Renormalization of the next-to-leading-power $γγ\to h $ and $gg\to h$ soft quark functions
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arXiv
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| Natura: | Preprint |
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2024
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| author | Beneke, Martin Ji, Yao Wang, Xing |
| author_facet | Beneke, Martin Ji, Yao Wang, Xing |
| contents | We calculate directly in position space the one-loop renormalization kernels of the soft operators $O_γ$ and $O_g$ that appear in the soft-quark contributions to, respectively, the subleading-power $γγ\to h$ and $gg\to h$ form factors mediated by the $b$-quark. We present an IR/rapidity divergence-free definition for $O_g$ 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 $O_γ$ to all orders in perturbation theory. Application of this relation allows us to bootstrap the kernel of $O_γ$ to the two-loop level. We construct an ansatz for the kernel of $O_g$ at higher orders. We test this ansatz against the consistency requirement at two-loop and find they differ only by a particular constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17738 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Renormalization of the next-to-leading-power $γγ\to h $ and $gg\to h$ soft quark functions Beneke, Martin Ji, Yao Wang, Xing High Energy Physics - Phenomenology We calculate directly in position space the one-loop renormalization kernels of the soft operators $O_γ$ and $O_g$ that appear in the soft-quark contributions to, respectively, the subleading-power $γγ\to h$ and $gg\to h$ form factors mediated by the $b$-quark. We present an IR/rapidity divergence-free definition for $O_g$ 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 $O_γ$ to all orders in perturbation theory. Application of this relation allows us to bootstrap the kernel of $O_γ$ to the two-loop level. We construct an ansatz for the kernel of $O_g$ at higher orders. We test this ansatz against the consistency requirement at two-loop and find they differ only by a particular constant. |
| title | Renormalization of the next-to-leading-power $γγ\to h $ and $gg\to h$ soft quark functions |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2403.17738 |