Related papers: Numerical multi-loop integrals and applications
Electroweak radiative corrections form a crucial ingredient in modern precision calculations for particle processes at high-energy colliders such as the Large Hadron Collider. The salient features of electroweak corrections as well as…
Precision studies of the Higgs boson at future $e^+e^-$ colliders can help to shed light on fundamental questions related to electroweak symmetry breaking, baryogenesis, the hierarchy problem, and dark matter. The main production process,…
Precision experiments, such as those performed at LEP and SLC, offer us an excellent opportunity to constrain extended gauge model parameters. To this end, it is often assumed, that in order to obtain more reliable estimates, one should…
I will present a new method for thinking about and for computing loop integrals based on differential equations. All required information is obtained by algebraic means and is encoded in a small set of simple quantities that I will…
The direct computation method(DCM) is developed to calculate the multi-loop amplitude for general masses and external momenta. The ultraviolet divergence is under control in dimensional regularization. In this paper we report on the…
With a key improvement, the auxiliary mass flow method is now able to compute Feynman integrals encountered in cutting-edge collider processes. We have successfully applied it to compute some integrals involved in two-loop electroweak…
We derive logarithmically enhanced two-loop virtual electroweak corrections for arbitrary fermion-scattering processes at the TeV scale. This extends results previously obtained for massless fermion scattering to processes that involve also…
We describe in some detail the present features of an automatic loop calculation program as well as the integration techniques that go into it. The program, called XLOOPS 1.0, allows one to calculate massive one- and two-loop Feynman…
We consider the two-loop corrections to the $HW^+W^-$ vertex at order $\alpha\alpha_s$. We construct a canonical basis for the two-loop integrals using the Baikov representation and the intersection theory. By solving the $\epsilon$-form…
We compute the complete two-loop electroweak corrections to the Higgsstralung process $e^+e^-\rightarrow HZ$ at the future Higgs factory. The Feynman integrals involved in the computation are decomposed into linear combinations of a minimal…
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, concerning the evaluation of the…
An overview is presented on the current status of main mathematical computation methods for the multi-loop corrections to single scale observables in quantum field theory and the associated mathematical number and function spaces and…
We present a new method for the numerical evaluation of arbitrary loop integrals in dimensional regularization. We first derive Mellin-Barnes integral representations and apply an algorithmic technique, based on the Cauchy theorem, to…
We study a recently-proposed approach to the numerical evaluation of multi-loop Feynman integrals using available sector decomposition programs. As our main example, we consider the two-loop integrals for the $\alpha \alpha_s$ corrections…
Recently, the calculation of fermionic electroweak two-loop corrections to the total width of the Z boson and hadronic Z-peak cross-section in the Standard Model has been presented in arXiv:1310.2256, where "fermionic" refers to diagrams…
Finite precision computations using digital computers involve the following inherent errors: (1) Round-off error of finite precision computations (2) Binary computer arithmetic precludes exact number representation of traditional decimal…
Higher-order contributions to the precision observables \Delta r, \sin^2\theta_eff and \Gamma_l are discussed. The Higgs-mass dependence of the observables is investigated at the two-loop level, and exact results are derived for the…
We present a semi-numerical method to compute one-loop corrections to multi-leg processes. We apply the method to the study of Higgs plus four parton and six gluon amplitudes.
The computation of Feynman integrals is often the bottleneck of multi-loop calculations. We propose and implement a new method to efficiently evaluate such integrals in the physical region through the numerical integration of a suitable set…
The paper discusses the two-loop (NNLO) electroweak radiative corrections to the parity violating electron-electron scattering asymmetry induced by squaring one-loop diagrams. The calculations are relevant for the ultra-precise 11 GeV…