No Arabic abstract
The correlation between multiplicities in two separated rapidity windows, the so-called long-range correlation (LRC), is studied in the framework of the model with independent identical emitters. Its shown that the LRC coefficient, defined for the scaled (relative) variables, nevertheless depends on the absolute width of the forward rapidity window and does not depend on the width of the backward one. The dependence of the LRC coefficient on the forward rapidity acceptance is explicitly found with only one theoretical parameter. The preliminary comparison with ALICE 7TeV pp collisions data shows that the multiplicity LRC in the data can be described in the framework of the suggested approach.
In this paper we continue our program to build a model for high energy soft interactions, that is based on the CGC/saturation approach.The main result of this paper is that we have discovered a mechanism that leads to large long range rapidity correlations, and results in large values of the correlation function $RLb y_1,y_2Rb ,geq ,1$, which is independent of $y_1$ and $ y_2$. Such behaviour of the correlation function, provides strong support for the idea, that at high energies the system of partons that is produced, is not only dense, but also has strong attractive forces acting between the partons.
The STAR Collaboration at RHIC presents a systematic study of high transverse momentum charged di-hadron correlations at small azimuthal pair separation dphino, in d+Au and central Au+Au collisions at $rts = 200$ GeV. Significant correlated yield for pairs with large longitudinal separation deta is observed in central Au+Au, in contrast to d+Au collisions. The associated yield distribution in detano$times$dphi can be decomposed into a narrow jet-like peak at small angular separation which has a similar shape to that found in d+Au collisions, and a component which is narrow in dphi and textcolor{black}{depends only weakly on} $deta$, the ridge. Using two systematically independent analyses, textcolor{black}{finite ridge yield} is found to persist for trigger $pt > 6$ GeVc, indicating that it is correlated with jet production. The transverse momentum spectrum of hadrons comprising the ridge is found to be similar to that of bulk particle production in the measured range ($2 < pt < 4 GeVc$).
We study ridge correlations of the glasma in pp collisions at $sqrt{s_{mathrm{NN}}}=7$ TeV by using the color glass condensate (CGC) formalism. The azimuthal collimation at long range rapidity is intrinsic to glasma dynamics and is reproduced here. When rapidity window enlarges, ridge correlations in two dimensional $Delta y$-$Deltaphi$ distribution and one dimensional $Deltaphi$ distribution at long range rapidity gap are enhanced. The enhancements are demonstrated to be the contributions of source gluons. The quantum evolution of the gluons presents unique correlation patterns in differential correlation function. These characters of two gluon correlations open a way of testing the production mechanism from experimental measurements.
We perform an analytical analysis of the long-range degree correlation of the giant component in an uncorrelated random network by employing generating functions. By introducing a characteristic length, we find that a pair of nodes in the giant component is negatively degree-correlated within the characteristic length and uncorrelated otherwise. At the critical point, where the giant component becomes fractal, the characteristic length diverges and the negative long-range degree correlation emerges. We further propose a correlation function for degrees of the $l$-distant node pairs, which behaves as an exponentially decreasing function of distance in the off-critical region. The correlation function obeys a power-law with an exponential cutoff near the critical point. The ErdH{o}s-R{e}nyi random graph is employed to confirm this critical behavior.
We propose an S matrix approach to the quantum black hole in which causality, unitarity and their interrelation play a prominent role. Assuming the t Hooft S matrix ansatz for a gravitating region surrounded by an asymptotically flat space-time we find a non-local transformation which changes the standard causality requirement but is a symmetry of the unitarity condition of the S matrix. This new S matrix then implies correlations between the in and out states of the theory with the involvement of a third entity which in the case of a quantum black hole, we argue is the horizon S matrix. Such correlations are thus linked to preserving the unitarity of the S matrix and to the fact that entangling unitary operators are nonlocal. The analysis is performed within the Bogoliubov S matrix framework by considering a spacetime consisting of causal complements with a boundary in between. No particular metric or lagrangian dynamics need be invoked even to obtain an evolution equation for the full S matrix. Constraints imposed by the new causality requirement and implications for the effectiveness of field theoretical descriptions and for complementarity are also discussed. We find that the tension between information preservation and complementarity may be resolved provided the full quantum gravity theory either through symmetries or fine tuning forbids the occurrence of closed time like curves of information flow. Then, even if causality is violated near the horizon at any intermediate stage, a standard causal ordering may be preserved for the observer away from the horizon. In the context of the black hole, the novelty of our formulation is that it appears well suited to understand unitarity at any intermediate stage of black hole evaporation. Moreover, it is applicable generally to all theories with long range correlations including the final state projection models.