A simple model for rapidity fluctuations in the initial state of ultra-relativistic heavy-ion collisions

Two-particle pseudorapidity correlations are analyzed in a simple model, where in the initial stage of the reaction multiple sources, extended in rapidity, are created. We show how the fluctuations of the length of the sources in rapidity generate correlations in the initial entropy deposition, which later contribute to the observed longitudinal correlations in hadron production. Our analysis, which is analytic and leads to straightforward formulas, allows us to understand the structure of the correlations, in particular to identify the component related to the fluctuation of the numbers of sources and the component from the length fluctuations. We also present the results in terms of the expansion in the basis of the Legendre polynomials. A number of further effects is discussed, such as smearing of the pseudorapidity distributions or resonance decays. Our results reproduce qualitatively and semiquantitatively the basic features of the recent measurements at the LHC.