CGC/saturation approach for high energy soft interactions: $v_2$ in proton-proton collisions

In this paper we continue our program to construct a model for high energy soft interactions, based on the CGC/saturation approach. We demonstrate that in our model, which describes diffractive physics as well as multiparticle production at high energy, the density variation mechanism leads to the value of $v_2$, which is about 60%–70% of the measured $v_2$. Bearing in mind that in the CGC/saturation approach there are two other mechanisms present, Bose enhancement in the wave function and local anisotropy, we believe that the azimuthal long range rapidity correlations in proton-proton collisions stem from the CGC/saturation physics, and not from quark-gluon plasma production.

Figure 1

(a) The set of the diagrams in the BFKL Pomeron calculus that produce the resulting (dressed) Green function of the Pomeron in the framework of high energy QCD. The red blobs denote the amplitude of dipole-dipole interaction at low energy. (b) The net diagrams, which include the interaction of the BFKL Pomerons with colliding hadrons. The sum of the diagrams reduces to (c) after integration over positions of $G_{3IP}$ in rapidity.

Figure 2

The Mueller diagram for the rapidity correlation between two particles produced in two parton showers. (a) The first Mueller diagram. (b) The structure of general diagrams. The double wavy lines describe the dressed BFKL Pomerons. The blobs stand for the vertices as shown in the legend.

Figure 3

The Mueller diagram for the single inclusive cross section. The double wavy lines describe the resulting Green function of the BFKL Pomerons ( ${\tilde{G}}^{\text{dressed}}$). The blobs stand for the vertices, which are the same as in Fig. 2.

Figure 4

Contours of integration in Eq. (42).

Figure 5

${\nu }_{22}\equiv v_{22}$ vs $p_T\equiv p_{\perp }$ for $p_{1\perp }=p_{2\perp }=p_T$. $R=3/Q_s$ at $Q_s=1\mathrm{GeV}$.

Figure 6

The large multiplicity event in our approach: production from (a) one parton shower and (b) two parton showers.

Figure 7

$N_{11}$ of Eq. (87) vs $r_{\perp }$ at different values of $Q\equiv Q_T$.

Figure 8

${\nu }_{22}\equiv v_{22}$ vs $p_T$ at (a) $\mathrm{W}=13\mathrm{TeV}$ and (b) $\mathrm{W}=2.76\mathrm{TeV}$.

Figure 9

${\nu }_2\equiv v_2$ vs $p_T$ at (a) $\mathrm{W}=13\mathrm{TeV}$ and (b) $\mathrm{W}=2.76\mathrm{TeV}$.

Figure 10

$v_2$ vs $p_T$ at $\mathrm{W}=2.76\mathrm{TeV}$ and at $\mathrm{W}=13\mathrm{TeV}$. The figure is taken from Ref. [71].

Figure 11

$v_2$ vs $p_T$ at $\mathrm{W}=13\mathrm{TeV}$ with the choice $Q_0=0.2m$ in Eq. (89).