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

Measurements of hadronic final states in e^{+}e^{-} 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}} ≈ 20-80\,\mathrm{GeV} s h a d ≈ 20 − 80 G e V 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^{-} e + e − runs at CM energies \sqrt{s} ≈ 40\,\mathrm{GeV} s ≈ 40 G e V and 60\,\mathrm{GeV} 60 G e V . Using realistic estimates and fast detector simulations, we show that data samples of about 10^{9} 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} ≈ 91, 160, 240, s ≈ 91 , 160 , 240 , and 365\,\mathrm{GeV} 365 G e V .