Femtoscopic signature of strong radial flow in high-multiplicity $pp$ collisions

Hydrodynamic simulations are used to calculate the identical pion Hanbury-Brown–Twiss (HBT) radii, as a function of the pair momentum $k_{\mathrm{T}}$. This dependence is sensitive to the magnitude of the collective radial flow in the transverse plane, and thus comparison to ALICE data enables us to derive its magnitude. By using hydro solutions with variable initial parameters we conclude that in this case fireball explosions start with a very small initial size, well below 1 $\mathrm{fm}$.

Figure 1

Sketch of how the radial flow (arrows directed radially from the fireball center) influences the HBT radii. At small $k_{\mathrm{T}}$ the whole fireball (the circle) is visible, but at larger $k_{\mathrm{T}}$ one sees only the part comoving in the same direction, shown by the shaded ellipse.

Figure 2

The temperature profiles of the Gubser solutions for different values of the parameter $q$, at $\tau =0.6\mathrm{fm}$ as a function of $r$.

Figure 3

Time evolutions of temperature and velocity for $q=0.7{\mathrm{fm}}^{-1}$ (left column) and $q=1.7{\mathrm{fm}}^{-1}$ (right column). Temperature (dashed line) and velocity (solid line) profiles at $\tau =0.6,1.8,3.0,4.2\mathrm{fm}$ are plotted as a function of the radial coordinate $r$. The dotted lines in the plots indicate the freezeout temperature $T_{\mathrm{f}}=0.12\mathrm{GeV}$.

Figure 4

Distribution of displacements in the out $\left(X_{\mathrm{o}}\right)$ and side $\left(X_{\mathrm{s}}\right)$ directions for $q=0.5{\mathrm{fm}}^{-1}$. Three figures are for different $k_{\mathrm{T}}$ bins.

Figure 5

Distribution of displacements in out $\left(X_{\mathrm{o}}\right)$ and side $\left(X_{\mathrm{s}}\right)$ directions for $q=1.5{\mathrm{fm}}^{-1}$.

Figure 6

HBT volume as a function of the pair transverse momentum $k_{\mathrm{T}}$ for various values of the parameter $q$. $d{N}_{\mathrm{ch}}/d\eta =27,T_{\mathrm{f}}=120\mathrm{MeV}$.

Figure 7

The ratio $R_o/R_s$ as a function of $k_{\mathrm{T}}$ for various values of $q$. The initial size is more compressed for a larger $q$, which results in stronger radial flow at freezeout.

Figure 8

$R_o/R_s$ calculated from the moments.

Figure 9

$\langle X_o^2\rangle /\langle X_s^2\rangle$ as a function of $k_{\mathrm{T}}$.

Figure 10

$\langle {\beta }^2{X}_t^2\rangle /\langle X_s^2\rangle$ as a function of $k_{\mathrm{T}}$.

Figure 11

$\langle \beta X_t{X}_o\rangle /\langle X_s^2\rangle$ as a function of $k_{\mathrm{T}}$.