# Probing Proton Structure at the Large Hadron electron Collider

## TL;DR

This paper evaluates how the proposed Large Hadron electron Collider (LHeC) can significantly improve our understanding of proton structure by reducing uncertainties in parton distribution functions, complementing the HL-LHC data.

## Contribution

The study demonstrates that LHeC measurements can substantially tighten constraints on proton PDFs, especially at small and intermediate momentum fractions, enhancing the physics potential of future colliders.

## Key findings

- LHeC can reduce PDF uncertainties by up to an order of magnitude.
- LHeC provides more significant constraints at small and intermediate x values.
- Combined LHeC and HL-LHC data offer complementary insights into proton structure.

## Abstract

For the foreseeable future, the exploration of the high-energy frontier will be the domain of the Large Hadron Collider (LHC). Of particular significance will be its high-luminosity upgrade (HL-LHC), which will operate until the mid-2030s. In this endeavour, for the full exploitation of the HL-LHC physics potential an improved understanding of the parton distribution functions (PDFs) of the proton is critical. The HL-LHC program would be uniquely complemented by the proposed Large Hadron electron Collider (LHeC), a high-energy lepton-proton and lepton-nucleus collider based at CERN. In this work, we build on our recent PDF projections for the HL-LHC to assess the constraining power of the LHeC measurements of inclusive and heavy quark structure functions. We find that the impact of the LHeC would be significant, reducing PDF uncertainties by up to an order of magnitude in comparison to state-of-the-art global fits. In comparison to the HL-LHC projections, the PDF constraints from the LHeC are in general more significant for small and intermediate values of the momentum fraction x. At higher values of x, the impact of the LHeC and HL-LHC data is expected to be of a comparable size, with the HL-LHC constraints being more competitive in some cases, and the LHeC ones in others. Our results illustrate the encouraging complementarity of the HL-LHC and the LHeC in terms of charting the quark and gluon structure of the proton.