Multiparticle azimuthal angular correlations in $pA$ collisions

In the Color Glass Condensate formalism, we evaluate the 3-dipole correlator up to the $\frac{1}{N_c^4}$ order with $N_c$ being the number of colors, and compute the azimuthal cumulant $c_{123}$ for 3-particle productions. In addition, we discuss the patterns appearing in the $n$-dipole formula in terms of $\frac{1}{N_c}$ expansions. This allows us to conjecture the $N_c$ scaling of $c_n\{m\}$, which is crosschecked by our calculation of $c_2\{4\}$ in the dilute limit.

Figure 1

The original configuration with three fermion loops goes through color transitions two times, then it becomes another two configurations with one and two fermion loops, respectively.

Figure 2

Left: $-c_{123}$ depending on $Q_s^2{B}_p$, where we truncate the expansion series at orders seven and eight. We see in the Taylor expansion approach, $-c_{123}$ converges quickly in small $Q_s^2{B}_p$ region, and gradually converges in large $Q_s^2{B}_p$ region. Right: The scaled cumulant $-c_{123}$ as a function of $Q_s^2{B}_p$, where the factors in the denominator are written by $v_n\equiv v_n\{2\}$ for short.

Figure 3

The left topology represents that all the four dipoles connect together. The right topology represents that dipoles 3,4 change from connected to disconnected, and finally dipoles 1,2,3 connect together. Both of them are of $\frac{1}{N_c^6}$ order.