# Exclusive $η_c$ production from small-$x$ evolved Odderon at a electron-ion collider

**Authors:** Sanjin Benić, Davor Horvatić, Abhiram Kaushik, Eric Andreas Vivoda  
**arXiv:** [2306.10626](https://arxiv.org/abs/2306.10626)  
**Date:** 2023-06-18  
**Summary page:** https://www.summarizepaper.com/en/paper/2306.10626v1/

## Key points

- Study focuses on exclusive production of $\eta_c$ in high energy electron-nucleon and electron-nucleus collisions
- Emphasis on sensitivity to the Odderon, a $C$-odd color singlet in perturbative QCD
- Utilizes Color Glass Condensate effective theory to analyze Odderon exchange at elevated collision energies
- Observes that cross section off a proton is primarily governed by Primakoff process at low momentum transfers, but Odderon influence increases at higher momentum transfers
- Neutron targets can provide valuable information about the Odderon due to suppression of Primakoff component at low-$t$
- Odderon cross section enhancement observed with nuclear targets due to mass number of nucleus
- Gluon saturation effects lead to distinct shift in diffractive patterns compared to Primakoff process, serving as a potential signal for detecting Odderon presence
- Findings situated within broader context of contemporary research in high-energy physics and nuclear interactions

## Summary

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In this study, we focus on the exclusive production of $\eta_c$ in high energy electron-nucleon and electron-nucleus collisions, with a particular emphasis on its sensitivity to the Odderon. The Odderon is a $C$-odd color singlet in perturbative QCD, composed of at least three $t$-channel gluons exchanged with the target. Utilizing the Color Glass Condensate effective theory, our analysis delves into the potential impact of Odderon exchange at elevated collision energies expected at a prospective electron-ion collider. By employing the Balitsky-Kovchegov evolution equation with running coupling corrections, we can evolve the Odderon distribution to small-$x$, revealing intriguing insights into its behavior. At low momentum transfers $t$, we observe that the cross section off a proton is predominantly governed by the Primakoff process. However, as momentum transfers increase ($|t|\geq1.5$ GeV$^2$), the influence of the Odderon becomes more pronounced. Moreover, we highlight that neutron targets could serve as valuable probes for extracting information about the Odderon at low-$t$. This is due to significant suppression of the Primakoff component in such scenarios. When considering nuclear targets, we find that the Odderon cross section experiences enhancement due to the mass number of the nucleus. Notably, our analysis reveals that gluon saturation effects induce a distinct shift in diffractive patterns compared to those arising from the Primakoff process. This shift could potentially serve as a distinctive signal for detecting an Odderon presence in high energy collisions. Furthermore, by referencing relevant literature spanning theoretical frameworks (such as perturbative QCD and Color Glass Condensate) to experimental studies conducted at facilities like STAR and LHeC Study Group, we situate our findings within a broader context of contemporary research in high-energy physics and nuclear interactions. Overall, our refined summary underscores both theoretical advancements and experimental implications related to exclusive $\eta_c$ production and its connection to probing phenomena like the Odderon in electron-nucleon and electron-nucleus collisions at future collider facilities.