PoS - Proceedings of Science
Volume 432 - 16th International Symposium on Radiative Corrections: Applications of Quantum Field Theory to Phenomenology (RADCOR2023) - Main session
Soft-overlap contribution to 𝑩𝒄 → 𝜼𝒄 form factors: diagrammatic resummation of double logarithms
P. Böer*, G. Bell, T. Feldmann, D. Horstmann and V. Shtabovenko
Full text: pdf
Pre-published on: October 16, 2023
Published on: January 22, 2024
Using diagrammatic resummation techniques, we investigate the double-logarithmic series of the ``soft-overlap'' contribution to $B_c \to \eta_c$ transition form factors at large hadronic recoil, assuming the scale hierarchy $m_b \gg m_c \gg \Lambda_{\rm QCD}$. In this case, the hadronic bound states can be treated in the non-relativistic approximation and the relevant hadronic matrix elements can be computed perturbatively. This setup defines one of the simplest examples to study the problem of endpoint singularities appearing in the factorization of exclusive $B$-decay amplitudes. We find that the leading double logarithms arise from a peculiar interplay of soft-quark ``endpoint logarithms'' from ladder diagrams with energy-ordered spectator-quark propagators, as well as standard Sudakov-type soft-gluon corrections. We elucidate the all-order systematics, and show that their resummation proceeds via a novel type of integral equations.
The current status of the calculation, which includes all double logarithms in the Abelian limit, is reported.
DOI: https://doi.org/10.22323/1.432.0086
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