Skewness of mean transverse momentum fluctuations in heavy-ion collisions

We propose the skewness of mean transverse momentum, $\langle p_t \rangle$, fluctuations as a fine probe of hydrodynamic behavior in relativistic nuclear collisions. We describe how the skewness of the $\langle p_t \rangle$ distribution can be analyzed experimentally, and we use hydrodynamic simulations to predict its value. We predict in particular that $\langle p_t \rangle$ 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 $\langle p_t \rangle$ to the fluctuations of the early-time thermodynamic quantities. We postulate that the large positive skewness of $\langle p_t \rangle$ fluctuations is a generic prediction of hydrodynamic models.