We propose observables $v_0$ and $v_0\left(p_T\right)$ which quantify the relative fluctuations in the total transverse momentum at fixed multiplicity. We first study the factorization of the fixed multiplicity momentum-dependent two-particle correlation function into a product of $v_0\left(p_T^a\right)$ and $v_0\left(p_T^b\right)$ within realistic hydrodynamic simulations. Then we present computations of $v_0\left(p_T\right)$ for different particle types. We determine the relation between the integrated $v_0$ and previously measured observables and compare results from a hybrid hydrodynamics-based model to experimental data. The effects of bulk viscosity and an initial pre-equilibrium stage on the results are quantified. We find that $v_0$ is strongly correlated with the initial state entropy per elliptic area, $S/A$. Using this result, we explain how the observed correlations between the elliptic flow and the transverse momentum (both in simulations and experiment) reflect the initial state correlations between $1/A$ and ellipticity ${\varepsilon }_2$ at fixed multiplicity. We argue that the systematic experimental study of $v_0$, with the same sophistication as used for the other $v_n$, can contribute significantly to our understanding of quark gluon plasma properties.

• Received 22 April 2020
• Accepted 17 July 2020

DOI:https://doi.org/10.1103/PhysRevC.102.034905