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Unknown proportionality constant in the jet energy-scale relation Q = a p_T x_L

Determine the value of the proportionality constant a in the relation Q = a p_T x_L that characterizes the energy scale at which transitions occur between the perturbative, confinement, and free-hadron regions in jet formation.

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Background

To delineate phases of jet evolution, the authors relate the energy scale Q of interactions to the jet transverse momentum p_T and the angular variable x_L through Q = a p_T x_L. They fit distributions to identify boundaries between perturbative, confinement, and free-hadron regions. While they infer indicative values for Q/a from simulation, they explicitly state that the constant a itself is unknown, making its determination an unresolved quantitative aspect of the jet formation scale-setting.

References

The constant $a$ is unknown but the boundaries derived from simulation suggest that $Q/a \approx 20\GeV$ for the transition between the perturbative and confinement regions and $\approx$\,0.8\GeV for the transition between the confinement and free-hadron regions.

— Measurement of energy correlators inside jets and determination of the strong coupling $α_\mathrm{S}(m_\mathrm{Z})$ (2402.13864 - Collaboration, 21 Feb 2024) in Main text, paragraph beginning “As the jet p_T increases…”, discussing region boundaries, near Figure 1