Elliptic flow coefficients from transverse momentum conservation

Abstract

We calculate the k-particle (k = 2, 4, 6, 8) azimuthal cumulants resulting from the conservation of transverse momentum. We find that c 2 {k} > 0 and depending on the transverse momenta, c 2 {k} can reach substantial values even for a relatively large number of particles. The impact of our results on the understanding of the onset of collectivity in small systems is emphasized. * E-Mail:bzdak@fis.agh.edu.pl † E-Mail:glma@sinap.ac.cn 1 v2{2} can even increase with decreasing event multiplicity in d+Au collisions at RHIC energies [44], which is likely due to the non-flow effects, such as the conservation of transverse momentum discussed in this paper.

A remark on the sign change of the four-particle azimuthal cumulant in small systems

“…As shown in Ref. [42] the first contribution from TMC, which is not vanishing at v 2 = 0, appears in A 2 /2. We obtain 3 2 We neglect v 3 which also contributes to c 2 {2} and c 2 {4} however, its effect is smaller than v 2 .…”

“…1 Here N is the number of produced particles subjected to TMC. As shown in [42], the contribution from TMC to (c 2 {k}) 1/k is of the order of a few percent even for a relatively large number of particles. In this paper we extend our analysis and calculate analytically c 2 {2} and c 2 {4} originating from TMC applied to particles characterized by the hydro-like elliptic flow.…”

“…Following calculations presented, e.g., in Refs. [42][43][44][45][46][47][48], the two-particle distribution with TMC is given by…”

“…Recently we calculated the effect of transverse momentum conservation (TMC) only [42], and we observed that…”

Multiparticle azimuthal cumulants in p+Pb collisions from a multiphase transport model

“…The c 2 {2} and c 2 {4} at these four stages are all calculated using the three-subevent method, as shown in Figures 3 and 4, respectively. At the initial stage, the conservation [57]. After parton cascade, c 2 {2} is enhanced and c 2 {4} changes sign from positive to negative at a certain value of N ch , which maybe due to the interplay between transverse momentum conservation and an anisotropic flow generated by parton cascade [58].…”