Soft Theorem to Three Loops in QCD and ${\cal N} = 4$ Super Yang-Mills Theory
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866909081850085376 |
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| author | Chen, Wen Luo, Ming-xing Yang, Tong-Zhi Zhu, Hua Xing |
| author_facet | Chen, Wen Luo, Ming-xing Yang, Tong-Zhi Zhu, Hua Xing |
| contents | The soft theorem states that scattering amplitude in gauge theory with a soft gauge-boson emission can be factorized into a hard scattering amplitude and a soft factor. In this paper, we present calculations of the soft factor for processes involving two hard colored partons, up to three loops in QCD. To accomplish this, we developed a systematic method for recursively calculating relevant Feynman integrals using the Feynman-Parameter representation. Our results constitute an important ingredient for the subtraction of infrared singularities at N$^4$LO in perturbative QCD. Using the principle of leading transcendentality between QCD and ${\cal N}=4$ super Yang-Mills theory, we determine the soft factor in the latter case to three loops with full-color dependence. As a by-product, we also obtain the finite constant $f_2^{(3)}$ in the Bern-Dixon-Smirnov ansatz analytically, which was previously known numerically only. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_03832 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Soft Theorem to Three Loops in QCD and ${\cal N} = 4$ Super Yang-Mills Theory Chen, Wen Luo, Ming-xing Yang, Tong-Zhi Zhu, Hua Xing High Energy Physics - Phenomenology High Energy Physics - Theory The soft theorem states that scattering amplitude in gauge theory with a soft gauge-boson emission can be factorized into a hard scattering amplitude and a soft factor. In this paper, we present calculations of the soft factor for processes involving two hard colored partons, up to three loops in QCD. To accomplish this, we developed a systematic method for recursively calculating relevant Feynman integrals using the Feynman-Parameter representation. Our results constitute an important ingredient for the subtraction of infrared singularities at N$^4$LO in perturbative QCD. Using the principle of leading transcendentality between QCD and ${\cal N}=4$ super Yang-Mills theory, we determine the soft factor in the latter case to three loops with full-color dependence. As a by-product, we also obtain the finite constant $f_2^{(3)}$ in the Bern-Dixon-Smirnov ansatz analytically, which was previously known numerically only. |
| title | Soft Theorem to Three Loops in QCD and ${\cal N} = 4$ Super Yang-Mills Theory |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2309.03832 |