Multiplicity-dependent $p_T$ distributions of identified particles in $pp$ collisions at 7 TeV within the HIJING/$B\overline{B}$ v2.0 model

Effects of strong longitudinal color fields (SLCF) on the identified (anti)particle transverse momentum ($p_T$) distributions in $pp$ collision at $\sqrt{s}=7\mathrm{TeV}$ are investigated within the framework of the HIJING/$B\overline{B}$ v2.0 model. The comparison with the experiment is performed in terms of the correlation between mean transverse momentum ($\langle p_T\rangle$) and multiplicity ($N_{\mathrm{ch}}^{*}$) of charged particles at central rapidity, as well as the ratios of the $p_T$ distributions to the one corresponding to the minimum bias (MB) $pp$ collisions at the same energy, each of them normalized to the corresponding charged particle density, for high multiplicity (HM, $N_{\mathrm{ch}}>100$) and low multiplicity (LM, $N_{\mathrm{ch}}<100$) class of events. The theoretical calculations show that an increase of the strength of color fields (as characterized by the effective values of the string tension $\kappa$), from $\kappa =2$ to $\kappa =5\mathrm{GeV}/\mathrm{fm}$, from LM to HM class of events, respectively, led to a ratio at low and intermediate $p_T$ (i.e., 1 GeV/$c <p_T<6$ GeV/$c$), consistent with recent data obtained at the Large Hadron Collider by the ALICE Collaboration. These results point out the necessity of introducing a multiplicity (or energy density) dependence for the effective value of the string tension. Moreover, the string tension $\kappa =5\mathrm{GeV}/\mathrm{fm}$, describing the $p_T$ spectra of identified particles (anti)particle in $pp$ collisions at $\sqrt{s}=7\mathrm{TeV}$ for high charged particle (HM) multiplicity event classes, has the same value as the one used in describing the $p_T$ spectra in central Pb-Pb collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. Therefore, we can conclude that at the LHC energies the global features of the interactions could be mostly determined by the properties of the initial chromoelectric flux tubes, while the system size may play a minor role.

Figure 1

Open symbols: HIJING/$B\overline{B}$ v2.0 predictions for the average transverse momentum ($\langle p_T\rangle$) of charged particles as a function of multiplicity at mid-pseudorapidity $N_{\mathrm{ch}}^{*}$. Left panel: $pp$ collisions at $\sqrt{s}=7\mathrm{TeV}$ for $0.15<p_T<10$ GeV/$c$ and mid-pseudorapidity $\left|\eta \right|<0.3$. Right panel: $p-\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=5.02\mathrm{TeV}$ for $0.15<p_T<10$ GeV/$c$ and midrapidity $\left|\eta \right|<0.3$. The theoretical results are obtained for different effective string tensions increasing from $\kappa =1\mathrm{GeV}/\mathrm{fm}$ (default) up to $\kappa =5\mathrm{GeV}/\mathrm{fm}$. The ALICE data (filled circles) are from Ref. [83]. The errors represent systematic uncertainties on $\langle p_T\rangle$. The statistical errors are negligible.

Figure 2

Open symbols: HIJING/$B\overline{B}$ v2.0 predictions for the average transverse momentum ($\langle p_T\rangle$) of identified particle for $0<p_T<10$ GeV/$c$ and midrapidity $\left|y\right|<0.5$ as function of charged particle multiplicity, $N_{\mathrm{ch}}^{*}$ in $pp$ collisions at $\sqrt{s}=7\mathrm{TeV}$. The results are obtained with an effective string tension value, $\kappa =2\mathrm{GeV}/\mathrm{fm}$ (left side) and $\kappa =5\mathrm{GeV}/\mathrm{fm}$ (right side). For clarity, we do not include the results for $\mathrm{\Lambda }$. The ALICE preliminary data (filled symbols) are from Refs. [68, 69, 71]. Only statistical error bars are shown.

Figure 3

Open symbols: HIJING/$B\overline{B}$ v2.0 predictions for the average transverse momentum ($\langle p_T\rangle$) of identified particle in the range $0<p_T<10$ GeV/$c$ and midrapidity $0.0<y_{cm}<0.5$ as function of charged particle multiplicity, $N_{\mathrm{ch}}^{*}$ in $p-\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=5.02\mathrm{TeV}$. The results (open symbols) are obtained with an effective string tension value, $\kappa =3\mathrm{GeV}/\mathrm{fm}$ (left side) and $\kappa =5\mathrm{GeV}/\mathrm{fm}$ (right side). For clarity, we do not include the results for $\mathrm{\Lambda }$. The ALICE data (filled symbols) are from Ref. [88]. Only statistical error bars are shown.

Figure 4

HIJING/$B\overline{B}$ v2.0 predictions for the invariant yields of identified particles in central Pb-Pb collisions (solid histograms) and $pp$ collisions (dashed histograms) at c.m. energy 2.76 TeV. The results are obtained using $\kappa =5\mathrm{GeV}/\mathrm{fm}$ ($\kappa =1.9\mathrm{GeV}/\mathrm{fm}$) for Pb-Pb ($pp$), respectively. The ALICE data are from Ref. [92]. The error include systematic uncertainties.

Figure 5

HIJING/$B\overline{B}$ v2.0 results for transverse momentum ($p_T$) distributions at midrapidity for charged pions in two multiplicity classes (see text for explanation). The results for high- (low-) multiplicity classes of events are presented in the panels (a) and (b) and panels (c) and (d), respectively. The solid (dashed) histograms are obtained using $\kappa =5\mathrm{GeV}/\mathrm{fm}$ ($\kappa =2\mathrm{GeV}/\mathrm{fm}$) for high (class I) and low (class V) multiplicity classes of events. The results for minimum-bias $pp$ collisions obtained for $\kappa =2\mathrm{GeV}/\mathrm{fm}$ (dotted histograms) are included and compared to data from ALICE [93] (open circles) and CMS Collaborations [94] (open squares). Panels (e) and (f) include the ratios $R_{\mathrm{mb}}$ obtained using $\kappa =2\mathrm{GeV}/\mathrm{fm}$ and $\kappa =5\mathrm{GeV}/\mathrm{fm}$, respectively. The upper dashed and solid histograms are for HM (class I), and the lower dashed and solid histograms are for LM (class V) class of events. The experimental ratio $R_{\mathrm{mb}}$ was calculated by us based on average $p_T$ spectra of particles and antiparticles measured (open stars) by the ALICE Collaboration [69, 70, 71]. Only statistical error bars are shown.

Figure 6

The same as in Fig. 5 for charged kaons.

Figure 7

The same as in Fig. 5 for protons and antiprotons.

Figure 8

The HIJING/$B\overline{B}$ v2.0 model predictions for $\mathrm{\Lambda }+\overline{\mathrm{\Lambda }}$ produced in $pp$ collisions at $\sqrt{s}=7\mathrm{TeV}$. The ratios of the normalized $p_T$ distributions, $R_{\mathrm{mb}}$ [see Eq. (1)] for six multiplicity classes (see text for explanation) based on average $p_T$ spectra of particle and antiparticle. From top to bottom, the calculations correspond to class I to class VI multiplicity events. Left: The results obtained with $\kappa =2\mathrm{GeV}/\mathrm{fm}$. Right: The results obtained with ($\kappa =5\mathrm{GeV}/\mathrm{fm}$).

Figure 9

The same as in Fig. 5 for events of high (class II) and low (class VI) multiplicities. The calculations are for $\mathrm{\Lambda }$ and $\overline{\mathrm{\Lambda }}$. The results for minimum-bias $pp$ collisions obtained with $\kappa =2\mathrm{GeV}/\mathrm{fm}$ (dotted histograms) are included and compared to data from the CMS Collaboration [94] (open squares). Only statistical error bars are shown.

Figure 10

The same as Fig. 5 for events of high (class II) and low (class V) multiplicities. The calculations are for ${\mathrm{\Xi }}^{-}$ and ${\overline{\mathrm{\Xi }}}^{+}$. The results for minimum-bias $pp$ collisions obtained with $\kappa =2\mathrm{GeV}/\mathrm{fm}$ (dotted histograms) are included and compared to data from the ALICE [68, 69, 71] (open circles) and CMS Collaborations [94] (open squares). Only statistical error bars are shown.

Figure 11

The same as in Fig. 5 for events of high (class II) and low (class V) multiplicities. The calculations are for ${\mathrm{\Omega }}^{-}$ and ${\overline{\mathrm{\Omega }}}^{+}$. The results for minimum-bias $pp$ collisions obtained with $\kappa =2\mathrm{GeV}/\mathrm{fm}$ (dotted histograms) are included and compared to data (open circles) from the ALICE Collaboration [68, 69, 71]. Only statistical error bars are shown.