Multiparticle azimuthal cumulants from transverse momentum conservation and collective flow

Abstract: We calculate the $n$th order of $2k$-particle azimuthal cumulants $c_n{2k}$ based on transverse momentum conservation (TMC) and collective flow $v_n$(n=2,3). We demonstrate that the TMC effect only leads to a nonzero $c_n{2k}$ with the sign of $(-1)^{nk}$ and the magnitude inversely proportional to $(N-2k)^{nk}$. The interplay between TMC and collective flow can change the signs of $c_2{4}$, $c_3{2}$ and $c_3{4}$ at some values of multiplicity $N$, which could provide a good probe to study the onset of collectivity and search for the substructure of proton in small colliding systems.