# Inclusive diffraction in future electron-proton and electron-ion colliders

## TL;DR

Future high-energy electron-proton and electron-ion colliders will vastly extend the kinematic range for studying inclusive diffraction, enabling precise extraction of diffractive parton densities and exploring nuclear diffraction with unprecedented accuracy.

## Contribution

This paper provides a detailed analysis of the potential for future colliders to study inclusive diffraction, extending kinematic coverage and improving the precision of diffractive parton density extractions.

## Key findings

- Extended kinematic range in x and Q^2 for LHeC and FCC colliders.
- Order of magnitude improvement in diffractive parton density extraction.
- Feasibility of measuring nuclear diffractive parton densities at EIC.

## Abstract

We analyse the possibilities for the study of inclusive diffraction offered by future electron--proton/nucleus colliders in the TeV regime, the Large Hadron-electron Collider as an upgrade of the HL-LHC and the Future Circular Collider in electron-hadron mode. Compared to $ep$ collisions at HERA, we find an extension of the available kinematic range in $x$ by a factor of order $20$ and of the maximum $Q^2$ by a factor of order $100$ for LHeC, while the FCC version would extend the coverage by a further order of magnitude both in $x$ and $Q^2$. This translates into a range of available momentum fraction of the diffractive exchange with respect to the hadron ($\xi$), down to $10^{-4}-10^{-5}$ for a wide range of the momentum fraction of the parton with respect to the diffractive exchange ($\beta$). Using the same framework and methodology employed in previous studies at HERA, considering only the experimental uncertainties and not those stemming from the functional form of the initial conditions or other ones of theoretical origin, and under very conservative assumptions for the luminosities and systematic errors, we find an improvement in the extraction of diffractive parton densities from fits to reduced cross sections for inclusive coherent diffraction in $ep$ by about an order of magnitude. For $eA$, we also perform the simulations for the Electron Ion Collider. We find that an extraction of the currently unmeasured nuclear diffractive parton densities is possible with similar accuracy to that in $ep$.