Abstract
The transverse momentum-dependent fragmentation functions (TMD FFs) of heavy (bottom and charm) quarks, which we recently introduced, are universal building blocks that enter predictions for a large number of observables involving final-state heavy quarks or hadrons. They enable the extension of fixed-order subtraction schemes to quasi-collinear limits, and are of particular interest in their own right as probes of the nonperturbative dynamics of hadronization. In this paper we calculate all TMD FFs involving heavy quarks and the associated TMD matrix element in heavy-quark effective theory (HQET) to next-to-leading order in the strong interaction. Our results confirm the renormalization properties, large-mass, and small-mass consistency relations predicted in our earlier work. We also derive and confirm a prediction for the large-z behavior of the heavy-quark TMD FF by extending, for the first time, the formalism of joint resummation to capture quark mass effects in heavy-quark fragmentation. Our final results in position space agree with those of a recent calculation by another group that used a highly orthogonal organization of singularities in the intermediate momentum-space steps, providing a strong independent cross check. As an immediate application, we present the complete quark mass dependence of the energy-energy correlator (EEC) in the back-to-back limit at \( \mathcal{O}\left({\alpha}_s\right) \).
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Acknowledgments
We thank Iain Stewart, Kyle Lee, and Maximilian Stahlhofen for helpful discussions. We thank the Erwin Schrödinger Institute for hospitality while parts of this work were performed. This work was supported in part by the Office of Nuclear Physics of the U.S. Department of Energy under Contract No. DE-SC0011090. Z.S. was also supported by a fellowship from the MIT Department of Physics. R.v.K. was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 101002090 COLORFREE). J.M. was supported by the D-ITP consortium, a program of NWO that is funded by the Dutch Ministry of Education, Culture and Science (OCW).
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von Kuk, R., Michel, J.K.L. & Sun, Z. Transverse momentum-dependent heavy-quark fragmentation at next-to-leading order. J. High Energ. Phys. 2024, 129 (2024). https://doi.org/10.1007/JHEP07(2024)129
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DOI: https://doi.org/10.1007/JHEP07(2024)129