EPOS LHC: Test of collective hadronization with data measured at the CERN Large Hadron Collider

Epos is a Monte Carlo event generator for minimum bias hadronic interactions, used for both heavy ion interactions and cosmic ray air shower simulations. Since the last public release in 2009, the Large Hadron Collider (LHC) experiments have provided a number of very interesting data sets comprising minimum bias $p\text{−}p,p$-Pb, and Pb-Pb interactions. We describe the changes required to the model to reproduce in detail the new data available from the LHC and the consequences in the interpretation of these data. In particular we discuss the effect of the collective hadronization in $p\text{−}p$ scattering. A different parametrization of flow has been introduced in the case of a small volume with high density of thermalized matter (core) reached in $p\text{−}p$ compared to large volume produced in heavy ion collisions. Both parametrizations depend only on the geometry and the amount of secondary particles entering in the core and not on the beam mass or energy. The transition between the two flow regimes can be tested with $p$-Pb data. Epos LHC is able to reproduce all minimum bias results for all particles with transverse momentum from $p_{\mathrm{t}}=0$ to a few GeV/$c$.

Figure 1

Space-time evolution of the particle production in a hadronic interaction. A hyperbola (line) represents particles with the same proper time. Panel (a) is the standard approach for $p\text{−}p$ scattering while (b) is a more complete treatment used usually for HI collision.

Figure 2

Elementary interaction in the epos model.

Figure 3

Schematic view of the space-time evolution of the particle production in a hadronic interaction in epos 1.99 or epos LHC. A hyperbola (line) represents particles with the same proper time. The same treatment is used for $p\text{−}p$ or $A\text{−}B$ but the collective hadronization, which can be local, is simplified compared to the full HI picture (done in epos 2 or 3).

Figure 4

Fraction of charged particles with $\left|\eta \right|<2.4$ coming from the core as a function of the total number of charged particles with $\left|\eta \right|<2.4$. The solid line is for simulation with epos at 7 TeV and the dashed line for 900 GeV $p\text{−}p$ scattering.

Figure 5

Total, inelastic, and elastic $p\text{−}p$ cross sections calculated with epos LHC (solid line) and epos 1.99 (dashed line). Points are data from [31] and the stars are the LHC measurements by the TOTEM experiment [30].

Figure 6

Pseudorapidity distribution of charged particles for events with at least one charged particle with $\left|\eta \right|<1$ for $p\text{−}p$ interactions at 900 GeV and 7 TeV. Simulations with epos LHC (solid line), epos 1.99 (dashed line), and epos 1.99 without core production (dash-dotted line) are compared to data points from the ALICE experiment [32].

Figure 7

Multiplicity distribution of charged particles with $p_{\mathrm{t}}>100$ MeV and $\left|\eta \right|<2.5$ for $p\text{−}p$ interactions at 7 TeV. Simulations with epos LHC (solid line), epos 1.99 (dashed line), and epos 1.99 without core production (dash-dotted line) are compared to data points from the ATLAS Collaboration [33].

Figure 8

Ratio of particle yield as a function of charged particle multiplicity for $\left|y\right|<1$ for non-single-diffractive (NSD) $p\text{−}p$ scattering at 7 TeV. Simulations are done with epos LHC (solid line), epos 1.99 (dashed line), and epos 1.99 without core production (dash-dotted line). Points are data from the CMS experiment [29].

Figure 9

Ratio $\mathrm{\Xi }/\pi$ as a function of particle density at midrapidity from epos LHC simulations with (solid line) and without core production (dash-dotted line).

Figure 10

Strange baryon yield as a function of rapidity for non-single-diffractive (NSD) $p\text{−}p$ scattering at 7 TeV. Simulations are done with epos LHC with core (solid line) and without core production (dash-dotted line). Points are data from the CMS experiment [36].

Figure 11

Average transverse momentum $\langle p_{\mathrm{t}}\rangle$ as a function of the number of charged particles for charged particles with $p_{\mathrm{t}}>0.1$ GeV and $\left|\eta \right|<2.5$ for $p\text{−}p$ interactions at 7 TeV. Simulations are done with epos LHC (solid line), epos 1.99 (dashed line), and epos LHC without core production (dash-dotted line). Points are data from the ATLAS experiment [33].

Figure 12

Average transverse momentum $\langle p_{\mathrm{t}}\rangle$ of identified particles $(\pi ,K$, and $p)$ as a function of the number of charged particles for particles with rapidity $\left|y\right|<1$ in $p\text{−}p$ collisions at 7 TeV. Simulations are done with epos LHC with (solid line) and without (dash-dotted line) core formation. Points are data from the CMS experiment [29].

Figure 13

Transverse momentum $p_{\mathrm{t}}$ distribution of charged particles with $\left|\eta \right|<2.5$ produced in minimum bias $p\text{−}p$ collisions at 7 TeV. Simulations are done with epos LHC with (solid line) and without (dash-dotted line) core formation. The contributions of particles coming from the core hadronization are shown as a dotted line while particles coming directly from string fragmentation are represented by a dashed line. Points are data from the ATLAS experiment [33].

Figure 14

Transverse momentum distribution of identified particles $(\pi ,K$, and $p)$ for $\left|y\right|<1$ for NSD $p\text{−}p$ scattering at 7 TeV. Simulations are done with epos LHC with (solid line) and without (dash-dotted line) core formation. Points are data from the CMS experiment [29].

Figure 15

Transverse momentum distribution of strange baryons ($\mathrm{\Lambda }$ and $\mathrm{\Xi }$) for $\left|y\right|<1$ for NSD $p\text{−}p$ scattering at 7 TeV. Simulations are done with epos LHC with (solid line) and without (dash-dotted line) core formation. Points are data from the CMS experiment [36].

Figure 16

Ratio of particle yield as a function of transverse momentum for $\left|y\right|<1$ for NSD $p\text{−}p$ scattering at 7 TeV. Simulations are done with epos LHC with (solid line) and without (dash-dotted line) core formation. Points are data from the CMS experiment [29].

Figure 17

Pseudorapidity distribution of charged particles in Pb-Pb collisions at 2.76 TeV/$A$ for centrality bins 0% to 10%, 10% to 20%, 30% to 40%, and 50% to 60%. Epos LHC simulations (solid line) are compared to the ATLAS (band) and ALICE (point) measurements [37, 38].

Figure 18

Nuclear modification factor for charged particles in the 5% most central events of Pb-Pb collisions at 2.76 TeV. Epos LHC simulations (solid line) are compared to the ALICE measurements [39] (points).

Figure 19

Average transverse momentum $\langle p_{\mathrm{t}}\rangle$ of identified particles ($\pi ,K$, and $p$) as a function of the number of charged particles for particles with rapidity $\left|y\right|<1$ in $p\text{−}p$ collisions at 7 TeV (solid line) and $p$-Pb collisions at 5 TeV (dashed line). Simulations are done with epos LHC including core formation. Points are data from the CMS experiment [29] for $p\text{−}p$ scattering.

Figure 20

Pseudorapidity distribution of charged particles from $p$-Pb collisions at 5.02 TeV. Simulations are done with epos LHC with (solid line) and without (dash-dotted line) core formation. Points are data from the ALICE experiment [40].

Figure 21

Nuclear modification factor of charged particles from $p$-Pb collisions at 5.02 TeV. Simulations are done with epos LHC, with (solid line) and without (dash-dotted line) core formation. Points are data from the ALICE experiment [41].

Figure 22

Nuclear modification factor for identified particles ${\pi }^0$ (dashed and dash-dotted lines) and proton $p$ (solid and dashed lines) from $p$-Pb collisions at 5.02 TeV. Simulations are done with epos LHC with (solid and dashed lines) and without (dotted and dash-dotted lines) core formation.

Figure 23

ATLAS measurement of the pseudorapidity distribution of charged particles with $p_{\mathrm{t}}\ge 500$ MeV in minimum bias collisions [33] compared to pythia6 (dashed line), pythia8 (dash-dotted line), and epos LHC (solid line) simulations.

Figure 24

Predicted pseudorapidity distribution of charged particles $p_{\mathrm{t}}\ge 500$ MeV in minimum bias collisions at the LHC at a cms energy of 14 TeV compared with pythia6 (dashed line), pythia8 (dash-dotted line), and epos LHC (solid line) simulations.

Figure 25

ATLAS measurement of charged particles with $p_{\mathrm{t}}\ge 500$ MeV produced in the underlying event, i.e., a region of ${60}^{\circ }\le \left|\mathrm{\Delta }\varphi \right|\le {120}^{\circ }$ around the leading particle [46] compared to pythia6 (dashed line), pythia8 (dashed-dotted line), and epos LHC (solid line) simulations.

Figure 26

ATLAS measurement of the pseudorapidity distribution of charged particles $p_{\mathrm{t}}\ge 100$ MeV in minimum bias collisions [33] compared to pythia6 (dashed line), pythia8 (dash-dotted line), and epos LHC (solid line) simulations.

Figure 27

Predicted pseudorapidity distribution of charged particles $p_{\mathrm{t}}\ge 100$ MeV in minimum bias collisions at the LHC at a cms energy of 14 TeV compared to pythia6 (dashed line), pythia8 (dash-dotted line), and epos LHC (solid line) simulations.

Figure 28

ATLAS measurement of the angular distribution of charged particle production with respect to the leading charged particle with $p_{\mathrm{t}}\ge 1$ GeV [46] compared to pythia6 (dashed line), pythia8 (dash-dotted line), and epos LHC (solid line) simulations.

Figure 29

ATLAS measurement of $p_{\mathrm{t}}$ of charged particle produced in minimum bias collisions at 7 TeV [33] compared to pythia6 (dashed line), pythia8 (dash-dotted line), and epos LHC (solid line) simulations.

Figure 30

ATLAS measurement of $\sum E_t$ as a function of pseudorapidity $\eta$ in minimum bias events at 7 TeV [56] compared to pythia6 (dashed line), pythia8 (dash-dotted line), and epos LHC (solid line) simulations.

Figure 31

ATLAS measurement of the pseudorapidity gap $\mathrm{\Delta }{\eta }^F$ for particles with $p_{\mathrm{t},\mathrm{cut}}>400$ MeV in minimum bias events at 7 TeV [57] compared to epos LHC (solid line), pythia6 (dashed line), and pythia8 (dash-dotted line) simulations.

Figure 32

CMS measurement of strange particles ($K_s^0,{\mathrm{\Lambda }}^0$, and ${\mathrm{\Xi }}^{\pm }$) yields as a function of rapidity in NSD events at 7 TeV [36] compared to epos LHC (solid line), pythia6 (dashed line), and pythia8 (dash-dotted line) simulations.

Figure 33

CMS measurement of transverse momentum distribution of strange particles ($K_s^0,{\mathrm{\Lambda }}^0$, and ${\mathrm{\Xi }}^{\pm }$) in NSD events at 7 TeV [36] compared to epos LHC (solid line), pythia6 (dashed line), and pythia8 (dash-dotted line) simulations.