CGC-induced longitudinal ridge in p-Pb collisions

Within the Color Glass Condensate (CGC) effective field theory, we investigate the long-range rapidity correlations in proton-lead (p-Pb) collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. A distinctive correlation rebound is observed, where the correlation bounces after reaching a minimum at large rapidity gaps ($|Δη|>2$). The rebound means a strong correlation appears at large rapidity gap. Studying the rebound structures can thus illuminate the formation of the ridge. We find that the rebound is most obvious when the transverse momenta of two measured particles are around 2 $\mathrm{GeV/c}$, and it moves to larger rapidity gaps at higher collision energies. Beyond that, the rapidity correlations in p-Pb collisions show asymmetry when the transverse momenta of two particles differ. The asymmetry, a unique signature of the asymmetric collisions, vanishes when the transverse momenta of two particles coincide. These findings provide direct insight into gluon saturation and quantum evolution.

💡 Research Summary

In this work the authors employ the Color Glass Condensate (CGC) effective field theory to study long‑range rapidity correlations in proton‑lead (p‑Pb) collisions at √sₙₙ = 5.02 TeV. The analysis focuses on the per‑trigger yield Y(Δy,Δϕ), defined as the ratio of the signal pair distribution S(Δy,Δϕ) to the mixed‑event background B(Δy,Δϕ). Within the CGC framework the signal is obtained from the double‑gluon inclusive distribution, while the background is constructed from the product of two single‑gluon spectra. The authors solve the running‑coupling Balitsky‑Kovchegov (rcBK) equation with the Albacete‑Armesto‑Milhano‑Quiroga‑Salgado (AAMQS) initial condition to generate the unintegrated gluon distribution (uGD) Φ(x,kₜ). This uGD, together with the kₜ‑factorization formulas for single‑ and double‑particle production, allows a fully differential calculation of Y(Δy,Δϕ) over the kinematic window 1 ≤ pₜ,qₜ ≤ 3 GeV/c and –2.865 ≤ y ≤ 1.935.

The resulting two‑dimensional yield exhibits two azimuthal peaks at Δϕ = 0 and π, reflecting the intrinsic glasma‑induced collimation. In the rapidity direction a striking “rebound” structure appears: after the correlation strength drops to a minimum at |Δy| ≈ 2, it rises again at larger rapidity separations. This rebound is most pronounced when both particles have transverse momenta around 2 GeV/c, i.e. near the sum of the saturation scales of the projectile proton and the lead nucleus. As the collision energy increases, the rebound shifts to larger |Δy|, consistent with the energy dependence of the saturation momentum Qₛ(x) ∝ x⁻λ.

A second key observation is the emergence of rapidity‑asymmetry when the trigger and associated particles carry different transverse momenta. Because p‑Pb collisions are intrinsically asymmetric in rapidity (the proton and lead nuclei move in opposite directions), particles with different pₜ probe different Bjorken‑x values in the projectile and target. Consequently the correlation function becomes asymmetric in Δy. When the two momenta are equal, the x‑values coincide and the asymmetry disappears, restoring the symmetric pattern observed in symmetric pp collisions.

The authors interpret the rebound as a direct signature of strong correlations between large‑x source gluons and their small‑x radiated descendants, mediated by the glasma flux‑tube structure. The momentum‑dependent asymmetry further underscores the role of the underlying x‑dependence of the uGD. Their CGC‑based calculations reproduce the qualitative features of the ridge observed in existing pp data and predict similar, even more prominent, structures in p‑Pb collisions.

Finally, the paper emphasizes that current experimental measurements of long‑range rapidity correlations in p‑Pb are limited. The authors call for dedicated analyses to measure the rebound and the momentum‑dependent asymmetry, which would provide stringent tests of gluon saturation and quantum evolution dynamics in small‑system collisions.