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

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 $365\,\mathrm{GeV}$.