[Paper Review] The in-medium scale evolution in jet modification

Abhijit Majumder|ArXiv.org|Jan 28, 2009

Plasma and Flow Control in Aerodynamics17 citations

TL;DR

This paper proposes a novel in-medium DGLAP-like evolution equation for jet fragmentation functions, incorporating higher-twist corrections from multiple gluon emissions in dense nuclear matter. By resumming next-to-leading twist single-gluon emission kernels alongside vacuum evolution, it enables distance-dependent virtuality evolution of fragmentation functions, significantly improving agreement with DIS data on nuclear attenuation—especially for heavy nuclei like Xe—compared to single-emission models.

ABSTRACT

The in-medium modification of the scale dependence of the fragmentation function in dense matter, brought about by higher twist corrections to the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations, is derived. A phenomenologically motivated resummation is outlined which incorporates the next-to-leading twist single gluon emission kernel along with the vacuum emission kernel and provides an in-medium virtuality evolution of the final fragmentation function of a hard jet propagating through dense matter. The concept of a fragmentation function is generalized to include a dependence on distance traveled in the medium. Following this, numerical implementations are carried out and compared to experimental results on the single inclusive suppression observed in Deep-Inelastic scattering (DIS) off a large nucleus.

Motivation & Objective

• To address the lack of scale evolution in medium-modified fragmentation functions, which are critical for modeling jet quenching in heavy-ion collisions.
• To extend the DGLAP evolution formalism to dense nuclear matter by incorporating higher-twist corrections from multiple parton emissions.
• To develop a phenomenologically motivated resummation of in-medium gluon radiation that captures virtuality evolution of fragmentation functions.
• To compare predictions with experimental data on single-hadron-inclusive suppression in deep-inelastic scattering (DIS) off large nuclei.
• To demonstrate the necessity of including multiple emissions and multiple scattering for accurate description of nuclear attenuation in heavy nuclei.

Proposed method

• Derives an in-medium evolution equation for fragmentation functions by generalizing the DGLAP formalism to include higher-twist corrections from single-gluon emission kernels in dense matter.
• Introduces a distance-dependent fragmentation function that evolves with the path length traveled in the medium, incorporating virtuality evolution via the in-medium kernel $ K_{q^{-},M^{2}}(y,\zeta) $.
• Uses a hard-sphere nuclear density distribution $ \rho(\zeta) = \rho_0 \theta(R_A - |\zeta|) $ as an input Ansatz for medium structure.
• Applies a phenomenological resummation of the next-to-leading twist emission kernel, combining it with the standard vacuum DGLAP kernel to model in-medium shower evolution.
• Performs numerical implementations using the medium-modified fragmentation function in factorized cross sections for DIS on $ ^{20}Ne $, $ ^{84}Kr $, and $ ^{132}Xe $.
• Compares results to HERMES data, testing both single-emission and multiple-emission models, and includes a phenomenological extension to account for hadronic energy loss.

Experimental results

Research questions

• RQ1 How does the scale dependence of the fragmentation function evolve in dense nuclear matter when higher-twist corrections are included?
• RQ2 To what extent does multiple gluon emission improve the description of nuclear attenuation in DIS compared to single-emission models?
• RQ3 Can a resummed in-medium evolution equation for fragmentation functions reproduce experimental data on hadron suppression in large nuclei?
• RQ4 How does the inclusion of hadronic energy loss affect the agreement between theory and data at small $ z $?
• RQ5 What is the required range of the jet quenching parameter $ \hat{q}_0 $ to fit experimental data across different nuclei?

Key findings

• The inclusion of multiple emissions via the in-medium evolution equation (Eq. 7) leads to a marked improvement in agreement with experimental data on nuclear attenuation, especially for heavy nuclei like Xe.
• The single-emission model (red dashed line) shows systematic deviations from data for larger nuclei, particularly in the $ z \to 0 $ region, indicating the need for multiple emission effects.
• The full in-medium evolution model (blue solid line) achieves significantly better agreement with data across all three nuclei, demonstrating the importance of virtuality evolution in dense matter.
• A phenomenological extension that suppresses fragmentation from soft gluons (green dot-dashed line) yields the best agreement with Xe data, suggesting hadronic energy loss is non-negligible at small $ z $.
• The best-fit medium gluon density $ \rho_0 $ spans a range corresponding to $ \hat{q}_0 \approx 0.06 - 0.18 \, \text{GeV}^2/\text{fm} $, consistent with expectations from jet quenching studies.
• The results validate the use of resummed higher-twist corrections in modeling jet modification in dense matter, providing a foundation for future applications in heavy-ion collisions.