Recursion for Differential Cross-Section from the Optical Theorem
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915061747941376 |
|---|---|
| author | Garg, Vatsal Lee, Hojin Lee, Kanghoon |
| author_facet | Garg, Vatsal Lee, Hojin Lee, Kanghoon |
| contents | We present a novel framework for computing differential cross-sections in quantum field theory using the optical theorem and loop amplitudes, circumventing the traditional method of squaring scattering amplitudes. This approach addresses two major computational challenges in high-multiplicity processes: complexity from amplitude squaring and the extensive summations over color and helicity. Our method employs quantum off-shell recursion, a loop-level generalization of Berends--Giele recursion, combined with Veltman's largest time equation (LTE) through a doubling prescription of fields. By deriving Dyson--Schwinger equations within this doubled framework and constructing quantum perturbiner expansions, we develop recursive relations for generating LTEs. We validate our method by successfully reproducing the differential cross-section for tree-level $2 \to 2$ and $2 \to 4$ scalar scattering for $ϕ^{4}$ theory through one-loop and three-loop amplitude calculation respectively. This framework offers an efficient alternative to conventional methods and can be broadly applied to theories with color charges, such as QCD and the Standard Model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05575 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Recursion for Differential Cross-Section from the Optical Theorem Garg, Vatsal Lee, Hojin Lee, Kanghoon High Energy Physics - Phenomenology High Energy Physics - Theory We present a novel framework for computing differential cross-sections in quantum field theory using the optical theorem and loop amplitudes, circumventing the traditional method of squaring scattering amplitudes. This approach addresses two major computational challenges in high-multiplicity processes: complexity from amplitude squaring and the extensive summations over color and helicity. Our method employs quantum off-shell recursion, a loop-level generalization of Berends--Giele recursion, combined with Veltman's largest time equation (LTE) through a doubling prescription of fields. By deriving Dyson--Schwinger equations within this doubled framework and constructing quantum perturbiner expansions, we develop recursive relations for generating LTEs. We validate our method by successfully reproducing the differential cross-section for tree-level $2 \to 2$ and $2 \to 4$ scalar scattering for $ϕ^{4}$ theory through one-loop and three-loop amplitude calculation respectively. This framework offers an efficient alternative to conventional methods and can be broadly applied to theories with color charges, such as QCD and the Standard Model. |
| title | Recursion for Differential Cross-Section from the Optical Theorem |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2412.05575 |