Rapidity dependence of proton cumulants and correlation functions

The dependence of multiproton correlation functions and cumulants on the acceptance in rapidity and transverse momentum is studied. We find that the preliminary data of various cumulant ratios are consistent, within errors, with rapidity and transverse momentum-independent correlation functions. However, rapidity correlations which moderately increase with rapidity separation between protons are slightly favored. We propose to further explore the rapidity dependence of multiparticle correlation functions by measuring the dependence of the integrated reduced correlation functions as a function of the size of the rapidity window.

Figure 1

The cumulant ratio $K_4/K_2$ in central 0–5% Au + Au collisions at $\sqrt{s}=7.7\mathrm{GeV}$ as a function of the number of measured protons $\langle N\rangle$ for different acceptance windows in rapidity and transverse momentum (in units of GeV). For all data points $p_t>0.4\mathrm{GeV}$. The black solid line represents a prediction based on a constant correlation function, see Eq. (17). The shaded band is driven mostly by the large experimental uncertainty of $K_4$. Based on the preliminary STAR Collaboration data [42].

Figure 2

The cumulant ratio $K_3/K_2$ in central Au + Au collisions at $\sqrt{s}=7.7\mathrm{GeV}$ as a function of the rapidity acceptance $\mathrm{\Delta }y,\left|y\right|<\mathrm{\Delta }y/2$ for (a) ${\gamma }_2=0$ and different values of ${\gamma }_3$ from Eq. (19) and (b) ${\gamma }_3=0$ and different values of ${\gamma }_2$. Based on the preliminary STAR Collaboration data [42].

Figure 3

The cumulant ratio $K_4/K_2$ in central Au + Au collisions at $\sqrt{s}=7.7\mathrm{GeV}$ as a function of the rapidity acceptance $\mathrm{\Delta }y,\left|y\right|<\mathrm{\Delta }y/2$ for (a) different values of ${\gamma }_4$, (b) ${\gamma }_3$, and (c) ${\gamma }_2$ from Eq. (19). Based on the preliminary STAR Collaboration data [42].

Figure 4

The cumulant ratio $K_2/K_1$ in central Au + Au collisions at $\sqrt{s}=7.7\mathrm{GeV}$ as a function of the rapidity acceptance $\mathrm{\Delta }y,\left|y\right|<\mathrm{\Delta }y/2$ for different values of ${\gamma }_2$. Based on the preliminary STAR Collaboration data [42].

Figure 5

The ratio of the couplings $c_n\left(\mathrm{\Delta }y\right)/c_n^0-1$, see Eqs. (8) and (20) for ${\gamma }_2={10}^{-2},{\gamma }_3={10}^{-3}$ and ${\gamma }_4=2\times {10}^{-4}.\mathrm{\Delta }y$ denotes the size of the rapidity window $\left|y\right|<\mathrm{\Delta }y/2$, which the reduced correlation functions are integrated over.