Multiparticle azimuthal angular correlations in pA collisions

Abstract

In the Color Glass Condensate formalism, we evaluate the 3-dipole correlator up to the 1 N 4 c order with Nc being the number of colors, and compute the azimuthal cumulant c123 for 3-particle productions. In addition, we discuss the patterns appearing in the n-dipole formula in terms of 1 Nc expansions. This allows us to conjecture the Nc scaling of cn{m}, which is crosschecked by our calculation of c2{4} in the dilute limit. I. INTRODUCTIONExperimental data in deep inelastic scatterings (DIS) and proton-nucleus (pA) collisions indicates a sharp rise in the cross section at small Bjorken x, which is believed to be due to the fast growth of the gluon density in large nuclei. The gluon density increases steeply and tends to be saturated when going to a smaller x. The Color Glass Condensate (CGC) formalism [1-7] describes this gluon saturation regime by treating the fast-moving partons inside the dense nucleus as a classical color source of the soft gluons. In the McLerran-Venugopalan (MV) model [8], the small-x gluons are assumed as a classical Yang-Mills field. The soft gluons, whose color field A is associated with a random color source ρ, are radiated by the eikonal (high-energy and fixed at a transverse coordinate) partons [9].With the fact that the gluon density inside the nucleus is large, one can obtain a weak coupling constant g. Nevertheless, due to the strong nuclear field A ∼ 1 g , the high-density regime is nonlinear and cannot be handled perturbatively. The Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) renormalization group equation [10,11] governs the nonlinear evolution of the gluon distribution function in the saturation regime. In the dilute regime, this equation reduces to the linear BFKL equation, which describes the evolution of the unintegrated gluon density.Within the framework introduced above, multiparticle productions in high-energy collisions are represented by dipoles, quadrupoles, and higher-point functions. These multipoint functions are written in forms of the Gaussian average of Wilson lines in the fundamental representation for quarks and the adjoint representation for gluons. However, Ref. [12] shows that, in the large-N c limit, only dipoles and quadrupoles contribute to the particle production processes. The quadrupole corresponding to the Weiszäcker-Williams gluon distribution has been evaluated in Ref.[13] by the JIMWLK Hamiltonian method.The CGC formalism generates multiparticle correlations in dilute-dense scatterings (pA collisions) from the initial state . In order to study correlation observables, which include the nth moment of the m-particle cumulant c n {m} and the corresponding anisotropic flow v n {m}, one has to derive multidipole correlators. Some recent work has been done in Refs. [14,31,32,38]. In this paper, we evaluate the 3-dipole correlator up to the 1 N 4 c order by the color transition matrices method developed in Refs. [39][40][41][42]. It helps to obtain an n-dipole formula in forms of a power series at large N c . We calculate the 3-parti...

A brief overview of solar cycle variability effects on climate

“…21 This is because these are regions on the sun with lower temperatures as compared to others. 22 This temperature variation is caused by the orientation of the magnetic field lines surrounding the sun while coupling with those from our planet. With the coming of satellites on board, it is now easier to compute for average solar intensities in different regions of the planet.…”

Towards a zero-carbon nuclear energy future: a review

“…The construction period of innovative power plants is now around five years as compared to about fifteen years previously. 12 As a result, nations are shutting down their outlived general reactors and opting to build these new innovative ones with improved safety technology and cost effectiveness.…”

“…[8][9][10][11] At the moment, the greatest enemy to hydroelectricity is climate change. 12 This is because not only does it contribute to less water levels but also distraction to the infrastructure due to typhoons and cyclones. As a result, this gives more advantage to nuclear power utilization to grow worldwide.…”

The Collectivity of Heavy Mesons in Proton-Nucleus Collisions

“…In the CGC formalism, the differential spectrum for the production of a heavy quark-antiquark pair plus a spectator quark can be obtained by employing techniques developed in [62,[67][68][69][70][71][72][73] and calculating diagrams as illustrated in Fig. 1.…”