Abstract
The heavy jet mass event shape has large perturbative logarithms near the leading order kinematic threshold at \( \rho =\frac{1}{3} \). Catani and Webber named these logarithms Sudakov shoulders and resummed them at double-logarithmic level. A resummation to next-to-leading logarithmic level was achieved recently. Here, we extend the resummation using an effective field theory framework to next-to-next-to-leading logarithmic order and show how to combine it with the resummation of dijet logarithms. We also solve the open problem of an unphysical singularity in the resummed momentum space distribution, in a way similar to how it is resolved in the Drell-Yan qT spectrum: through a careful analysis of the kinematics and scale-setting in position space. The heavy jet mass Sudakov shoulder is the first observable that does not involve transverse momentum for which position space resummation is critical. These advances may lead to a more precise extraction of the strong coupling constant from e+e− data.
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Acknowledgments
The authors would like to thank T. Becher, P. Monni, A. Gao and Y. Li for useful conversations. M.D.S., XY.Z. and A.B. are supported in part by the U.S. Department of Energy under contract DE-SC0013607. I.S. and J.M. were supported in part by the U.S. Department of Energy contract DE-SC0011090. I.S. was also supported in part by the Simons Foundation through the Investigator grant 327942.
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Bhattacharya, A., Michel, J.K.L., Schwartz, M.D. et al. NNLL resummation of Sudakov shoulder logarithms in the heavy jet mass distribution. J. High Energ. Phys. 2023, 80 (2023). https://doi.org/10.1007/JHEP11(2023)080
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DOI: https://doi.org/10.1007/JHEP11(2023)080