_{\mathrm{T}}$ exhibit a bump at $p_{\mathrm{T}}\approx 3\mathrm{GeV}/c$; and for higher $p_{\mathrm{T}}$ ($>8\mathrm{GeV}/c$), the ratios are independent of ${\mathrm{N}}_{\mathrm{mpi}}$. While the size of the bump increases with increasing ${\mathrm{N}}_{\mathrm{mpi}}$, the behavior at high $p_{\mathrm{T}}$ 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 $p_{\mathrm{T}}$ 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 ($⟨p_{\mathrm{T}}⟩$) are used for training. The kinematic cuts are defined in accordance with the ALICE detector capabilities. For the validation of the method and to find possible model dependence, we also compare the results from pythia8.244 with herwig7.1. In addition, we also report that if we apply the trained BDT on existing ($\mathrm{INEL}>0$) $pp$ 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 $3.76\pm 1.01$ and $4.65\pm 1.01$, respectively.

Figure 1

Average number of MPI as a function of the center-of-mass energy for minimum-bias $pp$ collisions simulated with pythia8.244 tune 4C (solid line). The dotted line represents the expected value for simulations when MPI is switched off. The trained BDT were applied to tune 4C simulations and the obtained values are displayed for the cases which use the pythia tunes: 4C (full markers), Monash 2013 (open circles) and 2C (open triangles) for training. Results which uses herwig7 simulations for training are also displayed (stars). The boxes around the markers correspond to the systematic uncertainty associated to our reference results. Results for simulations which do not include color reconnection (red) or MPI (blue) are also shown for $\sqrt{s}=13\mathrm{TeV}$.

Figure 2

Distribution of the self-normalized ${\mathrm{N}}_{\mathrm{mpi}}$ for minimum-bias $pp$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$ simulated with pythia8.244 tune 4C (solid line). The distributions obtained from regression are displayed for the cases which use the tunes: 4C (full markers), Monash 2013 (open circles) and 2C (open triangles) for the training of BDT. BDT were also trained using simulations with a flat ${\mathrm{N}}_{\mathrm{mpi}}$ distribution, the result from regression is also shown (dashed line).

Figure 3

Primary charged pion $R_{pp}$ as a function of $p_{\mathrm{T}}$ (top) and proton-to-pion ratio as a function of $p_{\mathrm{T}}$ (bottom). Results are presented for different event classes based on the actual number of multiparton interactions (left), the target variable (middle), and mid-pseudorapidity charged-particle multiplicity (right). Results from simulations including color reconnection are shown with full markers, while the case where color reconnection is switched off is displayed with empty markers. The boxes around one indicate the estimated uncertainty associated to event selection.

Figure 4

Average number of MPI as a function of $\sqrt{s}$. Results from pythia8.244 (solid line) are compared to the estimated $⟨{\mathrm{N}}_{\mathrm{mpi}}⟩$ (markers) obtained from the application of the trained BDT to the existing ALICE data [23].