We calculate the triple-and quadruple-gluon inclusive distributions with arbitrary rapidity and azimuthal angle dependence in the gluon saturation regime by using glasma diagrams. Also, we predict higher dimensional ridges in triple-and quadruple-hadron correlations for p-p and p-Pb collisions at LHC, which have yet to be measured. In p-p and p-Pb collisions at the top LHC energies, gluon saturation is expected to occur since smaller Bjorken-x values are being probed. Glasma diagrams, which are enhanced at small-x, include gluon saturation effects, and they are used for calculating the long-range rapidity correlations ("ridges") and vn moments of the azimuthal distribution of detected hadrons. The glasma description reproduces the systematics of the data on both p-p and p-Pb ridges. As an alternative, relativistic hydrodynamics has also been applied to these small systems quite successfully. With the triple-and quadruple-gluon azimuthal correlations, this work aims to set the stage by going beyond the double-gluon azimuthal correlations in order to settle unambiguously the origin of "collectivity" in p-p and p-Pb collisions. We derive the triple-and quadruple-gluon azimuthal correlation functions in terms of unintegrated gluon distributions at arbitrary rapidities and azimuthal angles of produced gluons. Then, unintegrated gluon distributions from the running coupling Balitsky-Kovchegov evolution equation are used to calculate the triple-and quadruple-gluon correlations for various parameters of gluon momenta, initial scale for small-x evolution and beam energy.

We calculate the inclusive gluon correlation function for arbitrary number of gluons with full rapidity and transverse momentum dependence for the initial glasma state of the p-p, p-A and A-A collisions. The formula we derive via superdiagrams generates cumulants for any number of gluons. Higher order cumulants contain information on correlations between multiple gluons, and they are necessary for calculations of higher dimensional ridges as well as flow coefficients from multi-particle correlations. * ozonder@uw.edu 2

We consider a version of the McLerran-Venugopalan model by Lam and Mahlon where confinement is implemented via colored noise in the infrared. This model does not assume an infinite momentum frame nor that the boosted nuclei are infinitely thin; rather, nuclei have a finite extension in the longitudinal direction and therefore depend on the longitudinal coordinate. In this fully three dimensional framework an x dependence of the gluon distribution function emerges naturally. In order to fix the parameters of the model, we calculate the gluon distribution function and compare it with the JR09 parametrization of the data. We explore the parameter space of the model to attain a working framework that can be used to calculate the initial conditions in heavy ion collisions. * ozonder@umn.edu 2

The rapidity dependence of the initial energy density in heavy-ion collisions is calculated from a three-dimensional McLerran-Venugopalan model (3dMVn) introduced by Lam and Mahlon. This model is infrared safe since global color neutrality is enforced. In this framework, the nuclei have non-zero thickness in the longitudinal direction. This leads to Bjorken-x dependent unintegrated gluon distribution functions, which in turn result in a rapidity-dependent initial energy density after the collision. These unintegrated distribution functions are substituted in the initial energy density expression which has been derived for the boost-invariant case. We argue that using threedimensional (x-dependent) unintegrated distribution functions together with the boost-invariant energy formula is consistent given that the overlap of the two nuclei lasts less than the natural time scale for the evolution of the fields (1/Qs) after the collision. The initial energy density and its rapidity dependence are important initial conditions for the quark gluon plasma and its hydrodynamic evolution.