Collective interaction of QCD strings and early stages of high-multiplicity $pA$ collisions

We study the early stages of “central” $pA$ and peripheral $AA$ collisions. Several observables indicate that at a sufficiently large number of participant nucleons the system undergoes a transition into a new “explosive” regime. By defining a string-string interaction through the $\sigma$ meson exchange and performing molecular dynamics simulation, we argue that one should expect a strong collective implosion of the multistring “spaghetti” state, creating significant compression of the system in the transverse plane. Another consequence is the collectivization of the “$\sigma$ clouds” of all strings into a chirally symmetric fireball. We find that these effects happen provided the number of strings $N_s>30$ or so, as only such a number can compensate a small $\sigma$-string coupling. These findings should help us to understand the subsequent explosive behavior observed for the particle multiplicities roughly corresponding to this number of strings.

Figure 1

Top: Basic mechanism of a two-string production, resulting from color reconnection. Bottom: Sketch of the simplest multistring state, produced in $pA$ collisions or very peripheral $AA$ collisions, known as “spaghetti.”

Figure 2

Probability distribution over the number of charged tracks in the CMS detector acceptance $P\left(N_{\mathrm{tr}}\right)$ [12]. The (purple) line is the Poisson distribution with $\langle N_p\rangle =16$, arbitrarily normalized to touch the data points.

Figure 3

Normalized chiral condensate as a function of the radial coordinate transverse to the QCD string. Points are from the lattice data [13]. The curve is expression (7) with $C=0.26$ and $s_{\mathrm{string}}=0.176$ fm.

Figure 4

The mean field (normalized as explained in the text) versus the transverse radius in units of inverse $m_{\sigma }$. Dashed and solid curves correspond to the source radii $R=1.5$ and 0.7 fm, respectively.

Figure 5

Example of changing transverse positions of the 50-string set: the four plots correspond to one initial configuration evolved to times $\tau =0.1$, 0.5, 1, and 1.5 fm/$c$. Distances are given in femtometers, and $g_N{\sigma }_T=0.2$.

Figure 6

Example of peripheral $AA$ collisions, with $b=11$ fm, $g_N{\sigma }_T=0.2$, and the 50-string set. The four plots of the string transverse positions $x,y$ (fm) correspond to times $\tau =0.1$, 0.5, 1.0, and 2.6 fm/$c$.

Figure 7

The (dimensionless) kinetic energy (upper curve) and potential energy (lower curve) of the system for the same example as shown in Fig. 7, as a function of time $t(\mathrm{fm}/c)$. The horizontal line with points is their sum, $E_{\mathrm{tot}}$, which is conserved.

Figure 8

Kinetic energy (dimensionless) versus simulation time $(\mathrm{fm}/c)$, for few $pA$ runs with $N_s=50$. The seven curves (bottom to top) correspond to increasing coupling constants $g_N{\sigma }_T=0.01$, 0.02, 0.03, 0.05, 0.08, 0.10,and 0.20. The shaded region at the right corresponds to the time which is considered to be too late for strings to exist, due to their breaking.

Figure 9

Left: Central $pA$ collisions. Right: Peripheral $AA$ collisions. The vertical axis is the effective coupling constant $g_N{\sigma }_T$ (dimensionless). The horizontal axis is the maximal energy density ${\epsilon }_{\max }$ $(\mathrm{GeV}/{\mathrm{fm}}^3)$ defined by the procedure explained in the text. The five sets shown by different symbols correspond to string numbers $N_s=10$, 20, 30, 40, and 50 (left to right), respectively.

Figure 10

Instantaneous collective potential (in units of $2g_N{\sigma }_T$) for an $AA$ configuration with $b=11$ fm, $g_N{\sigma }_T=0.2,N_s=50$ at the moment in time $\tau =1$ fm/$c$. White regions correspond to the chirally restored phase.