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

Measurements of hadronic final states in e^{+}e^{-} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>−</mml:mo> </mml:msup> </mml:mrow> </mml:math> 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} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msqrt> <mml:msub> <mml:mi>s</mml:mi> <mml:mstyle mathvariant="normal"> <mml:mi>h</mml:mi> <mml:mi>a</mml:mi> <mml:mi>d</mml:mi> </mml:mstyle> </mml:msub> </mml:msqrt> <mml:mo>≈</mml:mo> <mml:mn>20</mml:mn> <mml:mo>−</mml:mo> <mml:mn>80</mml:mn> <mml:mspace width="0.167em"/> <mml:mstyle mathvariant="normal"> <mml:mi>G</mml:mi> <mml:mi>e</mml:mi> <mml:mi>V</mml:mi> </mml:mstyle> </mml:mrow> </mml:math> 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^{-} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>−</mml:mo> </mml:msup> </mml:mrow> </mml:math> runs at CM energies \sqrt{s} ≈ 40\,\mathrm{GeV} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> <mml:mo>≈</mml:mo> <mml:mn>40</mml:mn> <mml:mspace width="0.167em"/> <mml:mstyle mathvariant="normal"> <mml:mi>G</mml:mi> <mml:mi>e</mml:mi> <mml:mi>V</mml:mi> </mml:mstyle> </mml:mrow> </mml:math> and 60\,\mathrm{GeV} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mn>60</mml:mn> <mml:mspace width="0.167em"/> <mml:mstyle mathvariant="normal"> <mml:mi>G</mml:mi> <mml:mi>e</mml:mi> <mml:mi>V</mml:mi> </mml:mstyle> </mml:mrow> </mml:math> . Using realistic estimates and fast detector simulations, we show that data samples of about 10^{9} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>9</mml:mn> </mml:msup> </mml:math> 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, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> <mml:mo>≈</mml:mo> <mml:mn>91</mml:mn> <mml:mo>,</mml:mo> <mml:mn>160</mml:mn> <mml:mo>,</mml:mo> <mml:mn>240</mml:mn> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> and 365\,\mathrm{GeV} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mn>365</mml:mn> <mml:mspace width="0.167em"/> <mml:mstyle mathvariant="normal"> <mml:mi>G</mml:mi> <mml:mi>e</mml:mi> <mml:mi>V</mml:mi> </mml:mstyle> </mml:mrow> </mml:math> .