Thermalization in a small hadron gas system and high-multiplicity $pp$ events

We study the system-size dependence of Knudsen number, a measure of degree of thermalization, for hadron resonance gas that follows the lattice quantum chromodynamics equation of state at zero chemical potential. A comparison between Knudsen numbers for the $\mathrm{AuAu}$ collisions at RHIC and the hadron gas of size similar to the size of high-multiplicity $pp$ events at LHC, reassures the applicability of hydrodynamics in interpreting the features of particle production in high-multiplicity $pp$ events.

Figure 1

The pressure for different system sizes: (a) infinite, (b) $R$ = 5 fm, (c) $R$ = 3 fm, and (d) $R$ = 2.5 fm of hadron gas with different effects as a function of $T$ is compared with LQCD data [17].

Figure 2

The energy density for different options as mentioned in the caption of Fig. 1.

Figure 3

(a)The number density for infinite as well as finite system sizes ($R$ = 5, 3, and 2.5 fm) of hadron resonance gas, including the Hagedorn states and the EV effect, as a function of temperature. (b) Corresponding ${\sigma }_{\pi \pi }$ in a thermalized pion gas as given in [27].

Figure 4

The ratio of number density of finite ($R$ = 5, 3, and 2.5 fm) and the infinite system size of hadron resonance gas, including the Hagedorn states and the EV effect as a function of temperature.

Figure 5

Temperature dependent pion mean free path in different sizes of hadron gas, obtained by using the ${\sigma }_{\pi \pi }$ in a thermalized pion gas given in [27].

Figure 6

The Knudsen number as a function of the system size, $R$ of hadron resonance gas, for different options (described in the text) of approximation on cross sections, including the EV effect [and the Hagedorn states for options (i) and (iii)] at $T$ = 160 MeV.