Related papers: A new Method for Computing One-Loop Integrals
We set up a new, flexible approach for the tensor reduction of one-loop Feynman integrals. The 5-point tensor integrals up to rank R=5 are expressed by 4-point tensor integrals of rank R-1, such that the appearance of the inverse 5-point…
This paper reviews and generalizes Feynman's path integration methods which use time slicing with straight line segments and Fourier sine series. The generalizations are done from variational calculus considerations and in one dimension for…
The long-standing problem of representing the general massive one-loop Feynman integral as a meromorphic function of the space-time dimension $d$ has been solved for the basis of scalar one- to four-point functions with indices one. In 2003…
We present a projective framework for the construction of Integration by Parts (IBP) identities and differential equations for Feynman integrals, working in Feynman-parameter space. This framework originates with very early results which…
Complete Feynman diagram automatic computation systems are now coming of age after many years of development. They are made available to the high energy physics community through user-friendly interfaces. Theorists and experimentalists can…
The technique of decomposing Feynman diagrams at the one loop level into elementary integrals is generalized to the imaginary time Matsubara formalism. The three lowest integrals, containing one, two and three fermion lines, are provided in…
We use a result on mixed Tate motives due to Goncharov (arXiv:alg-geom/9601021) to show that the symbol of an arbitrary one-loop 2m-gon integral in 2m dimensions may be read off directly from its Feynman parameterization. The algorithm…
We introduce a novel, systematic method for the complete symbolic reduction of multi-loop Feynman integrals, leveraging the power of generating functions. The differential equations governing these generating functions naturally yield…
We invent an automated method for computing the divergent part of Feynman integrals in dimensional regularization. Our method exploits simplifications from four-dimensional integration-by-parts identities. Leveraging algorithms from the…
In this talk, we use several examples to elaborate on how a recently proposed algorithm can turn non-trivial Feynman integrals into an $\varepsilon $-factorised manner, regardless of their hidden geometric essence. In particular, some extra…
Motivated by the foundational work of Tarasov, who pointed out that the algebraic relations of the type considered here can lead to functional reduction of Feynman integrals, we suitably modify the original method to be able to implement…
The Mathematica toolkit AMBRE derives Mellin-Barnes (MB) representations for Feynman integrals in d=4-2eps dimensions. It may be applied for tadpoles as well as for multi-leg multi-loop scalar and tensor integrals. AMBRE uses a loop-by-loop…
A method for the evaluation of the epsilon expansion of multi-loop massless Feynman integrals is introduced. This method is based on the Gegenbauer polynomial technique and the expansion of the Gamma function in terms of harmonic sums.…
In these lectures I will give an introduction to Feynman integrals. In the first part of the course I review the basics of the perturbative expansion in quantum field theories. In the second part of the course I will discuss more advanced…
In a recent paper by the author (Chen in JHEP 02:115, 2020), the reduction of Feynman integrals in the parametric representation was considered. Tensor integrals were directly parametrized by using a generator method. The resulting…
We formulate and prove Cutkosky's Theorem regarding the discontinuity of Feynman integrals in the massive one-loop case up to the involved intersection index. This is done by applying the techniques to treat singular integrals developed in…
In this paper, the reduction of Feynman integrals in the parametric representation is considered. This method proves to be more efficient than the integration-by-part (IBP) method in the momentum space. Tensor integrals can directly be…
The calculation of hard scattering amplitudes up to NLO is automated in numerical tools, such as OpenLoops. The LHC and future experiments, however, demand high-precision predictions at NNLO and beyond for a wide range of particle…
We propose a novel method, called the dimension-changing transformation (DCT), to compute one-loop Feynman integrals and recently introduced fixed-branch integrals to arbitrary orders in $\epsilon$. The DCT relates one-loop Feynman…
We give a complete analytical computation of three-point one-loop integrals with one heavy propagator, up to the third tensor rank, for arbitrary values of external momenta and masses.