Skewness of mean transverse momentum fluctuations in heavy-ion collisions

Abstract

We propose the skewness of mean transverse momentum, $⟨p_t⟩$, fluctuations as a fine probe of hydrodynamic behavior in relativistic nuclear collisions. We describe how the skewness of the $⟨p_t⟩$ distribution can be analyzed experimentally, and we use hydrodynamic simulations to predict its value. We predict in particular that $⟨p_t⟩$ fluctuations have positive skew, which is significantly larger than if particles were emitted independently. We elucidate the origin of this result by deriving generic formulas relating the fluctuations of $⟨p_t⟩$ to the fluctuations of the early-time thermodynamic quantities. We postulate that the large positive skewness of $⟨p_t⟩$ fluctuations is a generic prediction of hydrodynamic models.

Comments: 13 pages; 4 figures; v2: corrections in Sec IIIA and appendix A; v3: published version; improved baseline for stat. fluctuations in Fig 3; Expanded discussion in Sec. V