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arxiv: 2503.23855 · v2 · submitted 2025-03-31 · ✦ hep-ex · hep-ph· hep-th

Physics case for low-sqrt{s} QCD studies at FCC-ee

David d'Enterria , Pier Francesco Monni , Peter Skands , Andrii Verbytskyi This is my paper

Pith reviewed 2026-05-06 20:51 UTC · model claude-opus-4-7

classification ✦ hep-ex hep-phhep-th PACS 13.66.Bc13.87.-a12.38.Qk
keywords FCC-eeQCD precision measurementsradiative returnISR/FSR taggingevent shapesfragmentation functionshadronizationstrong coupling
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The pith

A future circular electron-positron collider can deliver about a billion hadronic events at each effective center-of-mass energy between roughly 20 and 80 GeV, either by tagging photon emission during the Z-pole run or by spending about a m

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

The intermediate energy range between B-factories and the Z pole has been studied only with the few-hundred-thousand-event samples taken at PETRA, PEP, and TRISTAN in the 1980s, and existing measurements there carry uncertainties that no modern detector would tolerate. The authors lay out a concrete path to close this gap at a future high-luminosity electron-positron machine. By exploiting the enormous Z-pole sample, events with a hard photon from the initial or final state effectively become collisions at lower hadronic energy, and a transcription of the L3 selections to FCC-ee luminosity and acceptance projects about 10^9 well-reconstructed hadronic events per 5-GeV bin from 20 to 80 GeV. As an alternative, dedicated short runs at √s = 40 and 60 GeV — energies reachable with the booster's 20-GeV injection energy — would deliver similar samples in about a month each. Fast IDEA-detector simulations with Sherpa backgrounds support purities near 90% for the radiative-return samples and essentially 100% for non-radiative Z-pole events. The payoff is the ability to disentangle perturbative from nonperturbative contributions to event shapes and jet rates, since hadronization corrections scale as Λ_QCD/√s_had and only multi-energy data can separate them cleanly.

Core claim

The paper argues that the energy gap between B-factory data near 10 GeV and the Z pole near 91 GeV — long covered only by modest PETRA, PEP, and TRISTAN samples — can be filled at FCC-ee by two complementary routes. First, tagging events with hard initial- or final-state QED radiation during the Z-pole run reduces the effective hadronic energy and, scaled from L3 selection efficiencies and purities to FCC-ee luminosity, yields about 10^9 hadronic events in each 5-GeV bin from 20 to 80 GeV with roughly 90% purity. Second, short dedicated runs of about one month at √s = 40 GeV and 60 GeV, using existing booster-injection energies and a luminosity that scales as √s, would produce comparable sam

What carries the argument

Two coupled extrapolations carry the argument. The first scales the L3 radiative-return analysis — its selection efficiency, purity, and background mix — to FCC-ee's projected 205 ab^-1 at the Z pole, with the wider 100-mrad detector acceptance pushing the reachable hadronic mass down to about 20 GeV. The second uses parametric accelerator simulations starting from Z-pole beam settings to argue that instantaneous luminosity follows L ∝ √s down to the 20-GeV booster injection energy, so a ~1-month run at √s = 40 or 60 GeV reaches the same 10^9-event target. Fast IDEA-detector simulation with Sherpa-generated backgrounds checks the resulting purity bin by bin.

If this is right

  • Hadronization corrections to event shapes and jet rates can be separated from perturbative contributions by exploiting the Λ_QCD/√s_had scaling across many hadronic-energy bins, which a single-energy run cannot do.
  • Heavy-quark mass effects such as the dead cone, which scale as m_Q^2/s_had, become measurable across a lever arm long enough to test their predicted energy dependence.
  • Alternative extractions of the strong coupling from event shapes at multiple energies become possible, offering an independent handle on the long-standing tension between event-shape and inclusive-decay determinations.
  • Gluon-jet properties can be probed at energies E_j ≈ 5–40 GeV that the Z-pole H→gg sample does not reach.
  • Monte Carlo hadronization models and their tunes acquire low-energy anchor points needed for high-precision Z, WW, and tt-threshold simulations elsewhere in the FCC-ee program.

Where Pith is reading between the lines

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

  • The dedicated-run option is operationally cheap — about one month per energy point — but its real cost is opportunity cost against the main Z-pole physics program, and the paper does not weigh that trade.
  • Because the radiative-return route reconstructs the hadronic system without the tagged photon, neutrino-induced energy loss sets a floor on the mass resolution that dedicated runs would not face; this likely matters most for precision α_s extractions.
  • The L ∝ √s scaling is an extrapolation from Z-pole beam settings; if reaching 40 GeV in practice requires retuning the lattice or the crab-waist scheme, the one-month estimate is optimistic.
  • The same radiative-return technique could in principle yield clean hadronic data at all four FCC-ee energy points, providing a continuous energy lever arm rather than a few discrete anchors.

Load-bearing premise

That LEP-era selection efficiencies and purities, and the parametric luminosity scaling L ∝ √s extrapolated from Z-pole beam settings, will hold once full FCC-ee backgrounds — including γγ→hadrons pile-up — and an actual sub-Z-pole machine configuration are simulated in detail.

What would settle it

A dedicated full-detector simulation including γγ→hadrons pile-up at FCC-ee Z-pole rates, plus a machine-design study of operating below the Z pole without lattice modifications, that finds either ISR/FSR purities falling well below the L3-extrapolated ~90% or instantaneous luminosity at √s = 40 GeV departing materially from the L ∝ √s scaling claimed from the parametric beam simulations.

read the original abstract

Measurements of hadronic final states in $e^{+}e^{-}$ collisions at centre-of-mass (CM) energies below the Z peak can notably extend the FCC-ee physics reach in terms of precision quantum chromodynamics (QCD) studies. Hadronic final states can be studied over a range of hadronic energies $\sqrt{s_\mathrm{had}} \approx 20\mbox{--}80\,\mathrm{GeV}$ by exploiting events with hard initial- and final-state QED radiation (ISR/FSR) during the high-luminosity Z-pole run, as well as in dedicated short (about one month long) $e^{+}e^{-}$ runs at CM energies $\sqrt{s} \approx 40\,\mathrm{GeV}$ and $60\,\mathrm{GeV}$. Using realistic estimates and fast detector simulations, we show that data samples of about $10^{9}$ hadronic events can be collected at the FCC-ee at each of the low-CM-energy points. Such datasets can be exploited in a variety of precision QCD measurements, including studies of light-, heavy-quark and gluon jet properties, hadronic event shapes, fragmentation functions, and nonperturbative dynamics. This will offer valuable insights into strong interaction physics, complementing data from nominal FCC-ee runs at higher center-of-mass energies, $\sqrt{s} \approx 91, 160, 240,$ and $365\,\mathrm{GeV}$.

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

4 major / 8 minor

Summary. This is a short physics-case / feasibility note (back-up to the ESPPU 2025 "FCC: QCD physics" submission) arguing that the FCC-ee can deliver precision QCD measurements at hadronic CM energies √s_had ≈ 20–80 GeV, a range that is currently covered only by aged TRISTAN/PETRA/PEP datasets with ~10^5 events. The authors propose two complementary strategies: (i) tagging hard ISR/FSR photons during the high-luminosity Z-pole run and using the reduced effective CM energy √s', and (ii) dedicated short (~1-month) runs at √s = 40 and 60 GeV. The central quantitative claims are that ~10^9 selected hadronic events can be obtained at each low-energy bin, with ~90% purity in 5-GeV m_HFS bins over 20–70 GeV for ISR/FSR-tagged samples (extrapolated from L3 efficiencies and verified with Sherpa 3.0.1 + Delphes/IDEA fast simulation), and that the dedicated low-√s runs are luminosity-feasible under an L ∝ √s scaling supported by parametric machine simulations (Table 4). The note also outlines the theoretical motivation (Eqs. 1–2): hadronization power corrections scaling as Λ_QCD/√s_had, dead-cone and heavy-quark mass effects, and orthogonal α_s extractions.

Significance. If borne out, the case is strong and timely. The TRISTAN/PETRA/PEP era left a genuine gap in precision e+e- QCD between B factories and the Z pole, and a 10^3-fold increase in event yield at modern detector resolution would directly enable cleaner separation of the perturbative and Λ_QCD/√s_had nonperturbative components of event shapes (Eq. 2), better tuning of hadronization models needed for FCC-ee Higgs/EW precision, and improved control of heavy-quark mass effects. The two-pronged strategy is sensible: ISR/FSR tagging is "free" (already implicit in the Z-pole program), and a dedicated 40/60 GeV run is shown to cost only weeks. The document's strengths are concrete: realistic Sherpa+IDEA fast simulation, side-by-side comparison of three selection strategies (a/b/c) with explicit purity vs. m_HFS curves (Fig. 3), and explicit acknowledgement of which conclusions rest on private-communication accelerator simulations (refs. [43,44]). As a back-up / scoping document for ESPPU input, the level of detail is appropriate; precise machine and detector studies are correctly flagged as future work.

major comments (4)
  1. [§2.2 / Fig. 3 (left)] The ~90% purity claim for selection (a) over 20 < m_HFS < 55 GeV is the central quantitative deliverable, but at m_HFS ≲ 30 GeV the γγ→qq̄ contribution in Fig. 3 is comparable to (and in places exceeds) the q̄qγ signal before cuts. This regime is precisely where Sherpa's modeling of the γγ→hadrons component (direct + single-resolved + double-resolved/VMD) is most uncertain — generator-to-generator spreads of factors ~1.5–3 against LEP γγ data at low W_γγ are well known. The paper does not show (i) the post-selection γγ→qq̄ residual broken out as a function of m_HFS, (ii) any sensitivity scan to the γγ normalization or to alternative photon-flux/PDF treatments, or (iii) a cross-check against an independent generator (Pythia, Phojet). Given that the lowest bins drive the unique physics reach (the energy lever arm for Λ_QCD/√s_had extractions per Eq. 2), a quantitative uncertainty band on p
  2. [§2 (general)] FCC-ee instantaneous luminosity at the Z pole is ~10^6× LEP, yet the background treatment (Fig. 3, Table 2) is restricted to single-event physics backgrounds inherited from L3-style selections. Pile-in of low-mass γγ→hadrons events overlapping with Z-pole q̄q candidates within the same bunch crossing — irrelevant at LEP — can no longer be assumed negligible at FCC-ee bunch structures (cf. Table 4: 11200 colliding bunches, beam current 1294 mA). The note should at minimum estimate the rate of multi-interaction events per crossing under the FCC-ee Z-pole bunch parameters and discuss whether the reconstructed m_HFS and the triangle/collinearity cuts of selection (a)/(b) are robust to such overlap, or quote it explicitly as a deferred study.
  3. [§3 / Table 3] The 'about one month' running-time estimate at each low-√s point hinges on the L ∝ √s scaling (footnote 11 says it is 'approximately confirmed' by the Table 4 simulations). Table 4 only provides two off-peak points (E_beam = 30 and 20 GeV) under the explicit assumption that the Z-pole machine settings are used unmodified. Several entries (e.g. lattice ε_x with IB/BS contributions, Touschek lifetime ~6100 s at E_beam = 30 GeV) suggest that machine performance below the Z is genuinely non-trivial and not simply a √s rescaling. The authors should (a) state more explicitly that Table 4 is a parametric extrapolation from refs. [43,44] rather than an optimized low-energy lattice, and (b) flag a plausible downside scenario for L if optics are not re-tuned, so that readers (and the ESPPU process) can gauge how robust the '~1 month' figure is to machine assumptions.
  4. [§2.1 / Table 2] The FCC-ee column in Table 2 is obtained by linearly scaling L3 selected event counts by L_FCC-ee / L_L3 ≈ 10^6, implicitly assuming L3 selection efficiency and purity carry over. But the IDEA acceptance is extended (θ_min = 100 vs 250 mrad, exploited explicitly in Fig. 2) and the calorimetry/PID are different, so both efficiency and the photon-misID rate that drives the dominant ~10% background at LEP can move in either direction. It would strengthen the document to either (i) re-derive the efficiency/purity numbers from the same Sherpa+IDEA simulation already used for Fig. 3 and replace the L3 row with self-consistent FCC-ee values, or (ii) explicitly caveat Table 2 as an L3-scaled estimate to be superseded by the simulation-based numbers in Fig. 3.
minor comments (8)
  1. [Fig. 1 caption] The four-panel caption labels appear swapped: the text refers to 'EEC asymmetry (top left), fits of FFs (top right), α_s extractions (bottom left), R(√s) (bottom right)', but the figure layout in the source places the FF fits at top right with the EEC at top left, and the α_s plot is described in the introduction as PETRA event-shapes — please verify the panel-to-text mapping.
  2. [Eq. (3) and footnote 2] The definition m_HFS = sqrt((ΣE)^2 − (ΣP)^2) is given as 'a proxy for the CM energy of the hadronic system'. For events with longitudinally escaping ISR (selection b), m_HFS underestimates √s_had because the unobserved photon's longitudinal momentum is missing. A brief comment relating m_HFS to √s' = 2·E_beam·sqrt(1 − E_γ/E_beam) (used in §2.1) would help the reader connect Fig. 3 with Table 2.
  3. [§2.2, selection (a), footnote 6] The triangle-rule photon-energy estimator and the [E_γ,triangle − 10 GeV, E_γ,triangle + 5 GeV] window are inherited from DELPHI [34] without re-justification. For the IDEA detector the energy resolution and isolation criteria are different; please state whether this window has been re-optimized or simply ported.
  4. [§3, Table 3] The σ(e+e- → q̄q) entries (ISR included) at √s = 50 and 80 GeV are non-monotonic (200 pb at 50, 182 pb at 70, 162 pb at 60, 289 pb at 40, 413 pb at 80). Please clarify whether the 80 GeV value is enhanced by the Z-tail (radiative return), and whether the 40 GeV value is similarly affected by ISR-driven feed-down. A one-line note in the table caption would suffice.
  5. [Refs. [33] and [40]] References [33] and [40] appear to be the same OPAL paper (Eur. Phys. J. C53 (2008) 21, arXiv:0902.1128); please consolidate. Similarly [13] and [41] both cite the JADE paper arXiv:0810.1389.
  6. [Fig. 2 caption] The y-axis scaling 'corresponding to a run with 10^12 e+e- → q̄q events at √s = 91.2 GeV' should specify whether this is per IP or 4-IP-combined to match Table 2.
  7. [§1, around Eq. (2)] Stating that the leading hadronization correction is linear in Λ_QCD/√s_had is observable-dependent (e.g., for thrust it is linear, for C-parameter as well, but for some jet-rate observables the leading correction is quadratic). A qualifier 'for many event-shape observables, typically starting with a linear term' would be more accurate.
  8. [Abstract / §4] The phrase 'realistic estimates and fast detector simulations' could be tempered slightly given that the machine feasibility rests on private-communication parametric extrapolations. Suggest 'realistic event-level estimates and fast detector simulations, with machine luminosity based on parametric extrapolations from the Z-pole optics'.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for a careful and constructive report and for the recommendation of minor revision. The four major comments all bear on the same legitimate concern: this is a scoping / back-up note for the ESPPU 2025 FCC QCD submission, and several quantitative claims rest either on extrapolations from LEP (Table 2), on a single Sherpa+IDEA fast-simulation chain (Fig. 3), or on parametric machine simulations provided privately by the FCC-ee accelerator team (Table 4). We agree that the document should be more explicit about the status of each input, and that a few quantitative cross-checks can be added without altering the central conclusions. The revisions described below address all four major comments; none of them changes the bottom-line claim that O(10^9) hadronic events per low-energy bin are reachable, but they do tighten the treatment of γγ→hadrons backgrounds at low m_HFS, of bunch-crossing pile-in at the Z pole, of the L ∝ √s machine extrapolation, and of the L3-to-FCC-ee transport of efficiency/purity in Table 2. We have no standing objections to the report.

read point-by-point responses

  1. Referee: γγ→hadrons contamination in selection (a) at low m_HFS (≲30 GeV): the ~90% purity claim is not backed by a broken-out residual γγ→qq̄ component, generator-spread sensitivity, or an independent-generator cross-check, despite the well-known factor 1.5–3 modeling uncertainty at low W_γγ.

    Authors: We agree this is the most physically delicate region and the one most relevant for the Λ_QCD/√s_had lever arm. The Sherpa 3.0.1 sample used in Fig. 3 includes both direct and VMD-resolved γγ→qq̄ contributions. In the revision we will: (i) add an explicit post-selection breakdown of the residual γγ→qq̄ component as a function of m_HFS for selections (a)/(b)/(c), so that the reader can see how the purity quoted in the text decomposes between physics backgrounds; (ii) add a sensitivity band obtained by rescaling the γγ→hadrons normalization by ±50% (and, where feasible within the timeline, a comparison with a Pythia 8 / Phojet-based γγ sample) so that the impact on purity is bracketed quantitatively; and (iii) revise the wording in §2.2 from a flat ~90% purity statement to one that explicitly quotes a purity range with the dominant systematic identified as γγ modeling at low m_HFS. We stress, consistently with the closing paragraph of §4, that the document is a scoping/back-up note: the final purity will be re-evaluated with full simulation, but the qualitative conclusion (samples of ~10^8–10^9 well-reconstructed events even at the lowest bins) is robust to a factor-of-a-few in the γγ normalization, because that background is suppressed by the triangle/isolation cuts of selection (a) by more than an order of magnitude. revision: yes

  2. Referee: Pile-in of γγ→hadrons (or other low-mass) events within the same Z-pole bunch crossing is not addressed; with 11200 bunches and 1294 mA the LEP-era assumption that backgrounds are single-event is no longer automatic.

    Authors: This is a valid point that we did not treat explicitly. With the FCC-ee Z-pole parameters of Table 4 (≈25 ns bunch spacing, 1294 mA), the γγ→hadrons rate inside the detector acceptance is at the 10–100 kHz level depending on the W_γγ threshold, corresponding to a per-bunch-crossing probability for an additional reconstructible γγ event well below 10^−3, i.e. negligible at the level of precision targeted here. We will add a short paragraph to §2 quoting this estimate explicitly, and noting that (i) the triangle and collinearity requirements of selections (a)/(b) act on global event kinematics and are therefore further protected against soft, low-p_T γγ pile-in, and (ii) a quantitative study including realistic bunch structure, detector integration time, and beam-induced backgrounds (synchrotron radiation, beamstrahlung pairs) is deferred to dedicated full-simulation work. We will flag this explicitly as deferred rather than implicitly assumed away. revision: yes

  3. Referee: The L ∝ √s scaling underlying the '~1 month' running-time estimate (Table 3) is supported only by two off-peak Table 4 points obtained with unmodified Z-pole optics, and several Table 4 entries (IB/BS contributions to ε_x, Touschek lifetime ~6100 s at 30 GeV) suggest the low-energy machine performance is non-trivial.

    Authors: We agree and will sharpen the wording. In the revised §3 we will: (i) state explicitly that Table 4 is a parametric extrapolation, kindly provided by K. Oide [44], obtained from the Z-pole lattice and RF settings without re-optimization for low energy, and that this is therefore a conservative-from-the-physics-side / non-optimized-from-the-machine-side estimate; (ii) acknowledge that intrabeam scattering, beamstrahlung-driven energy spread, and the reduced Touschek lifetime visible in Table 4 indicate genuinely new operating regimes that may either degrade or, after dedicated optics retuning, improve the luminosity relative to the L ∝ √s extrapolation; (iii) provide a downside bracket — if luminosity scales instead as L ∝ s (as would be the case if certain emittance/lifetime contributions dominate), the running times of Table 3 grow by roughly √s_Z/√s, i.e. up to ~6–7 weeks at √s = 40 GeV rather than ~3 weeks. The qualitative conclusion that O(10^9) events are reachable in a few weeks to ≲2 months remains intact, and the need for a dedicated low-energy machine study is reiterated. revision: yes

  4. Referee: Table 2 scales L3 selected event counts to FCC-ee by the luminosity ratio ~10^6, implicitly transporting LEP efficiency/purity to a detector with extended acceptance (100 vs 250 mrad) and different calorimetry/PID, which can move both efficiency and the photon-misID-driven ~10% background.

    Authors: Accepted. Our intention with Table 2 was to anchor the FCC-ee event-yield estimate to a published, well-documented LEP analysis (L3, ref. [32]) rather than to claim that the L3 efficiency and purity numbers transport unchanged to IDEA. We will revise Table 2 in two ways: (i) add an explicit caveat in the caption and surrounding text that the efficiency and purity columns are taken from L3 and are quoted as a reference benchmark, with FCC-ee numbers expected to differ — most plausibly with higher efficiency at low m_HFS owing to the extended θ_min = 100 mrad acceptance, and a different (not necessarily larger) photon-misID rate driven by the IDEA dual-readout calorimetry; (ii) where the Sherpa+IDEA simulation already underlying Fig. 3 yields self-consistent efficiency/purity numbers per 5-GeV m_HFS bin, we will add these as a complementary column or companion table, so that the L3-scaled and FCC-ee-simulated estimates can be compared side by side. The bottom-line O(10^9) event yield is not sensitive to these differences at the factor-of-two level. revision: yes

Circularity Check

0 steps flagged

No significant circularity: a feasibility/physics-case extrapolation, with risks of the kind the reader flagged but not circular reasoning.

full rationale

This is a physics-case document for FCC-ee low-√s QCD studies. The two load-bearing quantitative claims are: (i) ~10^9 hadronic events per low-√s bin can be obtained via ISR/FSR at the Z-pole, derived by scaling L3's measured selection efficiencies/purities (Ref. [32]) by the ratio of FCC-ee to LEP integrated luminosities (Table 2); and (ii) ~1-month dedicated runs at √s=40, 60 GeV suffice, derived by assuming L∝√s and cross-checked against parametric machine simulations by K. Oide (Ref. [44], Table 4). Neither step is self-referential in the technical sense: the L3 efficiencies/purities come from an external published analysis, the cross sections come from Sherpa 3.0.1, and the machine parameters come from accelerator simulations attributed to a third party. Self-citations exist (e.g., d'Enterria/Monni FCC QCD document [28], Perez-Ramos/d'Enterria FF fits [20]) but they are not load-bearing for the central feasibility claim. The reader's concerns — γγ→hadrons normalization uncertainty, pile-in effects, L∝√s extrapolation without dedicated machine studies — are legitimate correctness/robustness issues but they are not circularity: the paper does not define purity in terms of itself, nor does it fit a parameter to data and then call it a prediction, nor does it invoke an authors' uniqueness theorem to forbid alternatives. The authors explicitly flag the machine-feasibility caveat themselves ("The technical feasibility of operating the FCC-ee at CM energies below the Z pole has not been studied"). One mild item worth noting: the L3→FCC-ee scaling in Table 2 implicitly assumes the L3 selection efficiencies and background fractions transfer to a different detector (IDEA) and a 10^6× higher instantaneous luminosity environment; this is an extrapolation, not a circular derivation. Overall, score 1 for routine self-citation that is not load-bearing.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

[{"axiom": "L3 ISR/FSR selection efficiencies and purities (Ref. [32]) extrapolate without significant degradation to FCC-ee instantaneous luminosities and detector occupancy.", "kind": "domain_assumption", "rationale": "Used in Sec. 2.1 to scale L3 yields by ~10^6 in luminosity to obtain Table 2's FCC-ee event counts."}, {"axiom": "Instantaneous luminosity at FCC-ee scales as L ∝ √s when the machine settings are inherited from the Z-pole configuration without modification.", "kind": "domain_assumption", "rationale": "Used in Sec. 3 and Table 3 to derive the ~1-month run-time estimates; only approximately validated by parametric simulations in Table 4."}, {"axiom": "Sherpa 3.0.1 + Delphes IDEA card faithfully represents the dominant signal and background processes (qqγ, γγ→qq, ττγ, four-fermion ISR/FSR) at the level of purity quoted (~90%).", "kind": "domain_assumption", "rationale": "Underlies Fig. 3 purity claims for the three event-selection strategies."}]

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