Longitudinal fluctuations and decorrelations of anisotropic flows at energies available at the CERN Large Hadron Collider and at the BNL Relativistic Heavy Ion Collider

We perform a systematic study on the decorrelation of anisotropic flows along the pseudorapidity in relativistic heavy-ion collisions at the CERN Large Hadron Collider (LHC) and BNL Relativistic Heavy Ion Collider (RHIC) energies. The dynamical evolution of the quark-gluon plasma fireball is simulated via the CLVisc (ideal) ($3+1$)-dimensional hydrodynamics model, with the fully fluctuating initial condition from the A-Multi-Phase-Transport (AMPT) model. A detailed analysis is performed of the longitudinal decorrelations of elliptic, triangular, and quadrangular flows in terms of flow vectors, flow magnitudes, and flow orientations (event planes). It is found that pure flow magnitudes have a smaller longitudinal decorrelation than pure flow orientations, and the decorrelation of flow vectors is a combined effect of both flow magnitudes and orientations. The longitudinal decorrelation of elliptic flow has a strong and nonmonotonic centrality dependence due to the initial elliptic collision geometry: the smallest decorrelation in midcentral collisions. In contrast, the decorrelations of triangular and quadrangular flows have a weak centrality dependence, with slightly larger decorrelations in more peripheral collisions. Our numerical results for Pb + Pb collisions at the LHC are in good agreement with the ATLAS data, while our RHIC results predict much larger longitudinal decorrelations compared to the LHC. We further analyze the longitudinal structures of the AMPT initial conditions and find that the final-state longitudinal decorrelation effects are strongly correlated with the lengths of the initial string structures in the AMPT model. The decorrelation effects are typically larger at lower collision energies and in more peripheral collisions due to the shorter lengths of the string structures in the initial states.

Figure 1

Determination of centrality classes for Pb + Pb collisions at 5.02A TeV according to the probability density distribution (PDF) of the initial parton multiplicity ($N_{\mathrm{parton}}$) in the AMPT model.

Figure 2

Charged hadron multiplicity as a function of pseudorapidity $\eta$ for Pb + Pb collisions at 5.02A TeV and 2.76A TeV at the LHC and for Au + Au collisions at 200A GeV at the RHIC from event-by-event ($3+1$)-dimensional ideal hydrodynamics simulation compared to the experimental data [72, 73, 74].

Figure 3

Correlation functions $r[n,k]\left(\eta \right)$ with $n=2,3,4$ and $k=1$ as a function of $\eta$ obtained from event-by-event ($3+1$)-dimensional ideal hydrodynamics simulations (dotted lines; this work) and viscous hydrodynamics simulations (dashed lines; from Ref. [69]) for six centralities in Pb + Pb collisions at 5.02A TeV. The CMS data for $r[2,1]\left(\eta \right)$ and $r[3,1]\left(\eta \right)$ are shown for comparison. The reference rapidity window is taken to be $4.4<{\eta }_{\mathrm{r}}<5.0$.

Figure 4

Correlation functions $r[n,k]\left(\eta \right)$, $r_M[n,k]\left(\eta \right)$, and $r_{\mathrm{\Phi }}[n,k]\left(\eta \right)$ with $n=2,3,4$ and $k=1$ as a function of $\eta$ obtained from event-by-event ($3+1$)-dimensional ideal hydrodynamics simulations for six centralities in Pb + Pb collisions at 5.02A TeV. The ATLAS data for $r[n,k]\left(\eta \right)$ are shown for comparison. The reference rapidity window is taken to be $4.0<{\eta }_{\mathrm{r}}<4.9$.

Figure 5

Correlation functions $r[n,k]\left(\eta \right)$, $r_M[n,k]\left(\eta \right)$, and $r_{\mathrm{\Phi }}[n,k]\left(\eta \right)$ with $n=2,3,4$ and $k=1$ as a function of $\eta$ obtained from event-by-event ($3+1$)-dimensional ideal hydrodynamics simulations for six centralities in Pb + Pb collisions at 2.76A TeV. The ATLAS data for $r[n,k]\left(\eta \right)$ are shown for comparison. The reference rapidity window is taken to be $4.0<{\eta }_{\mathrm{r}}<4.9$.

Figure 6

Correlation functions $r[n,k]\left(\eta \right)$, $r_M[n,k]\left(\eta \right)$, and $r_{\mathrm{\Phi }}[n,k]\left(\eta \right)$ with $n=2,3,4$ and $k=1$ as a function of $\eta$ obtained from event-by-event ($3+1$)-dimensional ideal hydrodynamics simulations for six centralities in Au + Au collisions at 200A GeV. The reference rapidity window is taken to be $3.0<{\eta }_{\mathrm{r}}<4.0$.

Figure 7

Slope parameters $f[n,k]$, $f_M[n,k]$, and $f_{\mathrm{\Phi }}[n,k]$ of the decorrelation functions $r[n,k]\left(\eta \right)$, $r_M[n,k]\left(\eta \right)$, and $r_{\mathrm{\Phi }}[n,k]\left(\eta \right)$ with $n=2,3,4$ and $k=1$, as a function of the collision centrality ($N_{\mathrm{part}}$) for Pb + Pb collisions at 5.02A TeV and 2.76A TeV at the LHC and for Au + Au collisions at 200A GeV. The ATLAS data for 5.02A TeV Pb + Pb collisions are shown for comparison.

Figure 8

Slope parameters $f[n,k]/k$ of the flow decorrelation functions $r[n,k]\left(\eta \right)$ for different values of $n=2,3,4$ and different values of $k=1,2,3$ as a function of the collision centrality ($N_{\mathrm{part}}$) for Pb + Pb collisions at 5.02A TeV and 2.76A TeV at the LHC and for Au + Au collisions at 200A GeV. The ATLAS data for 5.02A TeV Pb + Pb collisions are shown for comparison.

Figure 9

Slope parameters $f_M[n,k]/k$ and $f_{\mathrm{\Phi }}[n,k]/k$ of the flow decorrelation functions $r_M[n,k]\left(\eta \right)$ and $r_{\mathrm{\Phi }}[n,k]\left(\eta \right)$ for different values of $n=2,3,4$ and different values of $k=1,2,3$ as a function of the collision centrality ($N_{\mathrm{part}}$) for Pb + Pb collisions at 5.02A TeV and 2.76A TeV at the LHC and for Au + Au collisions at 200A GeV.

Figure 10

Comparison of the slope parameters $F[n,2]$ and $F_{\mathrm{\Phi }}[n,2]$ extracted from $R[n,2]\left(\eta \right)$ with the slope parameters $f[n,2]-f_M[n,2]$ and $f_{\mathrm{\Phi }}[n,2]$ extracted from $r[n,2]\left(\eta \right)$, $r_M[n,2]\left(\eta \right)$, and $r_{\mathrm{\Phi }}[n,2]\left(\eta \right)$, for different values of $n=2,3,4$ as a function of the centrality ($N_{\mathrm{part}}$) for Pb + Pb collisions at 5.02A TeV and 2.76A TeV at the LHC and for Au + Au collisions at 200A GeV.

Figure 11

Slope parameters $f[n,k]$ (with $n=2,3,4$ and $k=1$) as a function of the centrality ($N_{\mathrm{part}}$) for Pb + Pb collisions at 5.02A TeV and 2.76A TeV at the LHC and for Au + Au collisions at 200A GeV. The ATLAS data on $f[n,k]$ are compared.

Figure 12

Strings formed by the initial patrons for some typical events in Pb + Pb collisions at 5.02A TeV and 2.76A TeV and for Au + Au collisions at 200A GeV.

Figure 13

The slope parameter $f[n,k]$, $f_M[n,k]$, and $f_{\mathrm{\Phi }}[n,k]$ for $n=2,3,4$ and $k=1$ as a function of the mean string length $\langle l_s\rangle$ (the collision energy and the centrality class) for Pb + Pb collisions at 5.02A TeV and 2.76A TeV at the LHC and for Au + Au collisions at 200A GeV. In each plot, there are three separate curves denoting three collision energies (5.02A TeV, 2.76A TeV, and 200A GeV, respectively). For each curve (collision energy), there are five symbols denoting five centrality classes: from left to right, 40%–50%, 30%–40%, 20%–30%, 10%–20%, and 5%–10%, respectively.

Figure 14

The slope parameter $f[n,k]$, $f_M[n,k]$, and $f_{\mathrm{\Phi }}[n,k]$ for $n=2,3,4$ and $k=1$ as a function of the variance-to-mean-ratio ${\sigma }_{l_s}/\langle l_s\rangle$ of the string length (the collision energy and the centrality class) for Pb + Pb collisions at 5.02A TeV and 2.76A TeV at the LHC and for Au + Au collisions at 200A GeV. In each plot, there are three separate curves denoting three collision energies (5.02A TeV, 2.76A TeV, and 200A GeV, respectively). For each curve (collision energy), there are five symbols denoting five centrality classes; from right to left, 40%–50%, 30%–40%, 20%–30%, 10%–20%, and 5%–10%, respectively.