Exploring nuclear modification using one-point energy correlator at the electron-ion collider

TL;DR

The paper addresses how cold nuclear matter modifies energy-flow observables in SIDIS and in-jet contexts at the Electron-Ion Collider by developing a unified $TMD$-factorization framework for the one-point energy correlator (OPEC) in both the back-to-back and collinear limits. It constructs unsubtracted $f_q^{(u)}$ and $J_q^{(u)}$ objects, removes rapidity divergences to obtain physical $f_q$ and $J_q$, and implements RG evolution with Collins-Soper scales to predict nuclear effects through nTMD PDFs and nTMD FFs, including nonperturbative Sudakov factors. Phenomenological results show a clear suppression in $e+A$ relative to $e+p$ in both limits, with nuclear effects arising from both initial- and final-state nTMDs in the back-to-back case and dominated by final-state in-jet soft radiation for the collinear case; the suppression is quantified as $R_{eA}^{ ext{b.t.b.}}$ and $R_{eA}^{ ext{coll.}}$ across kinematics relevant to the EIC. The work demonstrates that OPEC is a sensitive, energy-weighted probe of TMD dynamics and cold nuclear matter, offering a differential observable for future EIC measurements that complements traditional TMD studies.

Abstract

We study the one-point energy correlator (OPEC) at both the back-to-back and collinear limits in electron-proton and electron-nucleus collisions. We provide the factorization formalism for the two types of OPEC and present phenomenological predictions in the kinematic region relevant for the future Electron-Ion Collider. Focusing on cold nuclear matter effects in electron-nucleus scattering, we demonstrate that the OPEC serves as a powerful probe of the transverse momentum dependent (TMD) physics and in characterizing the medium-induced transverse momentum broadening in cold nuclear matter.

Figures (7)

• Figure 1: Illustration of OPEC for DIS in the Breit frame, where the incoming proton or nucleus ($p$/$A$) moves along the $-z$ axis and the virtual photon $\gamma^*$ propagates along the $+z$ direction. Together with the incoming lepton, they define the lepton plane (shown in gray). The angle between the detector that measures hadron $h$ and the incoming proton or nucleus is denoted as $\theta_h$.
• Figure 2: Left: OPEC at the back-to-back region as a function of $\tau$. We choose a center-of-mass energy of $\sqrt{s} = 90~\mathrm{GeV}$, photon's virtuality $Q^2 = 20~\mathrm{GeV}^2$ and $x = 0.05$. The black and red solid curves represent the $e+p$ and $e+\mathrm{Au}$ results, respectively. Right: The corresponding nuclear modification factor $R_{eA}^{\mathrm{b.t.b.}}$ in \ref{['eq:Ratio-b2bEC']} as a function of $\tau$. The red solid curve represents the complete calculation of the numerator in $R_{eA}^{\mathrm{b.t.b.}}$ using both nTMD PDFs and nTMD FFs. In contrast, the red dashed line shows the $R_{eA}^{\mathrm{b.t.b.}}$ obtained using nTMD PDFs and vacuum TMD FFs, whereas the dotted line is computed using the vacuum TMD PDFs and nTMD FFs.
• Figure 3: Left: OPEC at the back-to-back region for $e+p$ and $e+\mathrm{Au}$ collisions as a function of Bjorken $x$. Right: The corresponding nuclear modification factor as a function of Bjorken $x$. The meaning of dashed and dotted red lines in the right panel is identical to that in \ref{['fig:EEC_DIS_vs_tau']}.
• Figure 4: Back-to-back electron and jet production in unpolarized electron-proton or electron-nucleus collisions. A hadron within the jet is measured. The jet axis and the beam direction define the $xz$-plane. A detailed illustration of the jet cone and hadron kinematics is given in \ref{['fig:cone']}.
• Figure 5: A hadron inside a jet characterized by its transverse momentum $\bm{j}_{\perp}$ and polar angle $\theta$, both measured relative to the jet axis $z_J$.