S. Groote
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View article: First order electroweak radiative corrections to the decay of the polarized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>W</mml:mi> </mml:mrow> </mml:math> boson
First order electroweak radiative corrections to the decay of the polarized boson Open
Analytic results for the next-to-leading order electroweak radiative corrections to the decay of the polarized W boson into a pair of heavy quarks are presented. Finite fermion masses are taken into account throughout this calculation, a…
View article: Zero Mass as a Borel Structure
Zero Mass as a Borel Structure Open
The Lorentz group Lor1,3=SO0(1,3) has two point fixgroups, namely SO(3) for time-like translations and SO0(1,1)×IR2 for light-like translations. However, for light-like translations, it is reasonable to consider a line fixgroup that leads …
View article: New Effects and Methods in Brownian Transport
New Effects and Methods in Brownian Transport Open
We consider the noise-induced transport of overdamped Brownian particles in a ratchet system driven by nonequilibrium symmetric three-level Markovian noise and additive white noise. In addition to a detailed analysis of this system, we con…
View article: Finite temperature QCD crossover at non-zero chemical potential: A Dyson–Schwinger approach
Finite temperature QCD crossover at non-zero chemical potential: A Dyson–Schwinger approach Open
We study QCD at finite temperature and non-zero chemical potential to derive the critical temperature at the chiral phase transition (crossover). We solve a set of Dyson–Schwinger partial differential equations using the exact solution for…
View article: Non-Perturbative Quantum Yang–Mills at Finite Temperature Beyond Lattice: A Dyson–Schwinger Approach
Non-Perturbative Quantum Yang–Mills at Finite Temperature Beyond Lattice: A Dyson–Schwinger Approach Open
Using a Dyson–Schwinger approach, we perform an analysis of the non-trivial ground state of thermal SU(N) Yang–Mills theory in the non-perturbative regime where chiral symmetry is dynamically broken by a mass gap. Basic thermodynamic obser…
View article: Dynamical Generation of Electroweak Scale From the Conformal Sector: A Strongly Coupled Higgs via the Dyson–Schwinger Approach
Dynamical Generation of Electroweak Scale From the Conformal Sector: A Strongly Coupled Higgs via the Dyson–Schwinger Approach Open
A novel pathway to generate the electroweak (EW) scale via non‐perturbative dynamics of a conformally invariant scalar sector at the classical level is proposed. A method is provided to estimate the non‐perturbative EW scale generation usi…
View article: Finite temperature QCD crossover at non-zero chemical potential: A Dyson-Schwinger approach
Finite temperature QCD crossover at non-zero chemical potential: A Dyson-Schwinger approach Open
We study QCD at finite temperature and non-zero chemical potential to derive the critical temperature at the chiral phase transition (crossover). We solve a set of Dyson--Schwinger partial differential equations using the exact solution fo…
View article: Some Exact Green Function Solutions for Non-Linear Classical Field Theories
Some Exact Green Function Solutions for Non-Linear Classical Field Theories Open
We consider some non-linear non-homogeneous partial differential equations (PDEs) and derive their exact Green function solution as a functional Taylor expansion in powers of the source. The kind of PDEs we consider are dispersive ones whe…
View article: Dynamical generation of electroweak scale from the conformal sector: A strongly coupled Higgs via the Dyson--Schwinger approach
Dynamical generation of electroweak scale from the conformal sector: A strongly coupled Higgs via the Dyson--Schwinger approach Open
We propose a novel pathway to generate the electroweak (EW) scale via non-perturbative dynamics of a conformally invariant scalar sector at the classical level. We provide a method to estimate the non-perturbative EW scale generation using…
View article: First order electroweak radiative corrections to the decay of the polarised $W$ boson
First order electroweak radiative corrections to the decay of the polarised $W$ boson Open
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, a…
View article: Renormalisable Non-Local Quark–Gluon Interaction: Mass Gap, Chiral Symmetry Breaking and Scale Invariance
Renormalisable Non-Local Quark–Gluon Interaction: Mass Gap, Chiral Symmetry Breaking and Scale Invariance Open
We derive a Nambu–Jona-Lasinio (NJL) model from a non-local gauge theory and show that it has confining properties at low energies. In particular, we present an extended approach to non-local QCD and a complete revision of the technique of…
View article: Riemann's hypothesis via Robin's Theorem
Riemann's hypothesis via Robin's Theorem Open
As essential condition for the validy of Robin's Theorem as a precondition for the proof of the Riemann hypothesis, we show that the minimum of the function $F={\rm e}^γ\,\ln(\ln\,n)-σ(n)/n$ is found to be positive. Therefore, $F>0$ holds …
View article: A Solvable Algebra for Massless Fermions
A Solvable Algebra for Massless Fermions Open
We derive the stabiliser group of the four-vector, also known as Wigner’s little group, in case of massless particle states, as the maximal solvable subgroup of the proper orthochronous Lorentz group of dimension four, known as the Borel s…
View article: Some exact Green function solutions for non-linear classical field theories
Some exact Green function solutions for non-linear classical field theories Open
We consider some non-linear non-homogeneous partial differential equations (PDEs) and derive their exact Green function solution as a functional Taylor expansion in powers of the source. The kind of PDEs we consider are dispersive ones whe…
View article: Double J/ψ production as a test of parton momentum correlations in double parton scattering
Double J/ψ production as a test of parton momentum correlations in double parton scattering Open
Using the GS09 model we predict the possible impact of the parton momentum correlation on the J/ψ-pair production at the Spin Physics Detector at the Nuclotron-based Ion Collider Facility. The double J/ψ production and the effective cross …
View article: Confinement in QCD and generic Yang-Mills theories with matter representations
Confinement in QCD and generic Yang-Mills theories with matter representations Open
We derive the low-energy limit of quantum chromodynamics (QCD) and provide evidence that in the 't Hooft limit, i.e. for a very large number of colors and increasing 't Hooft coupling, quark confinement is recovered. The low energy limit o…
View article: Analytic Error Function and Numeric Inverse Obtained by Geometric Means
Analytic Error Function and Numeric Inverse Obtained by Geometric Means Open
Using geometric considerations, we provided a clear derivation of the integral representation for the error function, known as the Craig formula. We calculated the corresponding power series expansion and proved the convergence. The same g…
View article: Analytic Error Function and Numeric Inverse Obtained by Geometric Means
Analytic Error Function and Numeric Inverse Obtained by Geometric Means Open
Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same geom…
View article: Analytic error function and numeric inverse obtained by geometric means
Analytic error function and numeric inverse obtained by geometric means Open
Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same geom…
View article: Renormalisable Non-local Quark-Gluon Interaction: Mass Gap, Chiral Symmetry Breaking & Scale Invariance
Renormalisable Non-local Quark-Gluon Interaction: Mass Gap, Chiral Symmetry Breaking & Scale Invariance Open
We derive a Nambu--Jona-Lasinio (NJL) model from a non-local gauge theory and show that it has confining properties at low energies. In particular, we present an extended approach to non-local QCD and a complete revision of the technique o…
View article: Quark confinement in QCD in the 't Hooft limit
Quark confinement in QCD in the 't Hooft limit Open
We treat quantum chromodynamics (QCD) using a set of Dyson-Schwinger equations derived, in differential form, with the Bender-Milton-Savage technique. In this way, we are able to derive the low energy limit that assumes the form of a non-l…
View article: Double $J/ψ$ production as a test of parton momentum correlations in double parton scattering
Double $J/ψ$ production as a test of parton momentum correlations in double parton scattering Open
Using the GS09 model we predict the possible impact of the parton momentum correlation on the $J/ψ$-pair production at the Spin Physics Detector at the Nuclotron-based Ion Collider Facility. The double $J/ψ$ production and the effective cr…
View article: Algebra with ternary cyclic relations, representations and quark model
Algebra with ternary cyclic relations, representations and quark model Open
We propose a unital associative algebra, which is motivated by a generalization of the Pauli exclusion principle proposed within the framework of the quark model. The generators of this algebra satisfy the following relations: The sum of s…
View article: A Solvable Algebra for Massless Fermions
A Solvable Algebra for Massless Fermions Open
We derive the stabiliser group of the four-vector, also known as Wigner’s little group, in case of massless particle states, as the maximal solvable subgroup of the proper orthochronous Lorentz group of dimension four, known as the B…
View article: A solvable algebra for massless fermions
A solvable algebra for massless fermions Open
We derive the stabiliser group of the four-vector, also known as Wigner's little group, in case of massless particle states, as the maximal solvable subgroup of the proper orthochronous Lorentz group of dimension four, known as the Borel s…
View article: Identical particle and lepton mass effects in the decay $H\to Z^\ast(\toτ^+τ^-)+Z^\ast(\toτ^+τ^-)$
Identical particle and lepton mass effects in the decay $H\to Z^\ast(\toτ^+τ^-)+Z^\ast(\toτ^+τ^-)$ Open
We consider identical particle and lepton mass effects in the cascade decay $H\to Z^\ast(\toτ^+τ^-)+Z^\ast(\toτ^+τ^-)$. Since the scale of the problem is set by the off-shellness $p_a^2$ and $p_b^2$ of the respective gauge bosons in the li…
View article: Evaluation of the Gauss Integral
Evaluation of the Gauss Integral Open
The normal or Gaussian distribution plays a prominent role in almost all fields of science. However, it is well known that the Gauss (or Euler–Poisson) integral over a finite boundary, as is necessary, for instance, for the error fun…
View article: Evaluation of the Gauss Integral
Evaluation of the Gauss Integral Open
The normal or Gaussian distribution plays a prominent role in almost all fields of science. However, it is well known that the Gauss (or Euler–Poisson) integral over a finite boundary, as is necessary, for instance, for the error function …