Jet Charge with Global Event Shapes: Probing Quark Flavor Dynamics

TL;DR

This work introduces the 1-Jettiness Jet Charge observable, enabling simultaneous access to quark flavor dynamics in both the initial-state nucleon and final-state hadronization by measuring the jet region charge ${\cal Q}$ within the global energy-flow variable $\tau_1$. It formulates a SCET-based factorization framework where the standard jet function is replaced by a universal charged jet function ${\cal G}^q({\cal Q},s_J,\mu)$, related to the ordinary jet function $J^q$ via a nonperturbative but universal kernel $R^q({\cal Q},y)$; the cross section in the resummation region $\tau_1\ll P_{J_T}$ is thus $d\sigma_{\rm resum}[{\cal Q},\tau_1,P_{J_T},y_J] = H \otimes B \otimes {\cal G} \otimes {\cal S}$. The authors establish universality of the charged jet function across observables (e.g., N-Jettiness, thrust), provide a general nonperturbative modeling strategy for $R^q$ including simple and PYTHIA-informed parameterizations, and demonstrate via PYTHIA simulations that jet-charge binning in $\tau_1$-dependent distributions enhances flavor separation in nucleon PDFs and offers sensitivity to hadronization dynamics. The framework is directly applicable to the EIC and existing HERA data, with extensions to polarized PDFs and charged-current DIS outlined for future work. Overall, this approach provides a principled path to disentangle flavor effects in both parton distributions and hadronization using jet charge within global event shape analyses.

Abstract

We propose measuring the jet electric charge of jet regions, defined within the framework of global event shapes, as a probe of quark flavor dynamics within the nucleon and the hadronization process. In particular, we consider a measurement of the jet region charge while simultaneously keeping track of the energy flow throughout the event, as characterized by the global event shape. As a concrete example, we focus on the measurement of the 1-Jettiness jet charge ($Q$), the jet charge of the jet region ($J$) defined within the framework of the 1-Jettiness global event shape ($τ_1$) for the Deep Inelastic Scattering (DIS) process, $e^- + p \to e^- + J + X$, with unpolarized or longitudinally polarized protons. The 1-Jettiness distribution, binned according to jet charge, allows for enhanced quark flavor separation of the initial state unpolarized or polarized PDFs. On the other hand, the jet charge distribution binned by 1-Jettiness can serve as a probe of quark flavor dynamics in the final state hadronization process. We derive a factorization theorem for simultaneous measurements of $τ_1$ and $Q$ in the resummation region, $τ_1 \ll P_{J_T}$, where $P_{J_T}$ denotes the transverse momentum of the jet region. The factorization theorem contains a new universal charged jet function, generalizing the standard jet function to include a jet charge measurement. Therefore these universal functions can be extracted from a global analysis of N-jettiness and thrust at $e^+e^-$ colliders. We provide simulation studies to demonstrate the sensitivity of the 1-Jettiness jet charge observable to quark flavor dynamics in nucleon structure and explore the possibility of probing the final state hadronization process. This observable is well-suited for applications in existing HERA data and the future Electron-Ion Collider (EIC).

Figures (9)

• Figure 1: Pythia 8.312 simulation data (blue dots) for the normalized 1-Jettiness $\tau_1$-distribution compared to the theoretical prediction at the N$^3$LL level of accuracy with a soft function model that describes hadronization effects. The scale variations (pink band), describing the theoretical uncertainty, are normalized to the central curve (red) over the displayed range. The relevant EIC kinematics chosen are: $\sqrt{s}=90.0$ GeV, $P_{J_T}= [20.0,30.0]$ GeV, and $y_J=[-2.5,2.5]$.
• Figure 2: The fraction of jets initiated by the $u$-quark (top panel) and $d$-quark (bottom panel) in the positive $(Q_J>0.25)$, negative $(Q_J<-0.25)$, and central $(-0.25 < Q_J<0.25)$ Standard Jet Charge bins as a function of the squared jet mass, $M_J^2$. The dashed lines indicate the corresponding average values from the fraction of jets over all squared jet mass bins. The relevant EIC kinematics chosen for generating the Pythia 8.312 simulation data are: $\sqrt{s}=90.0$ GeV, $P_{J_T}= [20.0,30.0]$ GeV, and $y_J=[-2.5,2.5]$.
• Figure 3: The fraction of jets initiated by the $u$-quark (top panel) and $d$-quark (bottom panel) in the positive $(Q_J>0.25)$, negative $(Q_J<-0.25)$, and central $(-0.25 < Q_J<0.25)$ Dynamic Jet Charge bins as a function of the squared jet mass, $M_J^2$. The dashed lines indicate the corresponding average values from the fraction of jets over all squared jet mass bins. The relevant EIC kinematics chosen for generating the Pythia 8.312 simulation data are: $\sqrt{s}=90.0$ GeV, $P_{J_T}= [20.0,30.0]$ GeV, and $y_J=[-2.5,2.5]$.
• Figure 4: The normalized 1-Jettiness $\tau_1$-distribution (black) using Pythia data along with the relative contributions of different quark flavors. The relevant EIC kinematics chosen are: $\sqrt{s}=90.0$ GeV, $P_{J_T}= [20.0,30.0]$ GeV, and $y_J=[-2.5,2.5]$.
• Figure 5: The normalized 1-Jettiness $\tau_1$-distribution (black) using Pythia data along with the relative contributions from the negative (blue), central (gray), and positive (red) standard jet charge bins corresponding to ${\cal Q} <-0.25$, $-0.25< {\cal Q} <0.25$, and ${\cal Q} >0.25$, respectuvely. The relevant EIC kinematics chosen are: $\sqrt{s}=90.0$ GeV, $P_{J_T}= [20.0,30.0]$ GeV, and $y_J=[-2.5,2.5]$.