Two-gluon correlations in heavy–light ion collisions: Energy and geometry dependence, IR divergences, and kT-factorization

Abstract

We study the properties of the cross section for two-gluon production in heavy-light ion collisions derived in our previous paper [1] in the saturation/Color Glass Condensate framework. Concentrating on the energy and geometry dependence of the corresponding correlation functions we find that the two-gluon correlator is a much slower function of the center-of-mass energy than the one-and two-gluon production cross sections. The geometry dependence of the correlation function leads to stronger azimuthal near-and away-side correlations in the tip-on-tip U+U collisions than in the side-on-side U+U collisions, an exactly opposite behavior from the correlations generated by the elliptic flow of the quark-gluon plasma: a study of azimuthal correlations in the U+U collisions may thus help to disentangle the two sources of correlations.We demonstrate that the cross section for two-gluon production in heavy-light ion collisions contains a power-law infrared (IR) divergence even for fixed produced gluon momenta: while saturation effects in the target regulate some of the power-law IR divergent terms in the lowest-order expression for the two-gluon correlator, other power-law IR divergent terms remain, possibly due to absence of saturation effects in the dilute projectile. Finally we rewrite our result for the two-gluon production cross-section in a kT -factorized form, obtaining a new factorized expression involving a convolution of one-and two-gluon Wigner distributions over both the transverse momenta and impact parameters. We show that the two-gluon production cross-section depends on two different types of unintegrated two-gluon Wigner distribution functions.

Rapidity dependence of the average transverse momentum in hadronic collisions

“…[18,19] there is no compelling reason why small systems should also exhibit a hydrodynamical behaviour even though a hydro approach is able to describe the experimental data [20,21]. On the other hand, the CGC approach also provides a qualitatively good description of the same data [22][23][24][25][26][27][28][29][30][31][32]. Therefore, the origin of the ridge in pp and pA collisions is still an open question.…”

Bose enhancement, the Liouville effective action, and the high multiplicity tail in p−A collisions

“…The same approximation for the quadrupole amplitude has been used previously in Ref. [18], in which its consistency with explicit modeling of the Wilson line correlators via the MV model has been verified. Note that this averaging procedure for the target is formally (disregarding subtleties related to the definition of the Haar measure) equivalent to the following form of the weight functional: …”

“…This feature was noted and discussed earlier in Refs. [13,18], see also Ref. [25], in which the first saturation correction in the projectile to the double inclusive production was derived.…”

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

“…Perhaps a more conservative way of generating the ridge correlation is due to the so-called "glasma graphs" proposed in the saturation/CGC framework in [17]: they require only a double interaction in both the projectile and the target. The glasma graphs generate both the long-range correlation in rapidity [17,[29][30][31][32][33][34][35][36][37][38][39][40][41] and the nearand away-side ridge correlations [42,43]. Since the glasma graphs had originally been put forward in [17], the corresponding two-gluon production cross section was improved by including multiple interactions (saturation effects) with one of the nuclei (the target) in [38,42].…”

“…Since the glasma graphs had originally been put forward in [17], the corresponding two-gluon production cross section was improved by including multiple interactions (saturation effects) with one of the nuclei (the target) in [38,42]. As usual in the saturation physics, the effect of extra rescatterings appears to be mainly in screening the infrared (IR) divergences [43]. In addition, one can show that multiple rescatterings violate the k T -factorization formula one could conjecture for two-gluon production based on the glasma graphs alone [43].…”