[Paper Review] Modeling nuclear parton distribution functions

H. Honkanen, M. Strikman+1 more|arXiv (Cornell University)|Oct 22, 2013

Particle physics theoretical and experimental studies3 references3 citations

TL;DR

This paper proposes a refined model for nuclear parton distribution functions (nPDFs) by combining the FGS1/2 theoretical framework for small-x nuclear shadowing with the phenomenological EKS98/EPS09 nPDF sets, incorporating corrections for the proper definition of Bjorken-x and equivalent photon contributions. The key result is that correcting for x-shift and photon contributions significantly alters predictions for forward pion production in p+Pb collisions at the LHC, especially in the EMC region and at high transverse momentum, with measurable effects on nuclear modification ratios.

ABSTRACT

The presence of nuclear medium and collective phenomena which involve several nucleons modify the parton distribution functions of nuclei (nPDFs) compared to those of a free nucleon. These modifications have been investigated by different groups using global analyses of high energy nuclear reaction world data resulting in modern nPDF parametrizations with error estimates, such as EPS09(s), HKN07 and nDS. These phenomenological nPDF sets roughly agree within their uncertainty bands, but have antiquarks for large-$x$ and gluons for the whole $x$-range poorly constrained by the available data. In the kinematics accessible at the LHC this has negative impact on the interpretation of the heavy-ion collision data, especially for the $p + A$ benchmarking runs. The EMC region is also sensitive to the proper definition of $x$, where the nuclear binding effects have to be taken into account, and for heavy nuclei one also needs to take into account that a fraction of the nucleus momentum is carried by the equivalent photons which modifies the momentum sum rule. We study how these effects affect the predictions for the nuclear modification ratios at the LHC kinematics using a model where we combine theoretical input for the leading twist nuclear shadowing (the FGS model) and the EKS98s/EPS09s nPDF set where the spatial dependence is formulated as a power series of the nuclear thickness functions $T_A$.

Motivation & Objective

• To address inaccuracies in nPDF parametrizations arising from improper definition of Bjorken-x in nuclear collisions.
• To quantify the impact of nuclear binding and equivalent photon contributions on gluon momentum fraction and nuclear modification ratios.
• To develop a theoretically motivated nPDF model combining FGS shadowing with EKS98/EPS09 parametrizations for improved LHC predictions.
• To assess the sensitivity of forward pion production in p+Pb collisions to x-shift and impact parameter-dependent effects.
• To provide a foundation for future NLO, impact-parameter-dependent nPDF sets with improved EMC region modeling.

Proposed method

• The model combines the FGS1/2 small-x nuclear shadowing framework with the EKS98/EPS09 nPDF sets, using polynomial interpolation between the two in the intermediate x-region.
• A correction is applied to the x-variable using the shift $ x_{\text{shift}} = x_p / (1 + r_x^A) $, where $ r_x^A $ accounts for nuclear binding energy and mass differences.
• The gluon distribution is rescaled via $ g_{\text{scale}} = (\eta_g - \eta_\gamma(A)) / \eta_g $ to conserve the momentum sum rule, accounting for equivalent photon contributions.
• The model is validated using p+Pb → π⁰ production cross sections at LHC energies, with factorization and renormalization scales set to $ p_T $.
• Impact parameter dependence is modeled via spatially dependent nuclear thickness functions $ T_A(\mathbf{s}) $, with centrality classes derived from the optical Glauber model.
• Results are compared to EKS98s and EPS09s nPDF sets, with emphasis on mid-rapidity and forward-rapidity pion production.

Experimental results

Research questions

• RQ1 How does the proper definition of Bjorken-x, accounting for nuclear binding, affect nPDF predictions in the EMC region?
• RQ2 To what extent do equivalent photons in high-energy nuclear collisions alter the momentum sum rule and gluon distribution in nPDFs?
• RQ3 How do x-shift corrections and photon contributions impact nuclear modification ratios $ R_{p\text{Pb}}^{\pi^0} $ in forward pion production at the LHC?
• RQ4 How do the FGS1/2 shadowing models compare with EKS98/EPS09 parametrizations in the forward rapidity regime?
• RQ5 What is the impact of spatially dependent nPDFs on centrality-dependent pion yields in p+Pb collisions?

Key findings

• The x-shift correction alone causes a measurable and significant deviation in $ R_{p\text{Pb}}^{\pi^0} $ at forward rapidity, especially above $ p_T \sim 10 $ GeV, with effects exceeding 5% in high-$ p_T $ regions.
• The gluon scaling factor $ g_{\text{scale}} $ is found to be $ 0.93 $ for $ ^{208}\text{Pb} $ at $ Q_0^2 = 2.5 $ GeV², reducing the gluon momentum fraction by ~7% due to equivalent photons.
• In mid-rapidity pion production, the FGS+EKS98 model shows only minor deviations (<3%) from EKS98 results, as the dominant contribution comes from small-x gluons.
• In forward rapidity, the FGS1 and FGS2 models become indistinguishable above $ p_T \sim 10 $ GeV, but both deviate significantly from EKS98 due to x-shift and shadowing effects.
• The impact parameter dependence of the EMC effect is expected to be strongest in the nuclear center due to local density and short-range correlation scaling, supporting spatially resolved nPDF modeling.
• The study demonstrates that neglecting x-shift and photon corrections leads to systematic errors in interpreting LHC p+Pb benchmarking data, particularly in the forward region.