Thermal blurring of event-by-event fluctuations generated by rapidity conversion

We study the effect of thermal blurring caused by the use of (momentum-space) rapidity as a proxy of coordinate-space rapidity in experimental measurements of conserved-charge fluctuations in relativistic heavy-ion collisions. In theoretical studies assuming statistical mechanics, calculated fluctuations are those in a spatial volume. Experiments, on the other hand, can measure fluctuations only in a momentum space in the final state. In a standard argument to compare experimental results for a momentum space with theoretical studies for a coordinate space, rapidities of particles are implicitly regarded as equivalent to their coordinate-space rapidity. We show that the relation of two fluctuations is significantly altered by the existence of the thermal motion, i.e., thermal blurring. We discuss that the thermal blurring can be regarded as a part of the diffusion process, and the effect can be understood by studying the rapidity window dependences of fluctuations. Centrality dependence of the thermal blurring effect is also discussed.

Figure 1

Particle density per unit rapidity $n\left(y\right)$ for several values of $w=m/T$ and the transverse velocity $\beta$.

Figure 2

Width $\sigma$ and kurtosis $\kappa$ of $n\left(y\right)$ as a function of $w=m/T$ for several values of transverse velocity $\beta$.

Figure 3

Width $\sigma$ and kurtosis $\kappa$ of $n\left(y\right)$ as a function of transverse velocity $\beta$ for several values of $w=m/T$.

Figure 4

Illustration of the rapidity window $\mathrm{\Delta }y$ and the probability $p_{\mathrm{\Delta }y}\left(Y\right)$ in Eq. (11).

Figure 5

Discrete system discussed in Sec. 3b.

Figure 6

Rapidity window dependences of the cumulants in normalization $R_n={\langle Q_{\mathrm{\Delta }y}^n\rangle }_{\mathrm{c}}/{\langle Q_{\mathrm{\Delta }y}\rangle }_{\mathrm{c}}$ with vanishing initial condition for several values of $w=m/T$ with $\beta =0.6$.

Figure 7

Centrality dependence of the second-order cumulant of net-electric charge and the comparison with the experimental result by ALICE Collaboration [14].