Hydrodynamic fluctuations near a critical endpoint and Hanbury-Brown–Twiss interferometry

The field of high-energy nuclear collisions has witnessed a surge of interest in the role played by hydrodynamic fluctuations. Hydrodynamic fluctuations may have significant effects on matter created in heavy-ion accelerators whose trajectories in the plane of temperature versus chemical potential pass near a possible critical endpoint. We extend previous studies to explore the impact of these fluctuations on Hanbury-Brown–Twiss interferometry of identical hadrons. With an appropriately defined correlation function we find that the fluctuations increase substantially when the trajectory passes near a critical endpoint and also displays a damped oscillatory behavior in the rapidity distance $\mathrm{\Delta }y$ unlike that originating from initial-state fluctuations.

Figure 1

The phase diagram showing the crossover curve and the three trajectories used in the computation. Taken from Ref. [23].

Figure 2

Two-point HBT correlation $C_{\mathrm{HBT}}$ as a function of the rapidity difference $\mathrm{\Delta }y$ for each of the three trajectories shown in Fig. 1 using proton pairs to define $R_l^2$.

Figure 3

Two-point HBT correlation $C_{\mathrm{HBT}}$ as a function of the rapidity difference $\mathrm{\Delta }y$ for each of the three trajectories shown in Fig. 1 using ${\pi }^{+}$ pairs to define $R_l^2$. The average pion chemical potential is zero. In panel (a) we assume that it does not fluctuate, while in panel (b) we assume that it fluctuates the same as the proton, or baryon, chemical potential.