Predictions for p+Pb at 4.4A TeV to Test Initial State Nuclear Shadowing at energies available at the CERN Large Hadron Collider

TL;DR

Problem: quantify the role of initial-state nuclear shadowing in $p+{\rm Pb}$ at 4.4$A$ TeV to calibrate the baseline for Pb+Pb jet quenching studies. Approach: compare collinear factorized pQCD predictions using DGLAP-evolved nPDFs (e.g., EKS99, EPS08) with fixed-$Q^2$ HIJING shadowing and CGC-based models across rapidities and centralities, computing $R_{p{\rm Pb}}(p_T)$ and related observables. Key findings: DGLAP-evolved shadowing yields $R_{p{\rm Pb}}(p_T>5\,\mathrm{GeV}/c) \approx 1\pm0.1$, while fixed-$Q^2$ shadowing and CGC models predict $R_{p{\rm Pb}}(p_T) \approx 0.6$–0.7$ at mid-rapidity and stronger suppression at forward rapidity; central collisions amplify the effect. Significance: measurements of $R_{p{\rm Pb}}$ at the LHC can decisively discriminate initial-state shadowing scenarios and refine interpretations of Pb+Pb jet quenching and bulk observables.

Abstract

Collinear factorized perturbative QCD model predictions are compared for p+Pb at 4.4A TeV to test nuclear shadowing of parton distribution at the Large Hadron Collider (LHC). The nuclear modification factor (NMF), R_{pPb}(y=0,p_T<20 GeV/c) = dn_{p Pb} /(N_{coll}(b)dn_{pp}), is computed with electron-nucleus (e+A) global fit with different nuclear shadow distributions and compared to fixed Q^2 shadow ansatz used in Monte Carlo Heavy Ion Jet Interacting Generator (HIJING) type models. Due to rapid DGLAP reduction of shadowing with increasing Q^2 used in e+A global fit, our results confirm that no significant initial state suppression is expected (R_{pPb} (p_T) = 1 \pm 0.1) in the p_T range 5 to 20 GeV/ c. In contrast, the fixed Q^2 shadowing models assumed in HIJING type models predict in the above p_T range a sizable suppression, R_{pPb} (p_T) = 0.6-0.7 at mid-pseudorapidity that is similar to the color glass condensate (CGC) model predictions. For central (N_{coll} = 12) p+ Pb collisions and at forward pseudorapidity (η= 6) the HIJING type models predict smaller values of nuclear modification factors (R_{pPb}(p_T)) than in minimum bias events at mid-pseudorapidity (η= 0). Observation of R_{pPb}(p_T= 5-20 GeV/c) less than 0.6 for minimum bias p+A collisions would pose a serious difficulty for separating initial from final state interactions in Pb+Pb collisions at LHC energies.

Figures (4)

• Figure 1: (Color online) (a) HIJING/BB̄2.0 predictions of charged particles pseudorapidity distribution $(dN_{\rm ch}/d\eta)$ for minimum bias (MB) $p$+Pb collisions at 4.4$A$ TeV. Solid YS curve includes fixed $Q^2$ shadowing functions from HIJING1.0 Wang:1991hta, while the dashed NS curve has no shadowing. (b) Ratio $R_{pPb}(\eta)$ calculated assuming $N_{\rm coll}({\rm MB})=6.4$
• Figure 2: (Color online) (a) Minimum bias transverse momentum distributions at mid-pseudorapidity $|\eta|<0.8$ predicted by HIJING/BB̄2.0 with (solid histogram) and without (dashed histogram) HIJING1.0 shadowing functions Wang:1991hta. The results for $p+p$ collisions at 4.4 TeV (dotted histogram) are also included. (b) The mid-pseudorapidity nuclear modification factor of charged hadrons $R_{p{\rm Pb}}$ from HIJING/BB̄2.0 model. The solid and thin dashed histograms have the same meaning as in part (a). They are compared to pQCD leading order (LO) predictions (dash dotted) Levai11 using HIJING2.0 shadowing functions Deng:2010mv, and to DGLAP $Q^2$ evolved nPDF, EKS99 (dotted) Eskola:1998df. Predictions of CGC model (thick dashed) Kharzeev:2003wz (KKT04) and CGC - rcBK model (thick solid) from Ref. Tribedy:2011aa are also included.
• Figure 3: (Color online) Predictions updated at 4.4$A$ TeV of Refs. Levai11 results for central $0-20\%$ ($b<3.5$ fm) $p+Pb$ at mid-rapidity. The original predictions at 0.2$A$ TeV for $d+{\rm Au}$ are also included. Compared are the results obtained with fixed $Q^2$ shadowing functions HIJING2.0 Deng:2010mv with (b-dep) and without (b-indep) impact parameter dependence. Predictions with DGLAP $Q^2$ evolved shadowing functions from Ref. Eskola:1998df (EKS99) and Ref. EPS08 (EPS08) are also shown. The data are from PHENIX Collaboration Adler:2006wg.
• Figure 4: (Color online) (a) The minimum bias (MB) NMF of charged particles at forward pseudorapidity $\eta = 6$, from HIJING/BB̄2.0 model (dashed histogram). The results are obtained with shadowing functions from the HIJING1.0 model Wang:1991hta. They are compared to pQCD leading order (LO) results at $\eta = 6$ (dash dotted) Levai11 using impact parameter dependent (b-dep) HIJING2.0 shadowing functions Deng:2010mv and to predictions obtained with DGLAP $Q^2$ evolved shadowing functions (dotted) with no impact parameter dependence (b-indep) from Ref. EPS08. For reference the results at mid-pseudorapidity, $|\eta|<0.8$ (solid histogram) are also included. (b) The results obtained for NMF of charged particles in central ($N_{\rm coll} = 12$) $p$+Pb collisions at 4.4$A$ TeV. The histograms and the lines have the same meaning as in part (a).