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| Natura: | Preprint |
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2024
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| Accesso online: | https://arxiv.org/abs/2405.00660 |
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| _version_ | 1866911861449949184 |
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| author | Cachazo, Freddy Leon, Pablo |
| author_facet | Cachazo, Freddy Leon, Pablo |
| contents | In this note we study tree-level scattering amplitudes of gravitons under a natural deformation which in the large $z$ limit can be interpreted either as a $k$-hard-particle limit or as a $(n-k)$-soft-particle limit. When $k=2$ this becomes the standard BCFW deformation while for $k=3$ it leads to the Risager deformation. The hard- to soft-limit map we define motivates a way of computing the leading order behavior of amplitudes for large $z$ directly from soft limits. We check the proposal by applying the $k=3$ and $k=4$ versions to NMHV and N$^2$MHV gravity amplitudes respectively. The former reproduces in a few lines the result recently obtained by using CHY-like techniques in \cite{BCL}. The N$^2$MHV formula is also remarkably simple and we give support for it using a CHY-like computation. In the $k=2$ case applied to any gravity amplitude, the multiple soft-limit analysis reproduces the correct ${\cal O}(z^{-2})$ behavior while explicitly showing the source of the mysterious cancellation among Feynman diagrams that tames the behavior from the ${\cal O}(z^{n-5})$ of individual Feynman diagrams down to the ${\cal O}(z^{-2})$ of the amplitude. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00660 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Connecting Infinity to Soft Factors Cachazo, Freddy Leon, Pablo High Energy Physics - Theory In this note we study tree-level scattering amplitudes of gravitons under a natural deformation which in the large $z$ limit can be interpreted either as a $k$-hard-particle limit or as a $(n-k)$-soft-particle limit. When $k=2$ this becomes the standard BCFW deformation while for $k=3$ it leads to the Risager deformation. The hard- to soft-limit map we define motivates a way of computing the leading order behavior of amplitudes for large $z$ directly from soft limits. We check the proposal by applying the $k=3$ and $k=4$ versions to NMHV and N$^2$MHV gravity amplitudes respectively. The former reproduces in a few lines the result recently obtained by using CHY-like techniques in \cite{BCL}. The N$^2$MHV formula is also remarkably simple and we give support for it using a CHY-like computation. In the $k=2$ case applied to any gravity amplitude, the multiple soft-limit analysis reproduces the correct ${\cal O}(z^{-2})$ behavior while explicitly showing the source of the mysterious cancellation among Feynman diagrams that tames the behavior from the ${\cal O}(z^{n-5})$ of individual Feynman diagrams down to the ${\cal O}(z^{-2})$ of the amplitude. |
| title | Connecting Infinity to Soft Factors |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2405.00660 |