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

TL;DR

The paper presents a case for expanding FCC‑ee’s QCD program to the 20–80 GeV hadronic range by leveraging ISR/FSR at the Z pole and by conducting dedicated short runs at √s ≈ 40 and 60 GeV. It argues that each low‑√s energy point can yield ≈10^9 hadronic events, enabling precision studies of light- and heavy-quark jets, gluon jets, event shapes, fragmentation functions, and nonperturbative dynamics, thereby improving hadronization models and heavy-quark mass effects while complementing higher‑energy FCC‑ee measurements. The study relies on LEP experience, fast detector simulations, and SHERPA/DELPHES analyses to estimate event yields, purities, and mass reconstruction performance, and it shows that dedicated low‑√s runs could deliver superior precision. Taken together, these measurements would deepen our understanding of QCD and provide valuable inputs for SM tests and future collider analyses.

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 $365\,\mathrm{GeV}$.

Figures (4)

• Figure 1: Examples of existing QCD measurements using $\HepParticle{\HepParticle{e}{}{}\xspace}{}{+}\xspace\HepParticle{\HepParticle{e}{}{}\xspace}{}{-}\xspace\xspace$ annihilation hadronic events over $\sqrt{s} \approx 10\hbox{--}80\,\text{GeV}$, showing the size of their (typically large) experimental uncertainties: EEC asymmetry measured by TOPAZ TOPAZ:1989yod (top left), fits of FFs at low hadron momenta TOPAZ:1994vocTPCTwoGamma:1988yjhPerez-Ramos:2013eba (top right), $\alpha_{S}$ extractions from event shapes and jet rates ParticleDataGroup:2024cfk (bottom left), and $R(\sqrt{s})$ ratio ParticleDataGroup:2024cfk (bottom right).
• Figure 2: Number of ISR/FSR events as a function of the HFS mass (in 5-$\text{GeV}$ bins) corresponding to a run with $10^{12}$$\HepParticle{\HepParticle{e}{}{}\xspace}{}{+}\xspace\HepParticle{\HepParticle{e}{}{}\xspace}{}{-}\xspace\xspace \to \HepParticle{q}{}{}\xspace\HepAntiParticle{\HepParticle{q}{}{}\xspace}{}{}\xspace\xspace$ events at $\sqrt{s} = 91.2\,\text{GeV}$, generated with PYTHIA 8 Bierlich:2022pfr. The left figure shows the number of hadronic events fully contained within a detector with geometric acceptance down to $\theta_\text{min} = 100$ mrad (FCC-ee-like) and 200 mrad (LEP-like) as a function of the generator-level hadronic CM energy. The same plot also shows the number of hadronic events for well-reconstructed light-quark (u, d, s) and heavy-quark (c, b) jets for a coverage down to $\theta_\text{min} = 100$ mrad. The right figure shows the number of $\HepParticle{\HepParticle{e}{}{}\xspace}{}{+}\xspace\HepParticle{\HepParticle{e}{}{}\xspace}{}{-}\xspace\xspace\to \HepParticle{u}{}{}\xspace\HepAntiParticle{\HepParticle{u}{}{}\xspace}{}{}\xspace\xspace,\HepParticle{d}{}{}\xspace\HepAntiParticle{\HepParticle{d}{}{}\xspace}{}{}\xspace\xspace,\HepParticle{s}{}{}\xspace\HepAntiParticle{\HepParticle{s}{}{}\xspace}{}{}\xspace\xspace$ and $\HepParticle{\HepParticle{e}{}{}\xspace}{}{+}\xspace\HepParticle{\HepParticle{e}{}{}\xspace}{}{-}\xspace\xspace\to\HepParticle{c}{}{}\xspace\HepAntiParticle{\HepParticle{c}{}{}\xspace}{}{}\xspace\xspace,\HepParticle{b}{}{}\xspace\HepAntiParticle{\HepParticle{b}{}{}\xspace}{}{}\xspace\xspace$ events as a function of their visible hadronic invariant mass, for those well ($\Delta m/m=|\sqrt{s_\text{had,true}} - m_\mathrm{HFS}|/\sqrt{s_\text{had,true}} < 5\%$) and badly ($\Delta m/m=|\sqrt{s_\text{had,true}} - m_\mathrm{HFS}|/\sqrt{s_\text{had,true}} > 5\%$) reconstructed for a detector with acceptance down to $\theta_\text{min} = 100$ mrad.
• Figure 3: Distribution of the visible HFS invariant mass for multiple processes in $\HepParticle{\HepParticle{e}{}{}\xspace}{}{+}\xspace\HepParticle{\HepParticle{e}{}{}\xspace}{}{-}\xspace\xspace$ collisions at $\sqrt{s} = 91.2\,\text{GeV}$ that pass the three kinematic selection criteria $a),\,b),\,c)$, outlined in the text. The ISR/FSR photon is excluded from the HFS mass calculation. All final states but $q\bar{q}$, $q\bar{q}\gamma$, and $\tau^+\tau^-$ are strongly suppressed by the selection requirements. The full visible signal in the detector will be the sum of the displayed processes. Left: Events passing selection $a)$, with large purity for $\HepParticle{q}{}{}\xspace\HepAntiParticle{\HepParticle{q}{}{}\xspace}{}{}\xspace\xspace\gamma$ samples. Center: Events passing selection $b)$, with high purity for $q\bar{q}$ samples with collinear radiation. Right: Events passing selection $c)$, with large purity for $q\bar{q}$ samples with negligible ISR/FSR emission.
• Figure 4: Correlation between the true mass ($m(\HepParticle{q}{}{}\xspace\HepAntiParticle{\HepParticle{q}{}{}\xspace}{}{}\xspace\xspace)$) and the HFS mass reconstructed at the detector level ($m_\mathrm{HFS}$) for $\HepParticle{\HepParticle{e}{}{}\xspace}{}{+}\xspace\HepParticle{\HepParticle{e}{}{}\xspace}{}{-}\xspace\xspace\to \mathrm{hadrons} + \gamma_\text{FSR}$ events passing the selection $a)$ (left), and for $\HepParticle{\HepParticle{e}{}{}\xspace}{}{+}\xspace\HepParticle{\HepParticle{e}{}{}\xspace}{}{-}\xspace\xspace\to \mathrm{hadrons}$ ISR events passing the selection $b)$ (right). The values are normalized across the $x$ axis and the color coding scale is given in %.