# University of Hertfordshire

## From Momentum Amplituhedron Boundaries to Amplitude Singularities and Back

Research output: Contribution to journalArticlepeer-review

### Standard

In: Journal of High Energy Physics, 28.07.2020.

Research output: Contribution to journalArticlepeer-review

### Bibtex

@article{d4e94aa0b6784e4887524484765a603c,
title = "From Momentum Amplituhedron Boundaries to Amplitude Singularities and Back",
abstract = "The momentum amplituhedron is a positive geometry encoding tree-level scattering amplitudes in $\mathcal{N}=4$ super Yang-Mills directly in spinor-helicity space. In this paper we classify all boundaries of the momentum amplituhedron $\mathcal{M}_{n,k}$ and explain how these boundaries are related to the expected factorization channels, and soft and collinear limits of tree amplitudes. Conversely, all physical singularities of tree amplitudes are encoded in this boundary stratification. Finally, we find that the momentum amplituhedron $\mathcal{M}_{n,k}$ has Euler characteristic equal to one, which provides a first step towards proving that it is homeomorphic to a ball. ",
keywords = "hep-th, math.CO",
author = "Livia Ferro and Tomasz Lukowski and Robert Moerman",
note = "20 pages, 7 figures",
year = "2020",
month = jul,
day = "28",
doi = "10.1007/JHEP07(2020)201",
language = "English",
journal = "Journal of High Energy Physics",
issn = "1126-6708",
publisher = "Springer Verlag",

}

### RIS

TY - JOUR

T1 - From Momentum Amplituhedron Boundaries to Amplitude Singularities and Back

AU - Ferro, Livia

AU - Lukowski, Tomasz

AU - Moerman, Robert

N1 - 20 pages, 7 figures

PY - 2020/7/28

Y1 - 2020/7/28

N2 - The momentum amplituhedron is a positive geometry encoding tree-level scattering amplitudes in $\mathcal{N}=4$ super Yang-Mills directly in spinor-helicity space. In this paper we classify all boundaries of the momentum amplituhedron $\mathcal{M}_{n,k}$ and explain how these boundaries are related to the expected factorization channels, and soft and collinear limits of tree amplitudes. Conversely, all physical singularities of tree amplitudes are encoded in this boundary stratification. Finally, we find that the momentum amplituhedron $\mathcal{M}_{n,k}$ has Euler characteristic equal to one, which provides a first step towards proving that it is homeomorphic to a ball.

AB - The momentum amplituhedron is a positive geometry encoding tree-level scattering amplitudes in $\mathcal{N}=4$ super Yang-Mills directly in spinor-helicity space. In this paper we classify all boundaries of the momentum amplituhedron $\mathcal{M}_{n,k}$ and explain how these boundaries are related to the expected factorization channels, and soft and collinear limits of tree amplitudes. Conversely, all physical singularities of tree amplitudes are encoded in this boundary stratification. Finally, we find that the momentum amplituhedron $\mathcal{M}_{n,k}$ has Euler characteristic equal to one, which provides a first step towards proving that it is homeomorphic to a ball.

KW - hep-th

KW - math.CO

U2 - 10.1007/JHEP07(2020)201

DO - 10.1007/JHEP07(2020)201

M3 - Article

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

M1 - 201

ER -