[Paper Review] Longitudinal Coherence in a Holographic Model of p-Pb Collisions

Jorge Casalderrey-Solana, Michał P. Heller+2 more|arXiv (Cornell University)|Dec 10, 2013

Cosmology and Gravitation Theories4 citations

TL;DR

This paper investigates longitudinal coherence in a holographic model of asymmetric p-Pb collisions using gravitational shock wave collisions in anti-de Sitter space. It finds that when the characteristic size of shock constituents is ≤0.26/T_hyd, the plasma's center-of-mass aligns with the total nucleon center-of-mass, not individual collisions, indicating coherent hydrodynamic response despite initial asymmetries.

ABSTRACT

As a model of the longitudinal structure in heavy ion collisions, we simulate gravitational shock wave collisions in anti-de Sitter space in which each shock is composed of multiple constituents. We find that all constituents act coherently, and their separation leaves no imprint on the resulting plasma, when this separation is $\lesssim 0.26 / T_{hyd}$, with $T_{hyd}$ the temperature of the plasma at the time when hydrodynamics first becomes applicable. In particular, the center-of-mass of the plasma coincides with the center-of-mass of all the constituents participating in the collision, as opposed to the center-of-mass of the individual collisions. We discuss the implications for nucleus-nucleus and proton-nucleus collisions.

Motivation & Objective

• To understand how initial longitudinal structure in asymmetric collisions affects hydrodynamic behavior in heavy-ion physics.
• To model p-Pb and d-A collisions using holographic gravity, focusing on longitudinal coherence.
• To determine under what conditions the plasma's center-of-mass reflects the total nucleon system rather than individual nucleon-nucleon collisions.
• To explore implications for flow signals and rapidity distributions in high-multiplicity p+A and d+A events.

Proposed method

• Model p-Pb collisions via two gravitational shock waves in AdS5 with Gaussian profiles for each constituent nucleon.
• Use the gauge/gravity duality to map shock wave collisions to strongly coupled plasma formation.
• Define shock profiles using F±(z±) = (N_c²/2π²)μ³/(w√(8π)) × [exp((z±−½ℓ±)²/(2w²)) + exp((z±+½ℓ±)²/(2w²))], representing double or single shocks.
• Compute energy density and plasma dynamics numerically to study hydrodynamization and center-of-mass position.
• Define characteristic shock size as ℓ_char ≈ 3.3w for single shocks or ≈ℓ± for double shocks when ℓ± ≫ w.
• Use T_hyd as the plasma temperature at hydrodynamization time to define the coherence scale ℓ_char ≤ 0.26/T_hyd.

Experimental results

Research questions

• RQ1 Under what conditions does the plasma formed in asymmetric collisions exhibit coherent behavior despite non-uniform initial shock structure?
• RQ2 Does the center-of-mass of the final plasma coincide with the total nucleon center-of-mass or with individual nucleon-nucleon collision centers?
• RQ3 How does the characteristic size of shock constituents affect the hydrodynamic response in holographic models of p-Pb collisions?
• RQ4 What is the quantitative threshold for longitudinal coherence in terms of T_hyd and shock size?
• RQ5 How do these results compare with weak-coupling predictions for rapidity distribution maxima in p+A collisions?

Key findings

• Longitudinal coherence occurs when the characteristic size of shock constituents is ≤0.26/T_hyd, leading to a single, coherent plasma response.
• The center-of-mass of the plasma coincides with the total nucleon center-of-mass, not the individual nucleon-nucleon collision centers, in the coherent regime.
• Even in asymmetric collisions (e.g., single vs. double shock), the plasma remains symmetric and coherent if ℓ_char ≤ 0.26/T_hyd.
• For p+A collisions at the LHC, the strong-coupling prediction for y_max differs by a factor of ~4 from weak-coupling estimates, making experimental measurement of y_max highly constraining.
• The plasma exhibits y-reflection symmetry around y_plasma, consistent with observations in d+A collisions at RHIC.
• The model predicts that event-by-event fluctuations in the number of participating nucleons lead to fluctuations in y_max, as y_part = ½ log(N_A/N_B) + y_NN.