相关论文: Loop Integrals, R Functions and their Analytic Con…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
This article presents a novel approach to enhance the accuracy of classical quadrature rules by incorporating correction terms. The proposed method is particularly effective when the position of an isolated discontinuity in the function and…
In this work we study a problem about analytic continuation along parallel algebraic curves.
We are used to thinking of an operator acting once, twice, and so on. However, an operator acting integer times can be consistently analytic continued to an operator acting complex times. Applications: (s,r) diagrams and an extension of…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
For a function defined on an arbitrary subset of a Riemann surface, we give conditions which allow the function to be extended conformally. One folkloric consequence is that two common definitions of an analytic arc in ${\mathbb C}$ are…
At variance with fully inclusive quantities, which have been computed already at the two- or three-loop level, most exclusive observables are still known only at one loop, as further progress was hampered up to very recently by the greater…
Analyzing in detail the analytic continuation of the Riemann zeta function we are able to generate several new identities which may be useful for application in physics and mathematics.
It is well-known that direct analytic continuation of DGLAP evolution kernel (splitting functions) from space-like to time-like kinematics breaks down at three loops. We identify the origin of this breakdown as splitting functions are not…
Loop integration results have been obtained using numerical integration and extrapolation. An extrapolation to the limit is performed with respect to a parameter in the integrand which tends to zero. Results are given for a non-scalar…
One-loop functions with loop masses larger than external masses and momenta can always be expanded in terms of external masses and momenta. The precision requested for observables determines the number of the expansion terms retained in the…
We give a complete analytical computation of three and two-point loop integrals occurring in heavy-particle theories, involving a velocity change, for arbitrary real values of the external masses and residual momenta.
We explore the analytic structure of three-point functions using contour deformations. This method allows continuing calculations analytically from the spacelike to the timelike regime. We first elucidate the case of two-point functions…
We derive an analytic expression for the scalar one-loop pentagon and hexagon functions which is convenient for subsequent numerical integration. These functions are of relevance in the computation of next-to-leading order radiative…
A complex-analytic structure within the unit disk of the complex plane is presented. It can be used to represent and analyze a large class of real functions. It is shown that any integrable real function can be obtained by means of the…
We uncover an unexpected connection between the physics of loop integrals and the mathematics of spline functions. One loop integrands are Laplace transforms of splines. This clarifies the geometry of the associated loop integrals, since a…
Taylor expansions of analytic functions are considered with respect to two points. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated. It is explained how these…
A class of log-trigonometric integrals are evaluated in terms of elliptic functions. From this, by using the elliptic integral singular values, one can obtain closed form evaluations of integrals such as \[…
Taylor expansions of analytic functions are considered with respect to several points, allowing confluence of any of them. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are…
Four 3-loop two-point functions are studied analytically and numerically using a simplified sector decomposition method. The coefficients of the ultraviolet divergent part are determined analytically, and those of the finite part are…