English
Related papers

Related papers: Integral Coefficients for One-Loop Amplitudes

200 papers

Representations are derived for the basic scalar one-loop vertex Feynman integrals as meromorphic functions of the space-time dimension $d$ in terms of (generalized) hypergeometric functions $_2F_1$ and $F_1$. Values at asymptotic or…

High Energy Physics - Phenomenology · Physics 2018-05-09 Johannes Bluemlein , Khiem Hong Phan , Tord Riemann

We compute the planar part of the two-loop five gluon amplitude with all helicities positive. To perform the calculation we develop a D-dimensional generalized unitarity procedure allowing us to reconstruct the amplitude by cutting into…

High Energy Physics - Phenomenology · Physics 2015-07-21 Simon Badger , Hjalte Frellesvig , Yang Zhang

I analyze the algebraic patterns underlying the structure of scattering amplitudes in quantum field theory. I focus on the decomposition of amplitudes in terms of independent functions and the systems of differential equations the latter…

High Energy Physics - Phenomenology · Physics 2015-07-14 Pierpaolo Mastrolia

We derive non-linear recursion equations for the leading infrared logarithms in massless non-renormalizable effective field theories. The derivation is based solely on the requirements of the unitarity, analyticity and crossing symmetry of…

High Energy Physics - Phenomenology · Physics 2014-11-20 J. Koschinski , M. V. Polyakov , A. A. Vladimirov

We propose an approach for calculating one-loop effective actions and vacuum energies in quantum field theory. Spectral functions are functions defined by the eigenvalues of an operator. One-loop effective actions and vacuum energies in…

High Energy Physics - Theory · Physics 2025-03-26 Yuan-Yuan Liu , Shi-Lin Li , Yu-Jie Chen , Wen-Du Li , Wu-Sheng Dai

Scattering amplitudes computed at a fixed loop order, along with any other object computed in perturbative quantum field theory, can be expressed as a linear combination of a finite basis of loop integrals. To compute loop amplitudes in…

High Energy Physics - Phenomenology · Physics 2018-10-04 Alessandro Georgoudis , Kasper J. Larsen , Yang Zhang

A general formalism for computing only the rational parts of oneloop QCD amplitudes is developed. Starting from the Feynman integral representation of the one-loop amplitude, we use tensor reduction and recursive relations to compute the…

High Energy Physics - Phenomenology · Physics 2009-11-11 Zhi-Guang Xiao , Gang Yang , Chuan-Jie Zhu

We use the infrared consistency of one-loop amplitudes in N=4 Yang-Mills theory to derive a compact analytic formula for a tree-level NNMHV gluon scattering amplitude in QCD, the first such formula known. We argue that the IR conditions,…

High Energy Physics - Theory · Physics 2009-11-10 Radu Roiban , Marcus Spradlin , Anastasia Volovich

Higher order coefficients of the inverse mass expansion of one-loop effective actions are obtained from a one-dimensional path integral representation. For the case of a massive scalar loop in the background of both a scalar potential and a…

High Energy Physics - Theory · Physics 2009-10-30 D. Fliegner , P. Haberl , M. G. Schmidt , C. Schubert

We propose a new approach that allows for the separate numerical calculation of the real and imaginary parts of finite loop integrals. We find that at one-loop the real part is given by the Loop-Tree Duality integral supplemented with…

High Energy Physics - Phenomenology · Physics 2022-02-01 Dario Kermanschah

The overall coefficient of the two-loop 4-particle amplitude in superstring theory is determined by making use of the factorization and unitarity. To accomplish this we computed in detail all the relevant tree and one-loop amplitudes…

High Energy Physics - Theory · Physics 2009-11-11 Zhi-Guang Xiao , Chuan-Jie Zhu

We analyze new data for self-avoiding polygons, on the square and triangular lattices, enumerated by both perimeter and area, providing evidence that the scaling function is the logarithm of an Airy function. The results imply universal…

Statistical Mechanics · Physics 2009-11-07 C. Richard , A. J. Guttmann , I. Jensen

We consider the factorisation of one-loop amplitudes at complex kinematic points. By determining the terms that are absent for real kinematics, we can construct a recursive ansatz for the purely rational pieces of one-loop amplitudes in…

High Energy Physics - Theory · Physics 2013-05-30 Sam D. Alston , David C. Dunbar , Warren B. Perkins

In this talk, the program package GOSAM is presented, which can be used for the automated calculation of one-loop amplitudes for multi-particle processes. The integrands are generated in terms of Feynman diagrams and can be reduced by…

High Energy Physics - Phenomenology · Physics 2012-01-19 G. Cullen , N. Greiner , G. Heinrich , G. Luisoni , P. Mastrolia , G. Ossola , T. Reiter , F. Tramontano

We compute a complete set of independent leading-color two-loop five-parton amplitudes in QCD. These constitute a fundamental ingredient for the next-to-next-to-leading order QCD corrections to three-jet production at hadron colliders. We…

High Energy Physics - Phenomenology · Physics 2019-04-09 S. Abreu , F. Febres Cordero , H. Ita , B. Page , V. Sotnikov

These notes are for the author's lectures, "Integral Reduction and Applied Algebraic Geometry Techniques" in the School and Workshop on Amplitudes in Beijing 2016. I introduce the applications of algebraic geometry methods on multi-loop…

High Energy Physics - Theory · Physics 2018-12-14 Yang Zhang

We derive universal formulae for integrating out heavy degrees of freedom in scalar field theories up to one-loop level in terms of covariant quantities associated with the geometry of the field manifold. The universal matching results can…

High Energy Physics - Phenomenology · Physics 2024-11-08 Xu-Xiang Li , Xiaochuan Lu , Zhengkang Zhang

In this letter, we exploit generalised unitarity in order to calculate the cut-constructible part of one-loop amplitudes in non-supersymmetric Yang-Mills theory. In particular, we rederive the n-gluon MHV amplitudes for both the adjacent…

High Energy Physics - Phenomenology · Physics 2010-02-03 Andreas Brandhuber , Massimiliano Vincon

The infrared divergent scalar three-point integrals are evaluated by the loop regularization method. Three kinds of infrared divergent integrals, i.e., massless triangle diagram, triangle diagrams with one and two massive internal lines,…

High Energy Physics - Phenomenology · Physics 2022-11-17 Jin Zhang

We present a new formulation of the loop-tree duality theorem for higher loop diagrams valid both for massless and massive cases. $l$-loop integrals are expressed as weighted sum of trees obtained from cutting $l$ internal propagators of…

High Energy Physics - Phenomenology · Physics 2019-11-22 Robert Runkel , Zoltán Szőr , Juan Pablo Vesga , Stefan Weinzierl