Long Range Correlations,Parton Percolation and Color Glass Condensate C.Pajares Dept Particle Physics and IGFAE University Santiago de Compostela,Spain The Ridge Correlation in High-Energy Collisions, INT workshop Seattle,May

Introduction to long range correlations STAR data and string like models nF-nB,nF-ptB,ptF-ptB correlations Clustering of color sources Scales of pp and Pb Pb collisions Similarities between CGC and percolation Ridge Structures Conclusions

A measurement of such correlations is the backward–forward dispersion D 2 FB = - where n B (n F ) is the number of particles in a backward (forward) rapidity number of collisions:, F and B multiplicities in one collision In a superposition of independent sources model, is proportional to the fluctuations on the number of independent sources (It is assumed that Forward and backward are defined in such a way that there is a rapidity window to eliminate short range correlations). BF LONG RANGE CORRELATIONS

with b in pp increases with energy. No LRC at RHIC.In hA increases with A,also in AA,increases with centrality The dependence of b with rapidity gap is quite interesting: In AA central is flat for large values of the rapidity window..Existence of long rapidity correlations at high density and/or high energy.It is possible to eliminate short range correlations even with no very large rapidity gap,by looking correlations of particles of very different azimuthal angle

1/K is the squared normalized fluctuations on effective number of strings(clusters)contributing to both forward and backward intervals The heigth of the ridge structure is proportional to n/k

--- Any model describing k and dn/dy and the systematics of their dependence on y,centrality and energy should give a good description of long range correlations --- The rapidity length of long range correlations is the same that the plateau of dn/dy(Assuming that k do not change in this rapidity range) --- As dn/dy for protons is much smaller than for pions, b for protons is much smaller than for pions(not at inter pt) --- Given a rapidity range and energy,k, is proportional to the inverse of the width of the multiplicity distribution, P(n)(very sensitive to the tail of the distribution) --- In some events,(for instance events with at least one high pt particle)the associated multiplicity distribution is nP(n)/mean(n),implying higher mean(n) and and therefore larger long range correlations

-- The strings must be extended in both hemispheres,otherwise either they do not obtained LRC(Hijing)or they have to include parton interactions(PACIAE).(PACIAE reproduces well b for central but not for peripheral) --Without parton interactions,in this model, the length in rapidity of the LRC is the same in pp than AA.In CGC this is not true due to the running couplig constant,which allows an increase of b with Na

Short range correlations are eliminated by using different azimuthal regions and/or rapidity gaps Sizable long range n-n,pt-n and pt-pt correlations (M.A.Braun et al Eur Phys C , PRL (2000)

Color strings are stretched between the projectile and target Strings = Particle sources: particles are created via sea qqbar production in the field of the string Color strings = Small areas in the transverse space filled with color field created by the colliding partons With growing energy and/or atomic number of colliding particles, the number of sources grows So the elementary color sources start to overlap, forming clusters, very much like disk in the 2-dimensional percolation theory In particular, at a certain critical density, a macroscopic cluster appears, which marks the percolation phase transition CLUSTERING OF COLOR SOURCES

(N. Armesto et al., PRL77 (96); J.Dias de Deus et al., PLB491 (00); M. Nardi and H. Satz(98). How?: Strings fuse forming clusters. At a certain critical density η c (central PbPb at SPS, central AgAg at RHIC, central pp at LHC ) a macroscopic cluster appears which marks the percolation phase transition (second order, non thermal). Hypothesis: clusters of overlapping strings are the sources of particle production, and central multiplicities and transverse momentum distributions are little affected by rescattering.

Energy-momentum of the cluster is the sum of the energy-momemtum of each string. As the individual color field of the individual string may be oriented in an arbitrary manner respective to one another,

Scales of pp and AA

Transverse size Effective number of clusters CGC low density high density rapidity extension

low density high density low density

high density (energy) CGC high density (energy)

low density first decreases with density (energy) Above an energy(density) k increases MULTIPLICITY DISTRIBUTIONS NEGATIVE BINOMIAL Poisson high densityBose-Einstein Multiplicity distributions (normalized, i.e. as a function of will be narrower (Quantum Optical prediction) single effective string)

Ridge Structure

In both CGC and string percolation the heigth of the ridge increases with energy and centrality At the same value of string density same value of the heigth (it was predicted ridge structure in high multiplicity pp events at LHC,as far the string density in pp at LHC is similar to Au-Au peripheral collisions at RHIC) Triggering a high pt particle, it means that you change the multiplicity distribution in a very define way.Now is larger (dn/dy)/k

Conclusions --- For pp high multiplicity events at LHC should occur the same phenomena observed at RHIC in Au-Au --- Normalized multiplicity distributions in pp will be narrower at higher energy --- Long range correlations extended more than 10 units of rapidity at LHC for AA.Large LRC in pp, extended several units of rapidity. --- There are pt-n and pt-pt long range correlations which can be distinguished from short range correlations using different azimuthal and rapidity regions --- Large similarities between CGC and percolation of strings.Similar predictions corresponding to similar physical picture.Percolation explains the transition low density-high density