Related papers: Numerical multi-loop integrals and applications
We examine the effect of numerical integration on the convergence of high order pyramidal finite element methods. Rational functions are indispensable to the construction of pyramidal interpolants so the conventional treatment of numerical…
In supersymmetric models, very heavy stop squarks introduce large logarithms into the computation of the Higgs boson mass. Although it has long been known that in simple cases these logs can be resummed using effective field theory…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
Logarithmic Number Systems (LNS) hold considerable promise in helping reduce the number of bits needed to represent a high dynamic range of real-numbers with finite precision, and also efficiently support multiplication and division.…
We construct a specific formalism for calculating the one-loop virtual corrections for standard model processes with an arbitrary number of external legs. The procedure explicitly separates the infrared and ultraviolet divergences…
Ab initio predictions of two-loop electroweak contributions to observables are increasingly essential for precision collider experiments, yet their evaluation remains very challenging. We connect recurrence techniques and dispersive method…
This article presents results for the last unknown two-loop contributions to the $Z$-boson partial widths and $Z$-peak cross-section. These are the so-called bosonic electroweak two-loop corrections, where "bosonic" refers to diagrams…
The rare K -> pi nu anti-nu decays play a central role in testing the Standard Model and its extensions. Upcoming experiments plan to measure the decay rates with high accuracy. Yet, unknown higher-order electroweak corrections result in a…
In this work we present the computation of the one-loop electroweak radiative corrections to the scattering process $WW\to HH$ within the context of the Higgs Effective Field Theory (HEFT). We assume that the fermionic interactions are like…
Precision electroweak measurements at LEP currently check the validity of the Standard Model to about one part in a thousand. Any successful model of physics beyond the Standard Model must be consistent with these observations. The impact…
The precise determination of the Higgs self-couplings is an essential task for understanding electroweak symmetry breaking and probing physics beyond the Standard Model (SM). The calculation of two-loop corrections to scalar couplings is…
Monte Carlo methods play a central role in particle physics, where they are indispensable for simulating scattering processes, modeling detector responses, and performing multi-dimensional integrals. However, traditional Monte Carlo methods…
We introduce data structures and algorithms to count numerical inaccuracies arising from usage of floating numbers described in IEEE 754. Here we describe how to estimate precision for some collection of functions most commonly used for…
The concept of effective order is a popular methodology in the deterministic literature for the construction of efficient and accurate integrators for differential equations over long times. The idea is to enhance the accuracy of a…
We use functional methods to compute one-loop effects in Heavy Quark Effective Theory. The covariant derivative expansion technique facilitates the efficient extraction of matching coefficients and renormalization group evolution equations.…
We consider two-loop leading and next-to-leading logarithmic virtual corrections to arbitrary processes with external massless fermions in the electroweak Standard Model at energies well above the electroweak scale. Using the…
We calculate radiative-recoil corrections of order $\alpha^2(Z\alpha)(m/M)E_F$ to hyperfine splitting in muonium generated by the diagrams with electron and muon polarization loops. These corrections are enhanced by the large logarithm of…
Recent progress in the calculation of multi-loop, multi-scale diagrams is reviewed. Expansion techniques combined with new developments in Computer algebra allow to evaluate the R ratio for massive quarks up to order $\alpha_s^2$ and,…
We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium due to insertions of one-loop polarization operator in the electron factor. The contribution generated by electron polarization insertions is a cubic…
Review of the electroweak sector of the minimal standard model, Basic LEP processes at the tree level, 1-loop radiative corrections in the on-shell renormalization scheme, Star scheme and oblique corrections, Introduction to oblique…