Long-range rapidity correlations in high energy AA collisions in Monte Carlo model with string fusion

The magnitude of long-range correlations between observables in two separated rapidity windows, proposed as a signature of the string fusion and percolation phenomenon, is studied in the framework of non-Glauber Monte Carlo string-parton model, based on the picture of elementary collisions of color dipoles. The predictions, obtained with and without string fusion, demonstrate effects of color string fusion on the observables in Pb-Pb collisions at the LHC: decrease of n-n correlation coefficient with centrality and negative pt-n correlations, if the sufficiently effective centrality estimator is applied. In general case it is shown that the values of n-n and pt-n correlation coefficients strongly depend on the method of collision centrality fixation. In contrast, the predictions obtained for pt-pt correlation have almost no effect of centrality determination method and the corresponding experimental data would produce the strong limitation on the transverse radius of a string.


I. INTRODUCTION
The study of long-range correlations between observables in two windows separated in rapidity was proposed [1] as a signature of the string fusion and percolation phenomenon, which is one of the collectivity effects [2] in ultrarelativistic heavy ion collisions. It was suggested to consider different types of correlations [3]: n-n, pt-n, pt-pt, where n is the event multiplicity of charged particles in a given rapidity window and pt is their event mean transverse momentum: The correlation coefficient is defined as the slope of the correlation function in normalized variables [4] dF | F= F , where B and F could be multiplicity or p t . Multiplicity fluctuations are defined as scaled variance of the charged multiplicity w = Var n/ n . The values of correlation coefficients in AA collisions could strongly depend on the method of * Electronic address: nvkinf@rambler.ru arXiv:1308.6618v1 [nucl-th] 29 Aug 2013 collision centrality fixation [4]. The present work is devoted to study of the correlation coefficients in Pb-Pb collisions at the LHC energy in the framework of the non-Glauber Monte Carlo stringparton model, and obtaining the predictions for the LHC in the conditions close to experimental.

II. NON-GLAUBER MONTE-CARLO MODEL
The present model [5,6] is based on partonic picture of nucleons interaction, accounting the energy and angular momentum conservation in the initial state of a nucleon. The nucleon is assumed to be composed of several set of pairs (quark-diquark and quark-antiquark), forming dipoles. The probability of dipoles interaction depends on the transverse coordinates of their ends [7,8] with some effective coupling constant. Multiplicity and transverse momentum are calculated in the approach of colour strings, stretched between projectile and target partons, taking into account their finite rapidity width and interaction in transverse plane -string fusion [9,10].
The main effect of the fusion of strings is modification of the mean transverse momentum and multiplicity, coming from a cluster of overlapping strings: where S k -area, where k strings are overlapping, σ 0 -single string transverse area, µ 0 and p 0mean multiplicity and transverse momentum from one string. A string (or cluster of overlapping strings) fragments independently in any rapidity interval according to Poisson distribution. The model parameters are constrained from the p-p data on total inelastic cross section and multiplicity and multiplicity in minimum bias p-Pb and Pb-Pb collisions [11].

III. RESULTS
The correlation coefficients in Pb-Pb collisions at 2.76 TeV in two rapidity windows width of 0.8 as a function of the gap between them are shown in fig. 1 (left).
We can observe almost flat behaviour in mid-rapidity and decrease of correlations with further and on the width of the forward window of b n-n (middle) and b pt-pt (right).
increase of the gap. Both pt-n and pt-pt correlations vanish at gap about 10 rapidity units, while n-n correlations are still present, and this behaviour is similar to pp case [6].
The dependence of the correlation coefficients on the forward rapidity windows width is shown in the middle and right part of fig. 1. The results demonstrate noticeable dependence of b n-n on the forward rapidity window size ∆y F . The points are fitted by b = ∆y F ∆y F + κ [14]. Note, that the fact, that pt-pt correlations are also in agreement with such fit, pointing to considerably high density of strings in Pb-Pb collisions (such asymptotic was obtained in [15] for AA collisions and it fails in pp case [6]). Results for multiplicity fluctuations w and correlation coefficients as function of centrality are shown in fig. 2. Both multiplicity fluctuations and n-n correlations are found decreasing with centrality for sufficiently narrow centrality bins, and in general their behaviour with centrality is similar in all cases. Important, that w is higher for N part -based centrality classes than for "vzero"based. We note, that decrease of n-n correlations with centrality in model with string fusion contradicts to the predictions of CGC model [16].
The results on pt-n correlations demonstrate always positive correlation coefficient for N partbased centrality classes, what can be related with the fact that if at fixed number of participants many strings are produced, they undergo fusion and give higher pt, while at fixed multiplicity in "vzero" windows (that means almost fixed number of strings) b pt-n < 0 for narrow vzero-based centrality classes: the fixed multiplicity is achieved either from a few independent strings (pt lower) or from many-strings cluster (pt higher). The pt-pt correlations are found dominating over pt-n and to have almost no effect from centrality determination issues. The results are consistent in centrality bins narrower than 5%. Thus this results could be easier compared with experimental data. At fig. 3 b pt-pt is plotted for different transverse radius of string. Pt-pt correlations are sensitive to this radius, and the experimental data on b pt-pt correlations would constrain its value. Multiplicity fluctuations and n-n correlations are shown in fig. 4 for the case of no string fusion.
In narrow centrality bins they are constant with centrality, that indicates that the decrease of w and b n-n is an effect of string fusion.

IV. SUMMARY AND CONCLUSIONS
Correlation coefficients and fluctuations strongly depend on the centrality bins and the methods of centrality determination. b n-n decreases with centrality for sufficiently small bin width in the model with string fusion, contrary to CGC model [16], and w demonstrate very similar behaviour.
Pt-n correlations are negative for "vzero" and positive for N part centrality classes. Pt-pt correlations have almost no effect from centrality determination issues and this is strongest prediction of string fusion model for experiment allowing to constrain the transverse radius of string.