Abstract
We show that, in the saturation/Color Glass Condensate framework, odd azimuthal harmonics of the two-gluon 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 non-zero.
Highlights
Over the past decade long-range rapidity correlations between the produced hadrons were observed in heavy ion (AA) and high-multiplicity proton-nucleus and proton-proton collisions at RHIC [1,2,3,4] and LHC [5,6,7,8]
Since the long-range rapidity correlations were first discovered in heavy ion collisions, it is natural to ascribe their origin to the dynamics of quark-gluon plasma (QGP) produced in such collisions
In this paper we have demonstrated analytically that the classical gluon fields of the saturation/color glass condensate (CGC) approach to heavy ion collisions do generate odd azimuthal harmonics in the two-gluon correlation function
Summary
Over the past decade long-range rapidity correlations between the produced hadrons were observed in heavy ion (AA) and high-multiplicity proton-nucleus (pA) and proton-proton (pp) collisions at RHIC [1,2,3,4] and LHC [5,6,7,8]. In [46] the authors observed that the symmetry of the digluon correlator under k1 ↔ k2, k1 → −k1, and k2 → −k2 is “accidental” and is not required by the symmetries in the problem They have argued that odd harmonics may arise if one includes saturation effects in the wave function of the projectile: to find odd harmonics one needs to augment the existing calculations of the two-gluon production cross section [38,42], in which the saturation effects were only included in the interaction with the target. We find the part of the twogluon production cross section responsible for odd harmonics at the order ðα2sA11=3Þ3: it is given by Eq (17) This is the leading contribution to the odd harmonics resulting from the two-gluon correlation function. V by observing that saturation/CGC dynamics does lead to the odd harmonics in digluon correlation functions, which may allow for further successes of the saturation approach to the correlation function phenomenology
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