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arxiv: 2606.19064 · v1 · pith:5NACDKZXnew · submitted 2026-06-17 · ✦ hep-ex · hep-ph

QCD studies and precision physics at the LHeC

Francesco Giuli This is my paper

Pith reviewed 2026-06-26 18:49 UTC · model grok-4.3

classification ✦ hep-ex hep-ph
keywords LHeCproton PDFsdeep-inelastic scatteringQCDparton distribution functionsstrong couplingweak mixing angleHL-LHC
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The pith

The LHeC would enable a coherent determination of all proton PDFs in a single experiment.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines the QCD and PDF reach of the proposed LHeC, which would add an energy recovery linac to the HL-LHC for TeV-scale electron-proton collisions. It argues that high luminosity combined with a wide lever arm in Bjorken x and Q² plus clean neutral-current and charged-current deep-inelastic scattering data would permit extracting every proton parton distribution function coherently in one experiment. The resulting tighter constraints on gluon, valence, strange and heavy-flavour distributions would sharpen parton luminosities for the HL-LHC, test perturbative and small-x QCD, and deliver competitive measurements of the strong coupling and weak mixing angle over a broad range of scales.

Core claim

The LHeC adds a high-current Energy Recovery Linac to the HL-LHC, delivering electron-proton collisions at centre-of-mass energies around the TeV scale. The combination of high luminosity, a very large lever arm in Bjorken x and Q², and clean neutral- and charged-current deep-inelastic scattering measurements would enable a coherent determination of all proton PDFs in a single experiment. The resulting constraints would substantially reduce uncertainties in the gluon, valence, strange and heavy-flavour distributions, provide stringent tests of perturbative and small-x QCD, and improve the parton luminosities that enter precision and discovery measurements at the HL-LHC and at future hadron c

What carries the argument

Coherent extraction of all proton PDFs from combined neutral-current and charged-current deep-inelastic scattering over a wide range in Bjorken x and Q² at high luminosity.

If this is right

  • Substantially reduce uncertainties in the gluon, valence, strange and heavy-flavour distributions
  • Provide stringent tests of perturbative and small-x QCD
  • Improve the parton luminosities that enter precision and discovery measurements at the HL-LHC and future hadron colliders
  • Deliver competitive determinations of the strong coupling and weak mixing angle including its running over a wide range of scales

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A single-experiment PDF set could reduce tensions that appear when data from multiple facilities are combined.
  • Tighter PDFs would increase the reach of new-physics searches that rely on accurate background predictions at hadron colliders.
  • Direct access to the running of the weak mixing angle over many orders of magnitude in scale would provide an independent electroweak test.
  • The programme could set performance benchmarks that future electron-hadron facilities would need to meet or exceed.

Load-bearing premise

The LHeC will be built and will deliver the high luminosity, energy-recovery performance, and detector capabilities assumed in the bridge-project study.

What would settle it

Operation of the LHeC that fails to produce the projected reduction in PDF uncertainties or yields results inconsistent with the expected clean DIS measurements would falsify the central claim.

Figures

Figures reproduced from arXiv: 2606.19064 by Francesco Giuli.

Figure 1
Figure 1. Figure 1: Kinematic coverage in (𝑥, 𝑄2 ) for DIS experiments. The LHeC extends the HERA reach by several orders of magnitude in both the low-𝑥 and high-𝑄 2 directions, entering regions relevant for precision QCD, electroweak, Higgs, top and BSM measurements. 1. Introduction The LHeC is proposed as a high-energy deep-inelastic scattering (DIS) facility based on a 50 GeV electron Energy Recovery Linac colliding with t… view at source ↗
Figure 2
Figure 2. Figure 2: Projected LHeC impact on representative PDFs at the starting scale 𝑄 2 = 1.9 GeV2 , shown as ratios to PDF4LHC21. The panels show, clockwise from top left, the gluon, 𝑠 + 𝑠¯, down-valence and up-valence distributions. The projected uncertainties for 50 fb−1 and 1 ab−1 are compared with the spread of current global analyses. orders of magnitude relative to the combined HERA inclusive programme [7]. This is … view at source ↗
Figure 3
Figure 3. Figure 3: Projected parton-luminosity impact at √ 𝑠 = 14 TeV, normalised to PDF4LHC21. Top: rapidity dependence of 𝑔𝑔 luminosities at 𝑄 = 125 GeV and 𝑞𝑞¯ luminosities at 𝑄 = 91 GeV. Bottom: invariant-mass dependence of the corresponding luminosities. The LHeC bands are much narrower than current global-PDF differences. 3. Impact on hadron-collider parton luminosities The PDF constraints from LHeC data propagate dire… view at source ↗
Figure 4
Figure 4. Figure 4: Projected LHeC determinations of 𝛼𝑠 (𝜇𝑅) from inclusive jets and from the combined DIS-plus-jets determination, compared with present measurements and future projections. The lower panel shows the relative precision as a function of the renormalisation scale. 4. Strong coupling The LHeC can determine 𝛼𝑠 through two largely complementary methods. Inclusive NC and CC DIS constrain 𝛼𝑠 through QCD scaling viol… view at source ↗
Figure 5
Figure 5. Figure 5: Projected sensitivity to the scale dependence of the weak mixing angle. Existing data, future fixed-target and EIC projections are compared with LHeC points spanning the electroweak-scale region. The lower panel shows the corresponding relative uncertainties. complementary to 𝑍-pole, fixed-target and hadron-collider determinations because it probes different initial states, momentum transfers and PDF corre… view at source ↗
Figure 6
Figure 6. Figure 6: Sensitivity of the longitudinal structure function 𝐹𝐿 in the high-energy, high-density region. The colour scale shows the relative difference in 𝐹𝐿 in the (𝑥, 𝑄2 ) plane for proton beams (left) and 197Au beams (right). The nuclear case enhances density effects and therefore provides a powerful lever arm for distinguishing linear small-𝑥 evolution from non-linear QCD dynamics in electron–ion collisions. mea… view at source ↗
read the original abstract

The Large Hadron electron Collider (LHeC) would add a high-current Energy Recovery Linac to the HL-LHC, delivering electron-proton collisions at centre-of-mass energies around the TeV scale. This contribution summarises the QCD and parton-distribution-function (PDF) aspects of the recent LHeC bridge-project study. The combination of high luminosity, a very large lever arm in Bjorken $x$ and $Q^2$, and clean neutral- and charged-current deep-inelastic scattering measurements would enable a coherent determination of all proton PDFs in a single experiment. The resulting constraints would substantially reduce uncertainties in the gluon, valence, strange and heavy-flavour distributions, provide stringent tests of perturbative and small-$x$ QCD, and improve the parton luminosities that enter precision and discovery measurements at the HL-LHC and at future hadron colliders. The same programme gives competitive and complementary determinations of the strong coupling and weak mixing angle, including measurements of its running over a wide range of scales.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript summarizes the QCD and PDF aspects of the recent LHeC bridge-project study. It claims that adding a high-current Energy Recovery Linac to the HL-LHC would deliver ep collisions at TeV-scale centre-of-mass energies with high luminosity and a large lever arm in Bjorken x and Q². Combined with clean neutral- and charged-current DIS measurements, this setup would enable a coherent determination of all proton PDFs in a single experiment, substantially reducing uncertainties on the gluon, valence, strange and heavy-flavour distributions, providing stringent tests of perturbative and small-x QCD, and improving parton luminosities relevant to HL-LHC and future hadron colliders. The same programme is stated to yield competitive determinations of α_s and the weak mixing angle, including its running over a wide range of scales.

Significance. If the projected LHeC performance is realized, the programme would provide a unique, self-consistent set of ep constraints on proton structure that complement pp data, with direct impact on precision LHC measurements and searches. The emphasis on simultaneous NC+CC coverage and the extended kinematic reach is a clear strength of the ep mode.

major comments (2)
  1. [Introduction / PDF section] The central claims rest entirely on performance projections taken from the bridge-project study. The manuscript should add an explicit subsection (e.g., near the introduction or in the PDF section) that lists the key input assumptions (luminosity, energy-recovery efficiency, detector acceptance and resolution) and states how they were propagated into the quoted PDF uncertainty reductions; without this, readers cannot assess the robustness of the quoted gains.
  2. [Abstract] The abstract and summary state that the LHeC would 'enable a coherent determination of all proton PDFs in a single experiment.' This phrasing should be qualified to make clear that the coherence is conditional on the assumed machine and detector parameters; the current wording risks being read as an unconditional claim.
minor comments (2)
  1. [Abstract] The manuscript refers to 'the recent LHeC bridge-project study' without a specific citation or arXiv number in the provided text; adding the reference would allow readers to trace the input projections.
  2. [Figures] Figure captions (if present in the full text) should explicitly state whether the shown uncertainty bands include only statistical or also systematic and PDF-parameterisation uncertainties.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and the recommendation for minor revision. The two major comments are addressed point by point below.

read point-by-point responses

  1. Referee: [Introduction / PDF section] The central claims rest entirely on performance projections taken from the bridge-project study. The manuscript should add an explicit subsection (e.g., near the introduction or in the PDF section) that lists the key input assumptions (luminosity, energy-recovery efficiency, detector acceptance and resolution) and states how they were propagated into the quoted PDF uncertainty reductions; without this, readers cannot assess the robustness of the quoted gains.

    Authors: We agree that an explicit listing of the key assumptions would improve transparency. The PDF results quoted in the manuscript are taken directly from the bridge-project study, whose performance projections (luminosity, energy-recovery efficiency, detector acceptance and resolution) are documented in that reference. We will add a dedicated subsection (placed after the introduction and before the main PDF discussion) that enumerates these assumptions and briefly describes their propagation into the uncertainty reductions, with explicit cross-references to the relevant sections of the bridge-project study. revision: yes

  2. Referee: [Abstract] The abstract and summary state that the LHeC would 'enable a coherent determination of all proton PDFs in a single experiment.' This phrasing should be qualified to make clear that the coherence is conditional on the assumed machine and detector parameters; the current wording risks being read as an unconditional claim.

    Authors: We accept the referee's observation. The phrasing in the abstract (and the parallel statement in the summary) can be read as unconditional. We will revise both locations to qualify the claim explicitly, for example by inserting 'subject to the assumed machine and detector parameters' immediately after 'enable a coherent determination of all proton PDFs in a single experiment'. revision: yes

Circularity Check

0 steps flagged

No circularity; forward-looking projections independent of fitted inputs

full rationale

The manuscript summarises projected PDF constraints and QCD tests from the LHeC bridge-project study. No derivation chain, equation, or 'prediction' is shown that reduces by construction to fitted parameters, self-citations, or ansatzes internal to the paper. The central claim is a conditional expectation based on assumed machine performance and is not a closed-loop calculation equivalent to its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central projections rest on machine-performance assumptions and the applicability of perturbative QCD over the stated kinematic range; no free parameters or invented entities are introduced in the abstract itself.

axioms (2)
  • domain assumption The LHeC will achieve the centre-of-mass energies, luminosities and detector performance stated in the bridge-project study.
    All quantitative projections presuppose successful construction and operation of the proposed machine.
  • domain assumption Perturbative QCD and the parton model remain valid across the extended x and Q² range accessed by LHeC.
    The ability to extract PDFs and test small-x QCD relies on this standard assumption holding.

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Reference graph

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