Toward three-loop Feynman massive diagram calculations

There are many methods of searching for traces of the so-called new physics in particle physics. One of them, and the main focus of this paper, is athe study of the Z-boson decay in e+e collisions. An improvement in the precision of calculations of the Standard Model (SM) electroweak pseudo-observables, such as scattering asymmetries, effective weak mixing angles, and decay widths, related to the Z-boson will meet severe experimental requirements at the planned e+e colliders and will increase the chance to detect non-standard effects in experimental analysis. To reach this goal, one has to calculate the next order of perturbative SM theory, namely three-loop Feynman integrals. We discuss the complexity of the problem, as well as the methods crucial for completing three-loop calculations. We show several numerical solutions for some three-loop Feynman integrals using sector decomposition, Mellin–Barnes (MB), and differential equation methods

Integral Reduction with Kira 2.0 and Finite Field Methods

We present the new version 2.0 of the Feynman integral reduction program Kira and describe the new features. The primary new feature is the reconstruction of the final coefficients in integration-by-parts reductions by means of finite field methods with the help of FireFly. This procedure can be parallelized on computer clusters with MPI. Furthermore, the support for user-provided systems of equations has been significantly improved. This mode provides the flexibility to integrate Kira into projects that employ specialized reduction formulas, direct reduction of amplitudes, or to problems involving linear system of equations not limited to relations among standard Feynman integrals. We show examples from state-of-the-art Feynman integral reduction problems and provide benchmarks of the new features, demonstrating significantly reduced main memory usage and improved performance w.r.t. previous versions of Kira

The complete set of two-loop master integrals for Higgs + jet production in QCD

In this paper we complete the computation of the two-loop master integrals relevant for Higgs plus one jet production initiated in arXiv:1609.06685, arXiv:1907.13156, arXiv:1907.13234. We compute the integrals by defining differential equations along contours in the kinematic space, and by solving them in terms of one-dimensional generalized power series. This method allows for the efficient evaluation of the integrals in all kinematic regions, with high numerical precision. We show the generality of our approach by considering both the top- and the bottom-quark contributions. This work along with arXiv:1609.06685, arXiv:1907.13156, arXiv:1907.13234 provides the full set of master integrals relevant for the NLO corrections to Higgs plus one jet production, and for the real-virtual contributions to the NNLO corrections to inclusive Higgs production in QCD in the full theory.Comment: 32 pages, references added, minor revisio

DiffExp, a Mathematica package for computing Feynman integrals in terms of one-dimensional series expansions

DiffExp is a Mathematica package for integrating families of Feynman integrals order-by-order in the dimensional regulator from their systems of differential equations, in terms of one-dimensional series expansions along lines in phase-space, which are truncated at a given order in the line parameter. DiffExp is based on the series expansion strategies that were explored in recent literature for the computation of families of Feynman integrals relevant for Higgs plus jet production with full heavy quark mass dependence at next-to-leading order. The main contribution of this paper, and its associated package, is to provide a public implementation of these series expansion methods, which works for any family of integrals for which the user provides a set of differential equations and boundary conditions (and for which the program is not computationally constrained). The main functions of the DiffExp package are discussed, and its use is illustrated by applying it to the three loop equal-mass and unequal-mass banana graph families

Four-loop large-n_f contributions to the non-singlet structure functions F_2 and F_L

We have calculated the n_f^2 and n_f^3 contributions to the flavour non-singlet structure functions F_2 and F_L in inclusive deep-inelastic scattering at the fourth order in the strong coupling alpha_s. The coefficient functions have been obtained by computing a very large number of Mellin-N moments using the method of differential equations, and then determining the analytic forms in N and Bjorken-x from these. Our new n_f^2 terms are numerically much larger than the n_f^3 leading large-nf parts which were already known; they agree with predictions of the threshold and high-energy resummations. Furthermore our calculation confirms the earlier determination of the four-loop n_f^2 part of the corresponding anomalous dimension. Via the no-pi^2 conjecture/theorem for Euclidean physical quantities, we predict the z4 n_f^3 part of the fifth-order anomalous dimension for the evolution of non-singlet quark distributions.Comment: 48 pages, LaTex, 5 eps-based figures. Analytical results in ancillary FORM file