Interpretation of charged-particle spectra in $p+p$ and $p+\mathrm{Pb}$ collisions at energies available at the CERN Large Hadron Collider using an improved hijing code with a collective cascade

We supplement the Heavy Ion Jet Interaction Generator (hijing) code with a collective cascade recipe and updated Martin-Stirling-Thorne-Watt (MSTW2009) parton distribution functions (PDFs) to describe nonsingle diffractive (NSD) $p+p$ and Pb collisions at CERN Large Hadron Collider energies. The collective cascade, developed in the space of an impact parameter, is used to induce nuclear modification of nucleons, that are involved in primary interactions, inside the dense nuclear medium. It is found that the improved hijing (Imhijing) code (that with MSTW2009 PDFs) reproduces rather well the pseudorapidity density, the multiplicity, and the transverse momentum distributions of charged particles within the pseudorapidity interval $|{\eta }_{\mathrm{c}.\mathrm{m}.\mathrm{system}}|<2.4$ in NSD $p+p$ collisions at $\sqrt{s_{\mathrm{NN}}}=0.9$, 2.36, and 7 TeV. The Imhijing with collective cascade calculations is also shown to be a good fit to the pseudorapidity density (in the laboratory system) and transverse momentum $\left(p_T\right)$ dependence of the nuclear modification of charged particles in NSD $p+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$. The effects of the collective cascade are clearly seen in the target $(3<{\eta }_{\mathrm{lab}}<4)$ and central (within $|{\eta }_{\mathrm{c}.\mathrm{m}.\mathrm{system}}|<0.3$ at $1<p_T<8\mathrm{GeV}/c)$ interaction regions when studying the pseudorapidity density and transverse momentum dependence of the nuclear modification factor of the charged particles, respectively.

Figure 1

A schematic of the Regge collective cascade for a single $p+A$ collision on the impact-parameter plane. All nucleons are shown as open circles, a primary interacting nucleon is marked by the closed circle, the set of individual Reggeon exchanges is marked by the wavy lines, and the square point is the Reggeon interaction vertex.

Figure 2

The average number of wounded nucleons $N_w$ as a function of impact parameter $\left(b\right)$. The solid and dotted lines denote the Imhijing calculations with and without collective cascade, respectively.

Figure 3

Pseudorapidity density of charged particles in NSD $p+p$ collisions at LHC energies as compared to the hijing results. The experimental data are from the CMS Collaboration [29, 30] and the ALICE Collaboration [27].

Figure 4

Multiplicity distributions of charged particles within $|{\eta }_{\mathrm{c}.\mathrm{m}.\mathrm{system}}|<2.4$ and $p_T>500\mathrm{MeV}/c$ in NSD $p+p$ collisions at LHC energies from the CMS Collaboration experiment [31] as compared to the hijing results. For clarity, only the histograms and the data for the smaller energy are given in absolute values. The other ones have been multiplied by ${10}^1$ and ${10}^2$ for other energies in increasing order.

Figure 5

Transverse momentum distributions of charged particles in the range of $|{\eta }_{\mathrm{c}.\mathrm{m}.\mathrm{system}}|<2.4$ in NSD $p+p$ collisions at LHC energies as compared to the hijing results. The square points with error bars denote the CMS Collaboration experimental data [29, 30]. For clarity, only the histograms and the data for the smaller energy are given in absolute values. The other ones have been multiplied by ${10}^1$ and ${10}^2$ for other energies in increasing order. (a) and (b) are the results calculated by the Imhijing and hijing 1.0, respectively. For both cases the ratios between the measured values and the Monte Carlo (MC) hijing calculations are shown in the lower part with the same convention.

Figure 6

Pseudorapidity density (in the laboratory system) of charged particles in NSD $p+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$ from the ALICE Collaboration experiment [7] as compared to the improved hijing results.

Figure 7

Transverse momentum distributions of charged particles at different pseudorapity intervals in NSD $p+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$ from the ALICE Collaboration experiment [1, 4] as compared to the improved hijing results.

Figure 8

The same as Fig. 7, but here the lines denote the standard hijing calculations.

Figure 9

Transverse momentum dependence of the nuclear modification factor of charged particles at different pseudorapity intervals in NSD $p+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$ from the ALICE Collaboration experiment [1, 4] as compared to the improved hijing results. The insets show a closeup of the region where the effect of the collective cascade is more pronounced.