Abstract
The projected energy correlator measures the energy deposited in multiple detectors as a function of the largest angular distance xL = (1 − cos χL)/2 between detectors. The collinear limit xL → 0 of the projected energy correlator is particularly interesting for understanding the jet-substructures, while the large logarithms of xL could potentially spoil the perturbation theory and must be resummed. As a necessary ingredient for its resummation at next-to-next-to-leading logarithmic (NNLL) accuracy, we calculate the two-loop jet functions for the projected three-point energy correlator (E3C), using direct integration method and the parameter space Integration-by-Part (IBP) method. We then present the NNLL resummation for e+e− annihilation and an approximate NNLL resummation for pp → jj process, where the two-loop hard constant is estimated in the latter case. The convergence is improved and the hadronization effect in the collinear limit is suppressed when considering the ratio of E3C distribution to two-point energy-energy correlator (EEC). Our results show potential in precision determination of strong coupling constant using energy correlators from both e+e− data and pp data.
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Acknowledgments
The authors thank Hao Chen, Kyle Lee, Meng Xiao, Tong-Zhi Yang, Yulei Ye for useful discussions. XYZ also thanks the MIT CTP for its hospitality while part of this work was performed. The work of WC, YL, ZX, and HXZ was supported by the National Natural Science Foundation of China under the Grant No. 11975200. The work of JG was sponsored by the National Natural Science Foundation of China under the Grant No.12275173 and No.11835005.
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Chen, W., Gao, J., Li, Y. et al. NNLL resummation for projected three-point energy correlator. J. High Energ. Phys. 2024, 43 (2024). https://doi.org/10.1007/JHEP05(2024)043
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DOI: https://doi.org/10.1007/JHEP05(2024)043