Abstract
We calculate directly in position space the one-loop renormalization kernels of the soft operators Oγ and Og that appear in the soft-quark contributions to, respectively, the subleading-power γγ → h and gg → h form factors mediated by the b-quark. We present an IR/rapidity divergence-free definition for Og and demonstrate that with a correspondent definition of the collinear function, a consistent factorization theorem is recovered. Using conformal symmetry techniques, we establish a relation between the evolution kernels of the leading-twist heavy-light light-ray operator, whose matrix element defines the B-meson light-cone distribution amplitude (LCDA), and Oγ to all orders in perturbation theory. Application of this relation allows us to bootstrap the kernel of Oγ to the two-loop level. We construct an ansatz for the kernel of Og at higher orders. We test this ansatz against the consistency requirement at two-loop and find they differ only by a particular constant.
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Acknowledgments
We thank A. Belitsky, P. Böer, V. Braun, A. Manashov, E. Sünderhauf, A. Vladimirov and J. Wang for discussions. This research was supported in part by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the Sino-German Collaborative Research Center TRR110 “Symmetries and the Emergence of Structure in QCD” (DFG Project-ID 196253076, NSFC Grant No. 12070131001, - TRR 110) and by the Excellence Cluster ORIGINS funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Grant No. EXC - 2094 - 390783311.
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Beneke, M., Ji, Y. & Wang, X. Renormalization of the next-to-leading-power γγ → h and gg → h soft quark functions. J. High Energ. Phys. 2024, 246 (2024). https://doi.org/10.1007/JHEP05(2024)246
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DOI: https://doi.org/10.1007/JHEP05(2024)246