Onset of radial flow in $p+p$ collisions

It has been debated for decades whether hadrons emerging from $p+p$ collisions exhibit collective expansion. The signal of the collective motion in $p+p$ collisions is not as clear or as clean as in heavy-ion collisions because of the low multiplicity and large fluctuation in $p+p$ collisions. The Tsallis blast-wave (TBW) model is a thermodynamic approach, introduced to handle the overwhelming correlation and fluctuation in the hadronic processes. We have systematically studied the identified particle spectra in $p+p$ collisions from the BNL Relativistic Heavy Ion Collider (RHIC) to the CERN Large Hadron Collider (LHC) using TBW and have found no appreciable radial flow in $p+p$ collisions below $\sqrt{s}=900$ GeV. At the LHC higher energy of 7 TeV in $p+p$ collisions, the radial flow velocity achieves an average value of $\langle \beta \rangle =0.320\pm 0.005$. This flow velocity is comparable to that in peripheral (40–60%) $\mathrm{Au}+\mathrm{Au}$ collisions at the RHIC. Breaking of the identified particle spectra $m_T$ scaling was also observed at the LHC from a model-independent test.

Figure 1

Identified particle $m_T$ spectra in $p+p$ collisions at $\sqrt{s}$ = 200 GeV (a), 540 GeV (b), 0.9 TeV (c), and 7 TeV (d). The symbols represent experimental measurements and the curves represent the TBW model fit results. At each energy, all of the $m_T$ spectra are rescaled to have the same value at $m_T=2\mathrm{GeV}/c^2$ as ${\pi }^{+}$. The references of the experimental measurement are summarized in Table 1.

Figure 2

$m_T$ scaling behavior of the identified particle spectra in $p+p$ collisions at $\sqrt{s}=200$ GeV (a), 540 GeV (b), 0.9 TeV (c), and 7 TeV (d). For mesons (baryons), the data points represent the ratio of rescaled $m_T$ spectra shown in Fig. 1 to the corresponding TBW curve of ${\pi }^{+}\left(p\right)$.

Figure 3

The azimuthal anisotropy coefficient $c_2$ versus $p_T$ for pions (solid circles), kaons (solid squares), and protons (open diamonds), illustrating the radial flow effect in Eq. (9). Both $p_2$ and $s_2$ are assumed to be 10%. $T$, $q_M$, and $q_B$ are fixed to the values extracted from 7 TeV data (67.9 MeV, 1.1315, and 1.1009, respectively). The points with different colors correspond to different radial flow velocities.