Two-Loop Vertices in Quantum Field Theory: Infrared Convergent Scalar Configurations

  title={Two-Loop Vertices in Quantum Field Theory: Infrared Convergent Scalar Configurations},
  author={Andrea Ferroglia and Giampiero Passarino and Massimo Passera and Sandro Uccirati},
  journal={Nuclear Physics},
Abstract A comprehensive study is performed of general massive, scalar, two-loop Feynman diagrams with three external legs. Algorithms for their numerical evaluation are introduced and discussed, numerical results are shown for all different topologies and comparisons with analytical results, whenever available, are performed. An internal cross-check, based on alternative procedures, is also applied. The analysis of infrared divergent configurations, as well as the treatment of tensor integrals… Expand
Two-loop tensor integrals in quantum field theory ☆
Abstract A comprehensive study is performed of general massive, tensor, two-loop Feynman diagrams with two and three external legs. Reduction to generalized scalar functions is discussed. IntegralExpand
Two-loop vertices in quantum field theory: Infrared and collinear divergent configurations
Abstract A comprehensive study is performed of two-loop Feynman diagrams with three external legs which, due to the exchange of massless gauge-bosons, give raise to infrared and collinearExpand
Numerical computation of two-loop box diagrams with masses
Abstract A new approach is presented to evaluate multi-loop integrals, which appear in the calculation of cross-sections in high-energy physics. It relies on a fully numerical method and isExpand
Numerical evaluation of non-infrared two-loop vertices
Some methods for the numerical computation of two-loop non-infrared vertices are reviewed. A new method is also proposed and compared to the old ones. Finally, some preliminary results are presented,Expand
Two-loop renormalization in the Standard Model. Part I: Prolegomena ☆
In this paper the building blocks for the two-loop renormalization of the Standard Model are introduced with a comprehensive discussion of the special vertices induced in the Lagrangian by aExpand
Massive Feynman integrals and electroweak corrections
Abstract We describe selected advances in the calculation of electroweak corrections to massive scattering problems at colliders, from the very beginning in the nineteen seventies until contemporaryExpand
Evaluating massive planar two-loop tensor vertex integrals
Using the parallel/orthogonal space method, we calculate the planar two-loop three-point diagram and two rotated reduced planar two-loop three-point diagrams. Together with the crossed topology,Expand
The two loop crossed ladder vertex diagram with two massive exchanges
We compute the (three) master integrals for the crossed ladder diagram with two exchanged quanta of equal mass. The differential equations obeyed by the master integrals are used to generate powerExpand
The effective electroweak mixing angle sin2θeff with two-loop fermionic contributions
Abstract We present the results from a calculation of the full electroweak two-loop fermionic contributions to the effective leptonic mixing angle of the Z boson, sin 2 θ eff , in the Standard Model.Expand
Two-loop threshold singularities, unstable particles and complex masses
The effect of threshold singularities induced by unstable particles on two-loop observables is investigated and it is shown how to cure them working in the complex-mass scheme. The impact onExpand


Two-loop tensor integrals in quantum field theory ☆
Abstract A comprehensive study is performed of general massive, tensor, two-loop Feynman diagrams with two and three external legs. Reduction to generalized scalar functions is discussed. IntegralExpand
Massive two-loop vertex functions
Abstract Calculating massive two-loop vertex functions by splitting integrations into parallel and orthogonal space components has been demonstrated to give a convenient twofold integralExpand
Reduction and evaluation of two-loop graphs with arbitrary masses
We describe a general analytic-numerical reduction scheme for evaluating any 2-loop diagrams with general kinematics and general renormalizable interactions, whereby ten special functions form aExpand
Massive two loop integrals in renormalizable theories
We propose a framework for calculating two-loop Feynman diagrams which appear within a renormalizable theory in the general mass case and at finite external momenta. Our approach is a combination ofExpand
Two-loop QED vertex correction from virtual heavy fermions
Abstract The O(α2) contribution of a virtual massive fermion to the electromagnetic vertex of a light fermion is calculated in perturbative QED for arbitrary external momentum transfer s. Besides theExpand
Analytical evaluation of certain on-shell two-loop three-point diagrams ∗
Abstract An analytical approach is applied to calculating some dimensionally regulated two-loop vertex diagrams with essential on-shell singularities. Such diagrams are important in evaluating theExpand
Two-loop form factors in QED
Abstract We evaluate the on shell form factors of the electron for arbitrary momentum transfer and finite electron mass, at two loops in QED, by integrating the corresponding dispersion relations,Expand
Scalar One Loop Integrals
The completely general one-loop scalar one-, two-, three- and four-point functions are studied. Also an integral occurring in connection with soft bremsstrahlung is considered. Formulas in terms ofExpand
Abstract The negative-dimensional integration method (NDIM) seems to be a very promising technique for evaluating massless and/or massive Feynman diagrams. It is unique in the sense that the methodExpand
Massive two-loop diagrams: The Higgs propagator
Abstract Formulae are provided to express any two-loop scalar integral with arbitrary masses and arbitrary external momenta in terms of an integral of one fairly simple function or of itsExpand