[Paper Review] Nuclear Reaction Mechanisms and the Cronin Effect

G. G. Barnaföldi, Gábor Papp+2 more|ArXiv.org|Jul 14, 2003

High-Energy Particle Collisions Research3 citations

TL;DR

This paper investigates the Cronin effect in pion production across pA collisions from SPS to RHIC energies using a next-to-leading order (NLO) pQCD-improved parton model with intrinsic partonic transverse momentum (kT). It demonstrates that incorporating kT distributions with ⟨kT²⟩ ≈ 2 GeV² successfully reproduces the Cronin peak in pA collisions, while nuclear shadowing effects become significant at RHIC energies, particularly in centrality-dependent dAu data where b-dependent shadowing reveals distinguishable structures in R_dAu(b).

ABSTRACT

The influence of nuclear multiscattering and shadowing on pion spectra is investigated in $pA$ collisions from CERN SPS to RHIC energies. The calculations are performed in a next-to-leading order (NLO) pQCD-improved parton model, including intrinsic partonic transverse momentum distributions. The nuclear modification of the pion spectra (Cronin effect) is considered at different targets in a wide energy range. Theoretical predictions are displayed for planned $pA$ experiments at CERN SPS and recent $dAu$ experimental results are analysed at RHIC.

Motivation & Objective

• To explain the Cronin effect in pion production across pA collisions from CERN SPS to RHIC energies.
• To investigate the role of nuclear multiscattering and shadowing in modifying pion spectra at high energies.
• To determine the impact of intrinsic partonic transverse momentum (kT) on reproducing experimental pion spectra in pp and pA collisions.
• To compare different nuclear shadowing models (b-independent vs. b-dependent) in dAu collisions at RHIC, especially in centrality-binned data.
• To test whether the nuclear modification factor R_dAu can distinguish between competing shadowing parameterizations using centrality-dependent measurements.

Proposed method

• Uses a next-to-leading order (NLO) pQCD-improved parton model with factorized 3D parton distribution functions (PDFs) incorporating intrinsic kT via a Gaussian distribution g(kT) = (1/π⟨kT²⟩)exp(−kT²/⟨kT²⟩).
• Applies fixed-scale prescriptions: factorization and renormalization scales set to Q = κ·pT/zc, and fragmentation scale QF = κ·pT, with κ ≈ O(1).
• Employs NLO PDFs (MRST(cg)) and fragmentation functions (KKP) down to Q² ≈ 1.25 GeV² to access low pT ≥ 2 GeV.
• Calculates pion production cross sections via convolution of PDFs, partonic cross sections (dσ̃/dv), and fragmentation functions (Dcπ(zc, QF²)).
• Incorporates nuclear effects via multiscattering (via C·h_pA(b)) and shadowing (EKS, updated HIJING b-independent and b-dependent models).
• Performs NLO calculations with kT-enhanced PDFs and compares results to pp data and pA data at SPS and RHIC, focusing on nuclear modification factor R_pA and R_dAu.

Experimental results

Research questions

• RQ1 How does the inclusion of intrinsic partonic transverse momentum (kT) affect the description of pion spectra in pp and pA collisions at NLO in pQCD?
• RQ2 What is the role of nuclear multiscattering and shadowing in shaping the Cronin peak in pion spectra across different target nuclei and energies?
• RQ3 How do different nuclear shadowing parameterizations (b-independent vs. b-dependent) affect the centrality dependence of R_dAu in dAu collisions at √s = 200 GeV?
• RQ4 Can the nuclear modification factor R_dAu in dAu collisions distinguish between competing shadowing models, especially in peripheral and central bins?
• RQ5 To what extent do the Cronin peak position and height depend on the intrinsic kT parameter ⟨kT²⟩ and target mass number A?

Key findings

• The inclusion of intrinsic kT with ⟨kT²⟩ ≈ 2 GeV² successfully reproduces the Cronin peak in pion spectra across the 20–200 GeV c.m. energy range in pA collisions.
• At SPS energies (158 AGeV), multiscattering dominates over shadowing, and the Cronin peak appears at pT ≈ 4 GeV with a height increasing with target mass number A.
• At RHIC energy (√s = 200 GeV), shadowing effects become significant (up to ~20%), and b-dependent shadowing leads to a unique structure in R_dAu(b), with R_dAu > 1 in central bins and R_dAu ≈ 1 in peripheral bins.
• Despite different b-dependence, minimum bias R_dAu results are nearly identical for b-independent and b-dependent shadowing models, due to averaging over impact parameters.
• Theoretical NLO predictions with kT-enhanced PDFs reproduce the PHENIX dAu minimum bias π⁰ data within experimental uncertainties, validating the model at RHIC energies.
• The Cronin peak position is insensitive to c.m. energy but strongly dependent on ⟨kT²⟩, with peak height scaling with the multiscattering term C·h_pA(b) and increasing with A.