TY - JOUR

T1 - All-mass n-gon integrals in n dimensions

AU - Bourjaily, Jacob L.

AU - Gardi, Einan

AU - McLeod, Andrew J.

AU - Vergu, Cristian

N1 - Funding Information:
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

PY - 2020/8/1

Y1 - 2020/8/1

N2 - We explore the correspondence between one-loop Feynman integrals and (hyperbolic) simplicial geometry to describe the all-mass case: integrals with generic external and internal masses. Specifically, we focus on n-particle integrals in exactly n space-time dimensions, as these integrals have particularly nice geometric properties and respect a dual conformal symmetry. In four dimensions, we leverage this geometric connection to give a concise dilogarithmic expression for the all-mass box in terms of the Murakami-Yano formula. In five dimensions, we use a generalized Gauss-Bonnet theorem to derive a similar dilogarithmic expression for the all-mass pentagon. We also use the Schläfli formula to write down the symbol of these integrals for all n. Finally, we discuss how the geometry behind these formulas depends on space-time signature, and we gather together many results related to these integrals from the mathematics and physics literature.

AB - We explore the correspondence between one-loop Feynman integrals and (hyperbolic) simplicial geometry to describe the all-mass case: integrals with generic external and internal masses. Specifically, we focus on n-particle integrals in exactly n space-time dimensions, as these integrals have particularly nice geometric properties and respect a dual conformal symmetry. In four dimensions, we leverage this geometric connection to give a concise dilogarithmic expression for the all-mass box in terms of the Murakami-Yano formula. In five dimensions, we use a generalized Gauss-Bonnet theorem to derive a similar dilogarithmic expression for the all-mass pentagon. We also use the Schläfli formula to write down the symbol of these integrals for all n. Finally, we discuss how the geometry behind these formulas depends on space-time signature, and we gather together many results related to these integrals from the mathematics and physics literature.

UR - http://www.scopus.com/inward/record.url?scp=85089093359&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85089093359&partnerID=8YFLogxK

U2 - 10.1007/JHEP08(2020)029

DO - 10.1007/JHEP08(2020)029

M3 - Article

AN - SCOPUS:85089093359

VL - 2020

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 8

M1 - 29

ER -