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We present a semi-analytic approach to forward-backward multiplicity correlations in ultra-relativistic nuclear collisions, based on particle emission from strings with fluctuating end-points. We show that with the constraints from rapidity spectra, one can obtain bounds for the magnitude of the standard measures of the forward-backward fluctuations. The method is generic under the assumption of independent production from sources. For definiteness, we use the wounded quark model for Au+Au and d+Au collisions at the energy of $sqrt{s_{NN}}=200$ GeV.
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In a framework of a semi-analytic model with longitudinally extended strings of fluctuating end-points, we demonstrate that the rapidity spectra and two-particle correlations in collisions of Pb-Pb, p-Pb, and p-p at the energies of the Large Hadron Collider can be universally reproduced. In our approach, the strings are pulled by wounded constituents appearing in the Glauber modeling at the partonic level. The obtained rapidity profile for the emission of hadrons from a string yields bounds for the distributions of the end-point fluctuations. Then, limits for the two-particle-correlations in pseudorapidity can be obtained. Our results are favorably compared to recent experimental data from the ATLAS Collaboration.
While string models describe initial state radiation in ultra-relativistic nuclear collisions well, they mainly differ in their end-point positions of the strings in spatial rapidity. We present a generic model where wounded constituents are amended with strings whose both end-point positions fluctuate and analyze semi-analytically various scenarios of string-end-point fluctuations. In particular we constrain the different cases to experimental data on rapidity spectra from collisions at $sqrt{s_{rm NN}}=200$~GeV, and explore their respective two-body correlations, which allows to partially discriminate the possible solutions.
We analyze a generic model where wounded quarks are amended with strings in which both end-point positions fluctuate in spatial rapidity. With the assumption that the strings emit particles independently of one another and with a uniform distribution in rapidity, we are able to analyze the model semi-analytically, which allows for its detailed understanding. Using as a constraint the one-body string emission functions obtained from the experimental data for collisions at $sqrt{s_{NN}}=200$ GeV, we explore the two-body correlations for various scenarios of string fluctuations. We find that the popular measures used to quantify the longitudinal fluctuations are limited with upper and lower bounds and assume close values for the most likely models of the end-point distributions, which may explain why various approaches yield here very similar results.
We suggest an extension of the standard concept of statistical ensembles. Namely, we introduce a class of ensembles with extensive quantities fluctuating according to an externally given distribution. As an example the influence of energy fluctuations on multiplicity fluctuations in limited segments of momentum space for a classical ultra-relativistic gas is considered.
Relativistic dissipative hydrodynamics including hydrodynamic fluctuations is formulated by putting an emphasis on non-linearity and causality. As a consequence of causality, dissipative currents become dynamical variables and noises appeared in an integral form of constitutive equations should be colored ones from fluctuation-dissipation relations. Nevertheless noises turn out to be white ones in its differential form when noises are assumed to be Gaussian. The obtained ifferential equations are very useful in numerical implementation of relativistic fluctuating hydrodynamics.
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