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Unknown theory normalization of the E3C/E2C ratio in the perturbative region

Establish the absolute normalization of the theoretical predictions for the differential E3C/E2C ratio in the perturbative x_L region, eliminating the need to introduce a free normalization parameter in each jet p_T bin when comparing to data.

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Background

The determination of the strong coupling α_s(m_Z) relies on comparing the measured E3C/E2C ratio to perturbative QCD predictions at approximate NNLL accuracy matched to NLO, corrected for nonperturbative effects. The analysis focuses on shape comparisons because the theory normalization in the perturbative x_L region is treated as unknown, necessitating a free parameter per p_T bin. Resolving this normalization would improve the predictive power and reduce reliance on empirical normalization when fitting to data.

References

Since the theory normalization is unknown in the perturbative region, a free parameter is introduced in each \pt bin, and we only consider the shape effects of the uncertainties.

— 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 preceding the chi-squared definition (Eq. χ²), in the section comparing measured ratios to NNLL predictions