Transverse-momentum–flow correlations in relativistic heavy-ion collisions

The correlation between the transverse momentum and the azimuthal asymmetry of the flow is studied. A correlation coefficient is defined between the average transverse momentum of hadrons emitted in an event and the square of the elliptic or triangular flow coefficient. The hydrodynamic model predicts a positive correlation of the transverse momentum with the elliptic flow, and almost no correlation with the triangular flow in Pb-Pb collisions at LHC energies. In $p$-Pb collisions the new correlation observable is very sensitive to the mechanism of energy deposition in the first stage of the collision.

Figure 1

Correlation coefficient between the elliptic flow coefficient squared $v_2{\left\{2\right\}}^2$ and the average transverse momentum of charged particles in an event for different centralities. The stars denote the Pearson coefficient [Eq. (4)], the circles denote the correlation coefficient without self-correlations [Eq. (8)] and the triangles denote the correlation coefficient calculated from oversampled events.

Figure 2

Same as Fig. 1, but for the triangular flow $v_3{\left\{2\right\}}^2$.

Figure 3

Correlation coefficient between the elliptic flow coefficient squared $v_2{\left\{2\right\}}^2$ and the average transverse momentum of charged particles in an event for different centralities. The stars denote correlations calculated in the range $\left|\eta \right|\in [1.75,-2.5]$ for $v_2^2$ and $\eta \in [-0.2,0.2]$ for $\left[p_{\perp }\right]$, the circles and triangles denote the correlation coefficient calculated with $\left|\eta \right|\in [1.75,-2.5]$ for $v_2^2$, and $\eta \in [-0.2,0.2]$ with 100% and 50% efficiency, respectively.

Figure 4

Correlation coefficient between the elliptic flow coefficient squared $v_2{\left\{2\right\}}^2$ and the average transverse momentum of charged particles in an event for different centralities. The triangles, circles, and stars denote the correlation coefficient for the flow calculated in the ranges $0.2<p_{\perp }<2$ GeV, $0.5<p_{\perp }<2$ GeV, and $0.4<p_{\perp }<0.7$ GeV, respectively. The average transverse momentum of charged particles in the event $\left[p_{\perp }\right]$ is calculated in the range $0.2<p_{\perp }<2$ GeV in all the cases.

Figure 5

Correlation coefficient between the elliptic flow coefficient squared (triangles) or the triangular flow coefficient squared (stars) and the average transverse momentum for $p$-Pb collisions at 5.02 TeV for two centralities, 0–3% and 10–20%. The hydrodynamic evolution is performed for two scenarios of energy deposition in the initial fireball: compact source (lower symbols) and standard Glauber model (upper symbols).