Probing nuclear dynamics in jet production with a global event shape

TL;DR

This paper introduces a global event shape, 1-jettiness $\tau_1$, as a tool to study jet production in electron-nucleus collisions within a Soft-Collinear Effective Theory framework. By focusing on the region $\tau_1 \ll P_{J_T}$, it derives a factorization formula $d^3\sigma \sim H \otimes B \otimes J \otimes \mathcal{S}$ and performs NNLL resummation, with the nuclear target dependence entering through nuclear PDFs $f_{i/A}$ via beam functions. It also develops a universal, non-perturbative soft-function model and analyzes power corrections that scale with $Q_s^2(A)/(\tau_1 t_a)$, showing how $\tau_1$-distributions and their ratios to the proton target can reveal EMC and shadowing effects while suppressing perturbative uncertainties. Numerical results using EPS09 demonstrate sensitivity to nuclear PDFs across $\tau_1$, $P_{J_T}$, and rapidity $y$, and reveal the potential of $e$-A colliders (EIC/LHeC) to probe cold nuclear matter dynamics with high precision.

Abstract

We study single jet production in electron-nucleus collisions e^- + N_A -> J + X, using the 1-jettiness (τ_1) global event shape. It inclusively quantifies the pattern of radiation in the final state, gives enhanced sensitivity to soft radiation at wide angles from the nuclear beam and final-state jet, and facilitates the resummation of large Sudakov logarithms associated with the veto on additional jets. Through their effect on the observed pattern of radiation, 1-jettiness can be a useful probe of nuclear PDFs and power corrections from dynamical effects in the nuclear medium. This formalism allows for the standard jet shape analysis while simultaneously providing sensitivity to soft radiation at wide angles from the jet. We use a factorization framework for cross-sections differential in $τ_1$ and the transverse momentum (P_{J_T}) and rapidity (y) of the jet, in the region τ_1<< P_{J_T}. The restriction $τ_1 << P_{J_T}$ allows only soft radiation between the nuclear beam and jet directions, thereby acting as a veto on additional jets. This region is also insensitive to the details of the jet algorithm, allowing for better theoretical control over resummation, while providing enhanced sensitivity to nuclear medium effects. We give numerical results at leading twist, with resummation at the next-to-next-to-leading logarithmic (NNLL) level of accuracy, for a variety of nuclear targets. Such studies would be ideal for the EIC and the LHeC proposals for a future electron-ion collider, where a range of nuclear targets are planned.

Figures (13)

• Figure 1: Schematic figure of the process $e^- + N_A \to J + X$ in the limit $\tau_1\ll P_{J_T}$. The restriction $\tau_1\ll P_{J_T}$ allows only soft radiation between the beam and jet directions. The factorization framework for this process is schematically shown in Eqs.(\ref{['schem-1']}) and (\ref{['schem-2']}).
• Figure 2: Cross-section differential in $\tau_1$ and y with NNLL resummation for a proton target, at $P_{J_T}=20$ GeV and center of mass energy of 90 GeV.
• Figure 3: Nuclear correction factors $R_i^{\text{Ur}}(x,\mu)$ for the NLO nuclear PDF for a Uranium target as defined in Eq.(\ref{['EPS09']}). The subscript $i$ runs over the parton species $i=\{u,d,s,g\}$. For the $u$ and $d$ quarks, separate $R$-factors are given for the valence (V) and sea quarks (S). The different curves in each graph correspond to different values for the scale $\mu$. By looking at the region of small Bjorken-$x$, the different curves from the bottom to the top correspond to $\mu=3$ GeV (Green), $\mu=5$ GeV (Blue), $\mu=10$ GeV (Red), and $\mu=20$ GeV (Purple). These plots were generated using publicly available code for the EPS09 PDF set Eskola:2009uj.
• Figure 4: Luminosity ratio for Uranium to proton using NLO PDFs for $\mu=3$ GeV (Green), $\mu=5$ GeV (Blue), $\mu=10$ GeV (Red), and $\mu=20$ GeV (Purple).
• Figure 5: $\tau_1$ distribution for a proton target with NLL$^\prime$ (lower red band) and NNLL (upper green band) resummation for $Q=90$ GeV, $P_{J_T}=20$ GeV and $y=0$. A more detailed description is given in the text.