Azimuthal quadrupole correlation from gluon interference in 200 GeV and 7 TeV $p+p$ collisions

The Balitskii-Fadin-Kuraev-Lipatov multi-Pomeron model of Levin and Rezaeian, with extension to the gluon saturation region, is applied to long-range pseudorapidity correlations on relative azimuth for low-momentum final-state hadrons produced in $\sqrt{s}=200\mathrm{GeV}$ and 7 TeV $p+p$ collisions. The multi-Pomeron exchange probabilities in the model were estimated by fitting the minimum-bias $p+p$ multiplicity frequency distributions. The multi-Pomeron model prediction for the amplitude of the minimum-bias average quadrupole correlation, proportional to $\cos 2({\varphi }_1-{\varphi }_2)$, is consistent with the 200 GeV data when theoretically expected gluon saturation momentum scales are used. Correlation predictions for the high-multiplicity 7 TeV $p+p$ collision data are also consistent with the long-range pseudorapidity correlations at small relative azimuth observed in the data. The results presented here show that the present application of a multiple-parton-shower gluon interference mechanism for generating the long-range pseudorapidity, azimuthal quadrupole correlation is not excluded by the data.

Figure 1

Panel (a): Minimum-bias multiplicity frequency distribution data for $\sqrt{s}=200\mathrm{GeV}$ $p+p$ NSD data for $|\eta |\le 0.5$ from UA5 [19] and Pomeron exchange model fits (curves) described in the text. Panel (b): Corresponding multi-Pomeron exchange probabilities for collisions as functions of multiplicity $n_{\text{ch}}$. Probabilities for $m=1$, 2, 3 are shown by the solid, dashed, and dash-dotted curves, respectively.

Figure 2

Same as Fig. 1, except for 7 TeV $p+p$ collisions from CMS [24]. Pomeron exchange model fits (curves) are described in the text.

Figure 3

Range of saturation scales $Q_{\mathrm{S}}^2(n_{\text{ch}})$ from theoretical predictions as discussed in Sec. 4 (shaded band). Saturation scales $Q_{\mathrm{S}}^2(n_{\text{ch}})$ are from the Levin and Rezaeian model application in Eq. (18) which are required to describe the experimental 200 GeV $p+p$ quadrupole correlation in Eq. (23) [9], assuming three saturation limits [Eq. (8)]. Solid, long-dashed, and short-dashed curves correspond to the full saturation limit and the semisaturation limit (BFKL region) with ${\mu }^2=1.6{\mathrm{GeV}}^2$ and $0.8{\mathrm{GeV}}^2$, respectively.

Figure 4

Quadrupole amplitudes for 200 GeV minimum-bias $p+p$ and $\mathrm{Au}+\mathrm{Au}$ centrality-dependent collisions (solid circles) [27]. The $p+p$ datum [9] is shown by the solid square symbol. Error bars, if not shown, are smaller than the symbols. LR model results assuming fixed $Q_{\mathrm{S}}^2=0.6{\mathrm{GeV}}^2$ (see text) are shown by the open squares. The LR model results for minimum-bias $p+p$ collisions, assuming the theoretical saturation scale range in Fig. 3 for the semisaturated ${\mu }^2=0.8{\mathrm{GeV}}^2$, $1.6{\mathrm{GeV}}^2$, and fully saturated limits are shown by the solid, long-dashed, and short-dashed vertical lines, respectively. The LR model results are offset from $\nu =1.25$ for clarity.

Figure 5

Measured and predicted quadrupole amplitudes for 200 GeV minimum-bias $p+p$ collisions repeated from Fig. 4 (solid square and vertical lines near $n_{\text{ch}}/\mathrm{\Delta }\eta =2.5$) in comparison with similar predictions and measured quadrupole amplitude (solid circle symbol) for the $N_{\text{trk}}^{\text{offline}}\ge 110$, $p_t>0.1\mathrm{GeV}/c$ 7 TeV $p+p$ collision data from CMS [1]. LR model results assuming the semisaturated ${\mu }^2=0.8{\mathrm{GeV}}^2$, $1.6{\mathrm{GeV}}^2$, and fully saturated limits are shown by the solid, long-dashed, and short-dashed vertical lines near $n_{\text{ch}}/\mathrm{\Delta }\eta =44$, respectively. The LR model results are horizontally offset for clarity. The upper dashed line indicates the maximum allowed quadrupole amplitude discussed in the text.