First saturation correction in high energy proton-nucleus collisions. Part III. Ensemble averaging

Abstract

In high energy proton-nucleus collisions, the gluon saturation effects from the nucleus are fully incorporated into the light-like Wilson lines. The gluon saturation effects from the proton, which are anticipated to be important either in the extreme high energy limit or towards the dense-dense (nucleus-nucleus) collision regimes, have been studied perturbatively within the Color Glass Condensate effective theory in previous papers of this series. A configuration-by-configuration expression for the single inclusive semi-hard gluon production including the first saturation correction was obtained. In this paper, we perform ensemble averaging in the McLerran-Venugopalan model and the Dipole Approximation. We find that, in the saturation correction, the effects of the initial state interactions are negligible while the final state interactions play most important role and give a positive-valued contribution to the semi-hard gluon spectrum. Furthermore, we show that the single gluon spectrum scales approximately 1/$$ {k}_{\perp}^4 $$ k ⊥ 4 at small k⊥, suggesting that a resummation of higher order saturation corrections is required to regulate the infrared region of the gluon spectrum.

Multiparticle production in proton–nucleus collisions beyond eikonal accuracy

“…The CGC offers a framework where particle production at the very early phases of the collision [8][9][10] and initial state correlations (see the review [11]) can be analysed. The origin of such initial state correlations lies in the quantum effects (Bose enhancement in the case of gluons) in the wave function of the colliding hadrons [12][13][14][15][16][17][18], but problems still exist to include subleading density effects (see recent efforts in [19][20][21]), and to understand the behaviour of correlations with centrality or multiplicity in the event [22,23]. Furthermore, odd coefficients of the azimuthal Fourier decomposition of the distribution of produced particles are absent in standard CGC calculations, and can only be generated by including density corrections [24,25], or a modification of the usual isotropic field ensembles in the target [26,27], or non-eikonal corrections.…”

“…This model has been called dipole approximation in[21], where its validity is also discussed 4. See Appendix A of Ref [56].…”

“…But for the Fourier transform of the quadrupole such difference is considerably larger, up to 30 %, and the convergence with increasing collision area much slower than for the double dipole. Further numerical checks and discussions can be found in[21].…”

CGC for ultra-peripheral Pb+Pb collisions at the Large Hadron Collider: a more realistic calculation

“…[24,25] and successfully applied to study particle production and correlations in refs. [26][27][28][29][30]. This approximation is well suited for a dense nuclear target in and close to saturation regime.…”

Multiparticle production in proton-nucleus collisions beyond eikonal accuracy

“…The CGC offers a framework where particle production at the very early phases of the collision [8][9][10] and initial state correlations (see the review [11]) can be analysed. The origin of such initial state correlations lies in the quantum effects (Bose enhancement in the case of gluons) in the wave function of the colliding hadrons [12][13][14][15][16][17][18], but problems still exist to include subleading density effects (see recent efforts in [19][20][21]), and to understand the behaviour of correlations with centrality or multiplicity in the event [22,23]. Furthermore, odd coefficients of the azimuthal Fourier decomposition of the distribution of produced particles are absent in standard CGC calculations, and can only be generated by including density corrections [24,25], or a modification of the usual isotropic field ensembles in the target [26,27], or non-eikonal corrections.…”