[Paper Review] Particle rapidity distribution in proton-nucleus collisions using the proton-contributor reference frame

G. Mart́inez Garćia|arXiv (Cornell University)|Aug 14, 2014

High-Energy Particle Collisions Research3 citations

TL;DR

This paper proposes the proton-contributor reference frame in p–A collisions, where particle rapidity distributions are symmetric around the center-of-mass of the proton and participating nucleons in the nucleus. By assuming these distributions mirror those in pp collisions but shifted by the rapidity gap between proton-nucleon and proton-contributor frames, the model qualitatively explains charged particle, J/ψ, and Z boson rapidity distributions in p–Pb collisions at √sNN = 5.02 TeV.

ABSTRACT

I define the proton-contributor reference frame in proton nucleus (p--A) collisions as the center of mass of the system formed by the proton and the participant nucleons of the nucleus. Assuming that the rapidity distribution of produced particles is symmetric in the proton-contributor reference frame, several measurements in p-Pb collisions at $\sqrt{s_{ m NN}} = 5.02 { m TeV}$ can be described qualitatively. These include rapidity distributions of charged particles, $J/ψ$ and Z bosons.

Motivation & Objective

• To address the lack of a clear reference frame for rapidity distributions in p–A collisions, where symmetry is not naturally defined as in pp or AA systems.
• To resolve the observed asymmetries in rapidity distributions of charged particles, J/ψ, and Z bosons in p–Pb collisions at LHC energies.
• To propose an alternative to the nucleon-nucleon center-of-mass frame by introducing the proton-contributor system, formed by the proton and all participant nucleons.
• To provide a phenomenological explanation for centrality-dependent particle yields and forward/backward ratios in p–Pb collisions using a single reference frame.
• To motivate new experimental observables based on the rapidity gap between proton-nucleon and proton-contributor frames.

Proposed method

• Define the proton-contributor (pC) system as the center-of-mass of the proton and all participant nucleons in the nucleus, using the Glauber model to compute its mass and momentum.
• Compute the rapidity of the pC system in the lab frame using relativistic kinematics: y_pC = tanh⁻¹(p_pC / E_pC), where p_pC and E_pC are the total momentum and energy of the pC system.
• Assume that the rapidity distribution of produced particles in p–A collisions is identical in shape to that in pp collisions but shifted by the rapidity gap Δy_pN-pC between the proton-nucleon and proton-contributor frames.
• Use the equation dN_probe_pA/dy(y) = N × dN_probe_pp/dy(y - Δy_pN-pC) to model particle yields, with N as a normalization factor.
• Calculate Δy_pN-pC using the rapidity of the proton-nucleon frame (y_pN) and the pC frame (y_pC), with y_pC ≈ -0.430 for minimum-bias p–Pb collisions (⟨N_coll⟩ ≈ 6).
• Compare model predictions to experimental data from ATLAS, ALICE, and CMS on charged particle pseudo-rapidity ratios, J/ψ suppression/enhancement, and Z boson backward-to-forward ratios.

Experimental results

Research questions

• RQ1 Can a single reference frame explain the observed rapidity distributions of multiple particle types in p–Pb collisions at √sNN = 5.02 TeV?
• RQ2 Does the proton-contributor frame, defined as the center-of-mass of the proton and participant nucleons, provide a better description of particle production than the proton-nucleon frame?
• RQ3 Why is the Z boson rapidity distribution in p–Pb collisions centered at y ≈ -0.430 in the lab frame, and can this be explained by a symmetric distribution in the pC frame?
• RQ4 How does the rapidity gap Δy_pN-pC affect the observed backward-to-forward ratio of Z bosons in p–Pb collisions?
• RQ5 Can the observed centrality dependence of charged particle yields be explained by assuming symmetric rapidity distributions in the pC frame?

Key findings

• The proton-contributor reference frame, with rapidity y_pC ≈ -0.430 in minimum-bias p–Pb collisions, aligns with the peak of the measured Z boson rapidity distribution in the lab frame.
• The model explains the centrality dependence of charged particle pseudo-rapidity ratios measured by ATLAS, with distributions shifting toward more negative rapidities in central events.
• The observed suppression of J/ψ at forward rapidity and enhancement at backward rapidity in ALICE data is qualitatively reproduced by assuming symmetric rapidity distributions in the pC frame.
• The backward-to-forward ratio of Z bosons measured by CMS is well reproduced by shifting the standard pp-like rapidity distribution to the pC frame, with Δy_pN-pC ≈ 0.895.
• The predicted Z boson rapidity distribution centered at y_pC ≈ -0.430 matches the experimental observation of a maximum at y ≈ -0.430 in the lab frame.
• The model suggests a new nuclear modification factor R^pC_pA(y) = Y_pA(y) / ⟨N_coll⟩ × Y_pp(y - Δy_pN-pC), which could serve as a new observable to test the pC frame hypothesis.