Cronin effect vs. geometrical shadowing in d+Au collisions at RHIC

TL;DR

The paper addresses the origin of the Cronin effect and potential dynamical shadowing in $pA$ and $dA$ collisions at RHIC, asking whether non-linear QCD dynamics suppress moderate-$p_T$ yields. It develops a Glauber-Eikonal (GE) framework that computes the full GE series using perturbative QCD parton-nucleon cross sections, preserves unitarity, and includes finite-$x$ kinematics and fragmentation via $D_{i\rightarrow h}$. The approach yields a dipole-nucleus interpretation of multiple scatterings and connects with classical Yang-Mills/MV saturation pictures, providing a robust baseline for geometrical shadowing. PP data at $\sqrt{s}=27.4$ GeV and $200$ GeV are used to fix the infrared regulator $p_0$, the $K$-factor, and an intrinsic transverse momentum width $\langle k_T^2\rangle = 0.52$ GeV$^2$, after which the model makes parameter-free predictions for $pA$ spectra. Applied to RHIC data at $\sqrt{s}=200$ GeV, the GE framework reproduces the Cronin enhancement at moderate $p_T$ and provides centrality-dependent expectations, with only mild excess at low $p_T$, and finds no strong evidence for CGC-like dynamical shadowing; the formalism serves as a baseline to quantify dynamical shadowing in future measurements.

Abstract

Multiple initial state parton interactions in p(d)+Au collisions are calculated in a Glauber-Eikonal formalism. The convolution of perturbative QCD parton-nucleon cross sections predicts naturally the competing pattern of low-pT suppression due geometrical shadowing, and a moderate-pT Cronin enhancement of hadron spectra. The formal equivalence to recent classical Yang-Mills calculations is demonstrated, but our approach is shown to be more general in the large x>0.01 domain because it automatically incorporates the finite kinematic constraints of both quark and gluon processes in the fragmentation regions, and accounts for the observed spectra in elementary pp-->π+X processes in the RHIC energy range, sqrt{s} = 20-200 GeV. The Glauber-Eikonal formalism can be used as a baseline to extract the magnitude of dynamical shadowing effects from the experimental data at differente centralities and pseudo-rapidities.

Figures (4)

• Figure 1: Top panel: pion transverse momentum spectrum at $\sqrt s = 27.4$ GeV and $\sqrt s = 200$ GeV. Solid lines are LO pQCD computations according to Eq. \ref{['ppcoll_pt']}, with $\langle k_T^2 \rangle=0.52$ GeV$^2$ and $Q_p=Q_h=m_T/2$. The regulator $p_0$ and the $K$-factor are given in Table \ref{['table:p0Kfits']}. Bottom panels: the data to theory ratio for different choices of parameters. Solid lines are for $Q_p=Q_h=m_T/2$, dashed lines $Q_p=Q_h=m_T$. The pair of thin lines is computed with no $k_T$ smearing, $\langle k_T^2 \rangle=0$ GeV$^2$, and the pair of thick lines is computed with $\langle k_T^2 \rangle=0.52$ GeV$^2$. In the $\pi^0$ case Adler03pp, the dashed area shows the relative statistical and point-to-point systematic error added in quadrature, and does not include the systematic uncertainty of 9.6%, on the absolute normalization of the spectrum. In the $\pi^\pm$ case Antreasyan79, the shaded area includes statistical error only, without a systematic uncertainty of 20% on the absolute normalization of the spectrum.
• Figure 2: Cronin effect in charged pion production at $\sqrt s=27.4$ GeV. Plotted is the ratio of the minimum bias charged pions $q_T$ spectrum at $\eta=0$ in $pW$ and $pBe$ collisions. The solid line is for a scale choice $Q_p=Q_h=m_T/2$ and intrinsic $\langle k_T \rangle=0.52$ GeV$^2$. The theoretical error due to the uncertainty in $p_0=0.8\pm0.1$ GeV is shown as a dotted band. The dashed line shows the result without intrinsic $k_T$ (the theoretical uncertainty is not shown in this case). Data points taken from Ref. Antreasyan79.
• Figure 3: Cronin ratio in minimum bias d+Au collisions at $\sqrt s=200$ GeV. Left: Cronin effect on neutral pion production. The solid line is for $Q_p=Q_h=m_T/2$ and $\langle k_T \rangle=0.52$ GeV$^2$. The theoretical error due to the uncertainty in $p_0=1.0\pm0.1$ GeV is shown as a dotted band. The dashed line is computed with no $k_T$ smearing, $\langle k_T^2 \rangle=0$ GeV$^2$, and its theretical uncertainty is not shown. Data points are from the PHENIX collaboration, Ref. PHENIX. Error bars represent statistical errors. The empty bands show systematic errors which can vary with $q_T$. The bar at the left indicates the systematic uncertainty in the absolute normalization of the pA cross section. Right: Cronin Effect on gluon (dashed line), quark (dot-dashed) and averaged quark and gluon production (solid), with $Q_p=Q_h=m_T/2$ and $\langle k_T^2 \rangle=0.52$ GeV$^2$.
• Figure 4: Central to peripheral ratio for neutral pion production in minimum bias d+Au collisions at $\sqrt s=200$ GeV. The central 0-20% bin corresponds to an average $b=3.5$ fm and the peripheral 60-88% bin to an average $b=6.5$ fm. The solid line is computed with a scale choice $Q_p=Q_h=m_T/2$ The theoretical error due to the uncertainty in $p_0=1.0\pm0.1$ GeV is shown as a dotted band.