Related papers: Numerical multi-loop integrals and applications
The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and…
Numerical calculation of two-loop electroweak corrections to the muon anomalous magnetic moment ($g$-2) is done based on, on shell renormalization scheme (OS) and free quark model (FQM). The GRACE-FORM system is used to generate Feynman…
We investigate the high-scale behaviour of Higgs sectors beyond the Standard Model, pointing out that the proper matching of the quartic couplings before applying the renormalisation group equations (RGEs) is of crucial importance for…
Two-loop electroweak corrections to the muon anomalous magnetic moment are automatically calculated by using GRACE-FORM system, as a trial to extend our system for two-loop calculation. We adopt the non-linear gauge (NLG) to check the…
We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium. These corrections are enhanced by the large logarithm of the electron-muon mass ratio. The leading logarithm cubed and logarithm squared contributions…
We review recent theoretical progress in the computation of radiative corrections beyond one loop within the standard model of electroweak interactions, both in the gauge and Higgs sectors. In the gauge sector, we discuss universal…
Large scale calculation for the radiative corrections required for the current and future collider experiments can be done automatically using the GRACE-LOOP system. Here several results for e+e- --> 3-body processes are presented including…
We present the full order alpha electroweak radiative corrections to e+e- -> e+e-H. The computation is performed with the help of GRACE-loop. The extraction of the full QED corrections is performed, these are quite large at threshold. The…
Electroweak Sudakov logarithms at high energy, of the form alpha/(sin^2theta_W)^n log^m s/M_{Z,W}^2, are summed using effective theory methods. The corrections are computed to processes involving two external particles in the standard…
Various properties of the general two-center two-electron integral over the explicitly correlated exponential function are analyzed for the potential use in high precision calculations for diatomic molecules. A compact one dimensional…
We compute analytically the complete electroweak two-loop corrections to the $B^0-{\bar B}^0$ mixing. These corrections fix the normalization of the electroweak coupling employed in the extraction of $|V_{td}|$ and reduce the theoretical…
The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with $N$ samples behaves like $1/\sqrt{N}$. This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in…
We calculate analytically the two-loop triangle integrals entering the $\mathcal{O}(\alpha\alpha_s)$ corrections to the $HZV$ vertex with $V=Z^*,\gamma^*$ using the method of differential equations. Our result provides a prototype to study…
We perform detailed calculations of electroweak radiative corrections to parity violating lepton scattering with a proton target up to quadratic and reducible two-loop level using a covariant approach. Our numerical results are presented at…
For the first time the next-to-leading-order electroweak corrections to the full off-shell production of two top quarks that decay leptonically are presented. This calculation includes all off-shell, non-resonant, and interference effects…
In this paper we investigate higher-order corrections to the energies of bound states in hydrogen subjected to the external blackbody radiation field. In particular, within the framework of thermal quantum electrodynamics and $S$-matrix…
The challenge of mastering computational tasks of enormous size tends to frequently override questioning the quality of the numerical outcome in terms of accuracy. By this we do not mean the accuracy within the discrete setting, which…
We propose to resum exactly any number of one-loop vacuum polarization insertions into the scale of the coupling of lowest order radiative corrections. This makes maximal use of the information contained in one-loop perturbative corrections…
We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows to overcome these…
Functional methods can be applied to the quantum effective action to efficiently determine counterterms and matching conditions for effective field theories. We extend the toolbox to two-loop order and beyond and show how to evaluate the…