Asymptotic expansions through the loop-tree duality

Abstract

Asymptotic expansions of Feynman amplitudes in the loop-tree duality formalism are implemented at integrand-level in the Euclidean space of the loop three-momentum, where the hierarchies among internal and external scales are well-defined. The ultraviolet behaviour of the individual contributions to the asymptotic expansion emerges only in the first terms of the expansion and is renormalized locally in four space-time dimensions. These two properties represent an advantage over the method of Expansion by Regions. We explore different approaches in different kinematical limits, and derive explicit asymptotic expressions for several benchmark configurations.

Four-loop scattering amplitudes journey into the forest

“…One of the most important features of LTD is the distinction between physical and unphysical singularities at integrand level [8,9]. Besides this, LTD has other interesting characteristics: for instance, in numerical implementations the number of integration variables is independent of the number of external legs [10][11][12][13][14], it straightforward provides asymptotic expansions [15][16][17][18], and promising local renormalization approaches [19,20]. Furthermore, an important associated development was the proposal of computing cross sections directly in four space-time dimensions through the so-called, Four Dimensional Unsubtraction (FDU) [21][22][23][24].…”

From Causal Representation of Multiloop Scattering Amplitudes to Quantum Computing

“…The LTD framework [25][26][27][28][29][30][31] opens any loop diagram into a sum of connected trees. This methodology has been deeply studied [32][33][34][35][36][37] and many applications have been developed [38][39][40][41][42][43][44][45][46][47]. In recent years the LTD has evolved in a significant way [48][49][50][51][52][53][54][55][56][57].…”

Four-loop scattering amplitudes through the loop-tree duality

“…[8,9]. Since the introduction of this formalism, a great effort has been dedicated to understand it in depth, and many interesting features have been found [10][11][12][13][14][15][16][17][18]. Two important applications were addressed through the LTD: local renormalization strategies [19,20] and the cross-section computation in four space-time dimensions at integrand level through the Four Dimensional Unsubtraction [21][22][23][24] Recently, a significant development was presented, a manifestly causal LTD reformulation to all orders [25].…”