Fluctuations of the multiplicity of produced particles in onium-nucleus collisions

We address the general features of event-by-event fluctuations of the multiplicity of gluons produced in the scattering of a dilute hadron off a large nucleus at high energy in the fragmentation region of the dilute hadron. We relate these fluctuations to the stochasticity of the number of quanta contained in the hadron at the time of the interaction. For simplicity, we address the ideal case in which the hadron is an onium and investigate different kinematical regimes in the rapidity and onium size. We show that at large rapidity, the multiplicity distribution exhibits an exponential tail in the large-multiplicity region, which is qualitatively consistent with the proton-nucleus data. But interestingly enough, the exponential shape is determined by confinement.

Figure 1

Kinematics of onium-nucleus scattering at fixed total rapidity $Y$. The rapidity of the nucleus ($x$ axis) defines the frame. The saturation lines of the onium and of the nucleus are shown. We choose a frame in which the nucleus has the rapidity $y_0$ along the negative $z$ axis, such that the onium is a dilute object for gluons of transverse momenta of the order of the saturation scale of the nucleus; the rapidity dependence of its gluon content is then given by the small-$x$ gluon branching process without saturation effects.

Figure 2

Left: Characteristic function of the BFKL kernel and the global saddle-point solutions for the second and the fourth moments. One sees that the higher the moment index, the more the anomalous dimensions corresponding to the first and the second steps of the evolution get attracted by the collinear and anticollinear singularities at $\gamma =1$ and $\gamma =0$ respectively. Right: Schematic representation of the evolution path selected by the moments $n^{(k)}$ in the $(\rho ,y)$ plane.

Figure 3

Left: Solution for the second moment in the case in which there is no global saddle point. ${\gamma }_c^{(2)}$ and ${\gamma }_{1c}^{(2)}$ are not completely fixed in this case; they, however, satisfy the relation $2{\gamma }_{1c}^{(2)}={\gamma }_c^{(2)}<\frac{1}{2}$. Right: Schematic representation of the evolution path selected by the moment $n^{(2)}$ in the $(\rho ,y)$ plane. There is no step backward. This kind of path is favored when $\overline{\alpha }y$ is not large compared to ${\rho }_s$.

Figure 4

Distribution of the fluctuations of the multiplicity around its expected value $\overline{n}$ from a Monte Carlo simulation of a simplified model (see Appendix pp2). The lines represent fits of the analytical formulas (50), (57), and (34) (from top to bottom).