How classical gluon fields generate odd azimuthal harmonics for the two-gluon correlation function in high-energy collisions

Abstract

We show that, in the saturation/color glass condensate framework, odd azimuthal harmonics of the twogluon correlation function with a long-range separation in rapidity are generated by the higher-order saturation corrections in the interactions with the projectile and the target. At the very least, the odd harmonics require three scatterings in the projectile and three scatterings in the target. We derive the leading-order expression for the two-gluon production cross section which generates odd harmonics: the expression includes all-order interactions with the target and three interactions with the projectile. We evaluate the obtained expression both analytically and numerically, confirming that the odd-harmonics contribution to the two-gluon production in the saturation framework is nonzero.

Systematics of azimuthal anisotropy harmonics in proton–nucleus collisions at the LHC from the Color Glass Condensate

“…Indeed, as shown explicitly recently [15][16][17], the first nontrivial ρ p k 2 ⊥,p correction breaks the accidental parity symmetry and gives a finite contribution to v 3 . Thus a nonzero value for odd azimuthal anisotropies in the CGC EFT can be understood to be a unique signature of the emerging coherence of the classical gluon field in the projectile.…”

Unified description of hadron yield ratios from dynamical core-corona initialization

“…One of those data shows sizable azimuthal anisotropy in final hadron distributions [8][9][10][11][12][13][14], which can be interpreted as a result of the hydrodynamic response of the QGP medium to the initial collision geometry [15][16][17][18][19][20][21][22]. Although this has been discussed actively from relativistic hydrodynamics, another interpretation is brought about also by the color glass condensate picture, which gives long-range correlation in rapidity in small colliding systems without invoking the QGP formation [23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Thus the origin of collectivity observed in small colliding system still remains to be understood.…”

CGC/saturation approach: re-visiting the problem of odd harmonics in angular correlations

“…8-a). For example σ CD 0 takes the form (29) where γ denotes the dipole amplitude at Y = Y 0 , and we assumed that exp 1 2 ∆Y ≫ 1. We need to find the scattering amplitude with one cut Pomeron, which is equal to…”

“…Several efforts to calculate corrections to the leading order CGC/saturation approach have been made (see Refs. [19,26,29] which demonstrated that this correction violates the symmetry which lead to a v n for odd n. If these corrections originate from the next-to-leading order corrections, they should have a parametrically strong suppression, while experimentally v 3 < v 2 but v 3 ≈ v 4 . If we believe that the CGC/saturation approach in leading order describes all other physical observables, then we interpret the experimental results, as an indication that the suppression of v 3 is of a numerical nature.…”