Related papers: A Systematic and Efficient Method to Compute Multi…
Modern particle physics is increasingly becoming a precision science that relies on advanced theoretical predictions for the analysis and interpretation of experimental results. The planned physics program at the LHC and future colliders…
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…
The 4-th order Runge-Kutta method in the complex plane is proposed for numerically advancing the solutions of a system of first order differential equations in one external invariant satisfied by the master integrals related to a Feynman…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
We consider the numerical integration of non-autonomous separable parabolic equations using high order splitting methods with complex coefficients (methods with real coefficients of order greater than two necessarily have negative…
I present a few new and recent ideas of the multiloop calculations.
We recently presented a new method for the evaluation of one-loop amplitude of arbitrary scattering processes, in which the reduction to scalar integrals is performed at the integrand level. In this talk, we review the main features of the…
We show that integro-differential generalized Langevin and non-Markovian master equations can be transformed into larger sets of ordinary differential equations. .On the basis of this transformation we develop a numerical method for solving…
We calculate analytically the master integrals of a planar double-box family for top-quark pair production using the method of differential equations. With a proper choice of the bases, the differential equations can be transformed to the…
Loop calculations involve the evaluation of divergent integrals. Usually [1] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers…
The standard procedure when evaluating integrals of a given family of Feynman integrals, corresponding to some Feynman graph, is to construct an algorithm which provides the possibility to write any particular integral as a linear…
Three-loop vacuum integrals are an important building block for the calculation of a wide range of three-loop corrections. Until now, only results for integrals with one and two independent mass scales are known, but in the electroweak…
We present recent developments on the topic of the integrand reduction of scattering amplitudes. Integrand-level methods allow to express an amplitude as a linear combination of Master Integrals, by performing operations on the…
We compute the master integrals that arise in the calculation of the leading penguin amplitudes in non-leptonic B-decays at two-loop order. The application of differential equations in a canonical basis enables us to give analytic results…
We propose a computationally efficient method to solve the dynamics of operators of bosonic quantum systems coupled to their environments. The method maps the operator under interest to a set of complex-valued functions, and its adjoint…
The calculation of the two-loop corrections to the three jet production rate and to event shapes in electron-positron annihilation requires the computation of a number of up to now unknown two-loop four-point master integrals with one…
Analytic results for the complete set of two-loop self-energy master integrals on shell with one mass are calculated.
We review the method of the calculation of multiloop integrals suggested in Ref.\cite{Lee2010}.
We present a novel way to compute the one-loop ring-improved effective potential numerically, which avoids the spurious appearence of complex expressions and at the same time is free from the renormalization ambiguities of the…
We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master…