The ridge in proton-proton collisions at the LHC

TL;DR

The paper addresses the CMS observation of a ridge in high-multiplicity proton-proton collisions at 7 TeV and argues that this phenomenon arises from initial-state gluon saturation described by the Color Glass Condensate, via Glasma flux tubes that produce long-range rapidity correlations. It derives a two-particle correlation function C2 in terms of unintegrated gluon distributions, with BK evolution governing their rapidity dependence and a saturation scale Q_s setting the transverse correlation scale. The authors show intrinsic Δφ collimation near zero and a centrality-dependent enhancement for p⊥ around Q_s, suggesting that flow is not essential to explain the ridge in p+p. They connect these results to similar ridge phenomena in A+A, discuss limitations and needed extensions (fragmentation, short-range jets), and propose further tests through higher-point correlations to validate the CGC/Glasma picture. Overall, the work highlights gluon saturation as a universal mechanism for initial-state correlations in high-energy hadronic collisions and extends the ridge paradigm to proton-proton systems.

Abstract

We show that the key features of the CMS result on the ridge correlation seen for high multiplicity events in sqrt(s)=7TeV proton-proton collisions at the LHC can be understood in the Color Glass Condensate framework of high energy QCD. The same formalism underlies the explanation of the ridge events seen in A+A collisions at RHIC, albeit it is likely that flow effects may enhance the magnitude of the signal in the latter.

Figures (7)

• Figure 1: Top: 3-D display of the two particle correlation $R$ as a function of $\Delta\eta$ and $\Delta\phi$ for minimum bias and high multiplicity events in two different $p_\perp$ windows. Bottom: The associated yield in different $p_\perp$ windows as a function of the number of charged particle tracks. From ref. CMS1.
• Figure 2: Top: 3-D display of the two particle correlation (analogous to $R$ in fig. \ref{['fig:one']}) for $p_\perp$-triggered events from the STAR collaboration Abelev:2009qa (note that the away-side peak around $\Delta \phi = \pi$ seen in fig. \ref{['fig:one']} has been removed). Bottom: Two-particle correlation data from the PHOBOS collaboration AlverA1 that reveals a long range component. The curves shown are obtained by adding our result (in eq. (\ref{['eq:double-inclusive']})) to the short range correlation from PYTHIA.
• Figure 3: This figure illustrates the argument from causality that long range correlations of particles (denoted $A$ and $B$ here) must occur at very early proper times. The doubly shaded region, corresponding to the intersection of the light cones of the two particles, is the space-time location where correlations can be formed.
• Figure 4: The unintegrated gluon distribution as a function of transverse momentum squared for running coupling for three values of the momentum fraction $x$.
• Figure 5: A typical diagram which gives an angular collimation.