Effect of transverse momentum conservation and flow on symmetric cumulants $sc_{2,3} \left \{ 4 \right \}$ and $sc_{2,3,4} \left \{ 6 \right \}$

Abstract

Symmetric cumulants can improve our understanding of the joint probability distribution function $ P\left ( v_{m},v_{n},v_{k}, \dots,\Psi _{m},\Psi _{n},\Psi _{k},\dots \right )$, potentially offering new insights into the nature of the fluctuations of the quark-gluon plasma produced in relativistic heavy-ion collisions. In this work, the four-particle symmetric cumulants $sc_{2,3} \left \{ 4 \right \}$, six-particle symmetric cumulants $sc_{2,3,4} \left \{ 6 \right \}$, and the normalized cumulants $nsc_{2,3} \left \{ 4 \right \}$ and $nsc_{2,3,4} \left \{ 6 \right \}$ originating from transverse momentum conservation, collective flow, and the interplay between the two effects are calculated. Our results on $sc_{2,3} \left \{ 4 \right \}$ are consistent with the ATLAS data using the subevent cumulant method, facilitating a more profound understanding of the origins of the symmetric cumulant in small systems. Our results on $sc_{2,3,4} \left \{ 6 \right \}$ serve as theoretical predictions for future experimental measurements in small systems.