$B_c \to η_c$ form factors at large recoil: Interplay of soft-quark and soft-gluon dynamics
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916951318593536 |
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| author | Bell, Guido Böer, Philipp Feldmann, Thorsten Horstmann, Dennis Shtabovenko, Vladyslav |
| author_facet | Bell, Guido Böer, Philipp Feldmann, Thorsten Horstmann, Dennis Shtabovenko, Vladyslav |
| contents | We perform an all-order analysis of double-logarithmic corrections to the so-called soft-overlap contribution to heavy-to-light transition form factors at large hadronic recoil. Specifically, we study $B_c \to η_c$ transitions within a perturbative non-relativistic framework, treating both the bottom and charm quarks as heavy with the hierarchy $m_b \gg m_c \ggΛ_{\rm QCD}$. Our diagrammatic analysis shows that double-logarithmic corrections arise from two distinct sources: Exponentiated soft-gluon effects described by standard Sudakov factors, and rapidity-ordered soft-quark configurations, leading to implicit integral equations, which so far have only been studied in the context of energetic muon-electron backward scattering. We find that the all-order structure of the double logarithms is governed by a novel type of coupled integral equations, which encode the non-trivial interplay between these two effects. Whereas a closed-form solution to these equations is currently unknown, we present useful iteration formulas, and derive the asymptotic behaviour of the soft-overlap form factor for infinitely large recoil energies, showing that the Sudakov suppression is somewhat weakened by the intertwined soft-quark and soft-gluon corrections. In a broader context, our findings shed light onto the physical origin and mathematical structure of endpoint divergences arising from soft-collinear factorization and the related Feynman mechanism for power-suppressed hard exclusive processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14149 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $B_c \to η_c$ form factors at large recoil: Interplay of soft-quark and soft-gluon dynamics Bell, Guido Böer, Philipp Feldmann, Thorsten Horstmann, Dennis Shtabovenko, Vladyslav High Energy Physics - Phenomenology We perform an all-order analysis of double-logarithmic corrections to the so-called soft-overlap contribution to heavy-to-light transition form factors at large hadronic recoil. Specifically, we study $B_c \to η_c$ transitions within a perturbative non-relativistic framework, treating both the bottom and charm quarks as heavy with the hierarchy $m_b \gg m_c \ggΛ_{\rm QCD}$. Our diagrammatic analysis shows that double-logarithmic corrections arise from two distinct sources: Exponentiated soft-gluon effects described by standard Sudakov factors, and rapidity-ordered soft-quark configurations, leading to implicit integral equations, which so far have only been studied in the context of energetic muon-electron backward scattering. We find that the all-order structure of the double logarithms is governed by a novel type of coupled integral equations, which encode the non-trivial interplay between these two effects. Whereas a closed-form solution to these equations is currently unknown, we present useful iteration formulas, and derive the asymptotic behaviour of the soft-overlap form factor for infinitely large recoil energies, showing that the Sudakov suppression is somewhat weakened by the intertwined soft-quark and soft-gluon corrections. In a broader context, our findings shed light onto the physical origin and mathematical structure of endpoint divergences arising from soft-collinear factorization and the related Feynman mechanism for power-suppressed hard exclusive processes. |
| title | $B_c \to η_c$ form factors at large recoil: Interplay of soft-quark and soft-gluon dynamics |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2412.14149 |