Explanation of systematics of CMS p+Pb high multiplicity di-hadron data at $\sqrt{s}_{\rm NN} = 5.02$ TeV

TL;DR

The paper analyzes CMS p+Pb di-hadron correlations at 5.02 TeV within the Color Glass Condensate framework, attributing the observed near-side ridge and away-side structure to a combination of Glasma graphs (saturation-driven near-side) and BFKL-like back-to-back emissions. By fixing EFT parameters to p+p results and varying the initial scales $Q_0^2$ for the proton and lead nucleus, the authors reproduce the CMS systematics across multiplicity and transverse-momentum windows, and provide predictions for unpublished kinematic configurations. A key conceptual point is that the yield enhancements arise from saturation-driven entanglement of gluon wavefunctions in the projectile and target, with the data favoring larger proton $Q_0^2$ values in rarer, high-multiplicity events. The findings support an initial-state CGC origin for the ridge in both p+p and p+Pb, while outlining concrete avenues for improvement and future experimental tests, including comparisons with hydrodynamic scenarios.

Abstract

In a recent article (arXiv:1210.3890), we showed that high multiplicity di-hadron proton- proton (p+p) data from the CMS experiment are in excellent agreement with computations in the Color Glass Condensate (CGC) Effective Field Theory (EFT). This agreement of the theory with several hundred data points provides a non-trivial description of both nearside ("ridge") and away-side azimuthal collimations of long range rapidity correlations in p+p collisions. Our prediction in arXiv:1210.3890 for proton-lead (p+Pb) collisions is consistent with results from the recent CMS p+Pb run at $\sqrt{s}_{\rm NN} = 5.02$ TeV for the largest track multiplicity $N_{\rm track}\sim 40$ we considered. The CMS p+Pb data shows the following striking features: i) a strong dependence of the ridge yield on $N_{\rm track}$, with a significantly larger signal than in p+p for the same $N_{\rm track}$, ii) a stronger $p_T$ dependence than in p+p for large $N_{\rm track}$, and iii) a nearside collimation for large $N_{\rm track}$ comparable to the awayside for the lower $p_T = p_{T}^{\rm trig.}=p_{T}^{\rm assoc.}$ di-hadron windows. We show here that these systematic features of the CMS p+Pb di-hadron data are all described by the CGC (with parameters fixed by the p+p data) when we extend our prediction in arXiv:1210.3890 to rarer high multiplicity events. We also predict the azimuthally collimated yield for yet unpublished windows in the $p_{T}^{\rm trig.}$ and $p_{T}^{\rm assoc.}$ matrix.

Figures (7)

• Figure 1: Anatomy of di-hadron correlations. The glasma graph on the left illustrates its its schematic contribution to the double inclusive cross-section (dashed orange curve). On the right is the back-to-back graph and the shape of its yield (dashed blue curve). The grey blobs denote emissions all the way from beam rapidities to those of the triggered gluons. The solid black curve represents the sum of contributions from glasma and back-to-back graphs. The shaded region represents the Associated Yield (AY) calculated using the zero-yield-at-minimum (ZYAM) procedure. Figure from ref. Dusling:2012cg.
• Figure 2: The nearside yield per trigger as a function of $N_{\rm trk}^{\rm offline}$ for $1\leq p_T \leq 2$, for $p_T=p^{\textrm{trig}}_T=p^{\textrm{asc}}_T$. Each of the p+Pb curves corresponds to a fixed initial saturation scale in the proton. The trajectory of a curve shows how the yield increases with a larger number of participants in the nucleus. The initial saturation scale in the Pb nucleus is related to the number of participants through $Q_0^2{\rm (lead)} = N_{\rm part}^{\rm Pb}\cdot 0.168~\rm{GeV}^2$. The values of $Q_0^2{\rm (proton)} = 0.168 - 0.672~{\rm GeV}^2$ (corresponding to saturation scales in the adjoint representation of $Q_S^2 \approx 0.7 - 1.6~{\rm GeV}^2$) represent estimates these quantities from median ("min. bias") impact parameters in the proton to very central impact parameters respectively.
• Figure 3: Left: The integrated nearside associated yield per trigger as a function of $N_{\rm trk}^{\rm offline}$ for $1\leq p_T\leq 2$. The two curves on which data from CMS:2012qk are overlaid are the $Q_0^2$(proton)=0.336 GeV$^2$ and $Q_0^2$(proton)=0.504 GeV$^2$ results from Fig. (\ref{['fig:multi']}). Right: The $p_T$ ($p^{\textrm{trig}}_T=p^{\textrm{asc}}_T$) dependence of the associated yield for the same $Q_0^2$(proton) values as the previous plot denoted by green (lower) and black (upper) dashed lines, for two different $N_{\rm part}^{\rm Pb}$ ranges. The data here are for $N_{\rm trk}^{\rm offline} \geq 110$ that is approximated (see Fig. \ref{['fig:multi']}) by the $N_{\rm part}^{\rm Pb}$ ranges considered.
• Figure 4: Correlated yield $d^2N/d\Delta\phi$ after ZYAM as a function of $\Delta \phi$ integrated over $2\leq \vert\Delta\eta\vert \leq 4$ for several multiplicity bins, each for a particular range in $p^{\textrm{trig}}_T=p^{\textrm{asc}}_T$. The data points are from the CMS collaboration CMS:2012qk. The theoretical curves are the result of adding the glasma and BFKL contributions with the band representing the variation in results when changing the K-factors from $K_{\rm glasma}=1, K_{\rm bfkl}=1.1$ to $K_{\rm glasma}=1.3, K_{\rm bfkl}=0.6$. The results for the different multiplicity windows correspond (from left to right) to: $Q_0^2$(proton)=0.168 GeV$^2$, $N_{\rm part}^{\rm Pb}=3$; $Q_0^2$(proton)=0.336 GeV$^2$, $N_{\rm part}^{\rm Pb}=6$; $Q_0^2$(proton)=0.336 GeV$^2$, $N_{\rm part}^{\rm Pb}=12$; $Q_0^2$(proton)=0.504 GeV$^2$, $N_{\rm part}^{\rm Pb}=14$; $Q_0^2$(proton)=0.504 GeV$^2$, $N_{\rm part}^{\rm Pb}=22$. Predictions are shown for very large multiplicity windows and higher values of $p^{\textrm{trig}}_T=p^{\textrm{asc}}_T$.
• Figure 5: Correlated yield $d^2N/d\Delta\phi$ after ZYAM as a function of $\vert \Delta \phi$ integrated over $2\leq \vert\Delta\eta\vert \leq 4$ for the most central multiplicity bin $N_{\rm trk}^{\rm offline} \geq 110$. The data points are from the CMS collaborationCMS:2012qk and have currently only been provided for the diagonal components $p^{\textrm{trig}}_T\sim p^{\textrm{asc}}_T$ of the correlation matrix. The curves are obtained by adding the glasma contributions ($K=1$) and the BFKL contribution ($K=1.1$). The solid black curve is the result for $Q_0^2$(proton) = 0.504 GeV$^2$ on $N_{\rm part}^{\rm Pb}$=14 and the dashed green is for $Q_0^2$(proton) = 0.336 GeV$^2$ on $N_{\rm part}^{\rm Pb}$=16.