Related papers: Dimensionally Regularized Box and Phase Space inte…
This is the first in a series of papers addressing the phenomenon of dimensional transmutation in nonrelativistic quantum mechanics within the framework of dimensional regularization. Scale-invariant potentials are identified and their…
Starting from the basic path integral in phase space we reconsider the functional approach to the RG flow of the one particle irreducible effective average action. On employing a balanced coarse-graining procedure for the canonical…
We consider the application of regularization by dimensional reduction to NLO corrections of hadronic processes. The general collinear singularity structure is discussed, the origin of the regularization-scheme dependence is identified and…
We illustrate the dimensional regularization technique using a simple problem from elementary electrostatics. We contrast this approach with the cutoff regularization approach, and demonstrate that dimensional regularization preserves the…
We introduce a novel spatio-temporal discretization for nonlinear Fokker-Planck equations on the multi-dimensional unit cube. This discretization is based on two structural properties of these equations: the first is the representation as a…
We construct a basis set of infra-red and/or collinearly divergent scalar one-loop integrals and give analytic formulas, for tadpole, bubble, triangle and box integrals, regulating the divergences (ultra-violet, infra-red or collinear) by…
The quantum corrections related to the ideal gas model that are often considered are those which are related to the particles nature: bosons or fermions. These corrections lead respectively to the Bose-Einstein and Fermi-Dirac statistics.…
Geometric moments and moment invariants of image artifacts have many uses in computer vision applications, e.g. shape classification or object position and orientation. Higher order moments are of interest to provide additional feature…
This paper concerns the intermediate dimensions, a spectrum of dimensions that interpolate between the Hausdorff and box dimensions. Potential theoretic methods are used to produce dimension bounds for images of sets under H\"older maps and…
Diagonalization of a large matrix is the computational bottleneck in many applications such as electronic structure calculations. We show that a speedup of over 30% can be achieved by exploiting 32-bit floating point operations, while…
The three-loop QCD contributions to the vacuum polarization functions of the $Z$ and $W$ bosons at zero momentum are calculated. The top quark is considered to be massive and the other quarks massless. Using these results, we calculate the…
Analytic results for the next-to-leading order electroweak radiative corrections to the decay of the polarised $W$ boson into a pair of heavy quarks are presented. Finite fermion masses are taken into account throughout this calculation,…
Characterizing the phase space distribution of particle beams in accelerators is a central part of accelerator understanding and performance optimization. However, conventional reconstruction-based techniques either use simplifying…
We compute the QCD corrections at next-to-leading order for the process $gg \rightarrow ZH$, including both the virtual two-loop terms and real-emission contributions. The two-loop box diagrams in the virtual corrections are approximated…
A Higgs boson in the intermediate mass range is considered. An effective Lagrangian approach is used in order to evaluate the top-induced QCD corrections of order $\alpha_s^3$ to the decay into light quarks and $O(\alpha_s^4)$ corrections…
Based on the nonrelativistic QCD factorization theorem, we resum QCD corrections to the inclusive decay rate of $\eta_c$ and $\eta_b$ in the large-$n_f$ limit using bubble chain resummation. By employing dimensional regularization, we show…
In this article, quadrature rules for the efficient computation of the stiffness matrix for the fractional Laplacian in three dimensions are presented. These rules are based on the Duffy transformation, which is a common tool for…
A method is introduced to calculate the UV-divergent parts at one-loop level in dimensional regularization. The method is based on the recursion, and the basic integrals are just the scaleless integrals after the recursive reduction, which…
We present the computation of the contributions to N3LO inclusive Higgs boson production due to two-loop amplitudes. Our result is a Laurent expansion in the dimensional regulator, with coefficients that are linear combinations of harmonic…
A hybrid computational method of plane-wave and cylindrical-wave expansions for distributed Bragg-reflector (DBR) pillars is proposed. The plane-wave expansion is employed to represent the one-dimensional periodic structure of the DBR. The…