Searcharxiv⌕ Search

arXiv subjects

Stefan Groote

Publications and source records attributed to Stefan Groote.

At least 19 recordsLinked to original sources
arXiv2026

Exact Lattice Identities and Continuum-Limit Dyson--Schwinger Equations for Yang-Mills Theory

Starting from SU(N) on the lattice, we give a rigorous derivation of the Dyson--Schwinger equations in the continuum limit. We formulate the Dyson--Schwinger identities for the lattice Yang--Mills theory directly in terms of the link variables $U_\mu(m)\in SU(N)$, exploiting the invariance of the Haar measure under left group translations. This provides an exact lattice derivation of the corresponding master equation for the Wilson action, expressed through left-invariant Lie derivatives acting on individual links. Because the construction is carried out directly on the compact gauge group, it avoids the ambiguities associated with introducing Lie-algebra valued gauge potentials as primary integration variables at finite lattice spacing. For practical applications, in a second part we then break down the gauge degree of freedom by choosing Feynman gauge. We analyze the continuum-limit form of the resulting lattice identities and derive equations for the one- and two-point connected functions. Under a further simplifying reduction, these equations close to a tractable scalar system. Our results establish a direct bridge between exact lattice identities and the functional equations commonly used in continuum nonperturbative studies of Yang--Mills theory.

hep-th↗
arXiv2026

Baryonic Bound States in the Non-Local NJL Model

Baryons, as three-quark bound states, require a covariant treatment in the intermediate-energy regime where perturbative QCD is no longer applicable and where nonperturbative correlations dominate. This article reformulates the content of the CERN Baltic Conference 2025 presentation on baryonic bound states in the non-local Nambu--Jona-Lasinio (NJL) model. We review how the relativistic Faddeev approach reduces the three-body quark problem to an effective quark--diquark bound-state problem, describe the scalar and axial-vector diquark channels, and show how the resulting quark--diquark Bethe--Salpeter equation can be written as an eigenvalue problem for the baryon mass. The non-local NJL framework, motivated by QCD-based nonlocal interactions and Dyson--Schwinger considerations, provides a compact description in which baryon masses and form factors are extracted from the numerical solution of coupled integral equations.

hep-ph↗
arXiv2026

Decay and structure of heavy flavour

In accordance to the aim of the constituing meeting of the COST action CA24159 ``Structure and Spectroscopy of Hadrons Research Project'' to introduce the different groups to the action, in this talk we give an overview over the subjects dealt with by the working group in Tartu related to hadron physics. We deal with the production and the nonleptonic decays of charmed baryons in the framework of the current algebra approach in terms of tensor invariants and explain how this approach can be used to approach CP violation via long distance effects in rescattering. New physics effects can be even seen in the classical neutron beta decay, but the helicity approach used here is also useful for e.g.\ calculating first order electroweak radiative corrections to the decay of the polarised $W$ boson. Identical particle and mass effects are seen in the Higgs decay into four leptons of the same type. The second main part starts with indications for the intrinsic charm mechanism, explaining the discrepancy between the results of SELEX and LHCb. The solution offered here is valid only if one considers nonlocal field operators. The nonlocal extension of the Nambu--Jona-Lasinio model, derived directly from QCD and combined with the relativistic Faddeev approach, allows for the description of hadronic states. We conclude by presenting open questions to the action.

hep-ph↗
arXiv2025

First order electroweak radiative corrections to the decay of the polarised $W$ boson

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, and in performing the collinear limit for the final quark states and all light fermions taking part in this process, the importance of mass effects is demonstrated. This gives hints for the deviation of the total decay rate and the branching ratios into massive fermions between experimental measurements and theoretical predictions.

hep-ph↗
arXiv2025

Zero mass as a Borel structure

The Lorentz group Lor$_{1,3}=$SO$_0(1,3)$ has two point fixgroups, namely SO$(3)$ for time-like translations and SO$_0(1,1)\times R^2$ for light-like translations. However, for light-like translations it is reasonable to consider a line fixgroup that leads to the Borel structure of the Lorentz group and gives appropriate helicities for massless particles. Therefore, whether a particle is massless or massive is not so much a physical question but rather a question of the underlying Lie group symmetry.

physics.gen-ph↗
arXiv2025

Finite temperature QCD crossover at non-zero chemical potential: A Dyson-Schwinger approach

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 the Yang--Mills quantum field theory based on elliptical functions. We derive a Nambu-Jona--Lasino (NJL) model of the quarks and obtain a very good agreement with recent lattice computations regarding the dependence of the critical temperature on the strong coupling scale. The solution depends on a single scale parameter, as typical for the theory and already known from studies about asymptotic freedom. The study is analytically derived from QCD.

hep-ph↗
arXiv2025

Non-perturbative quantum Yang--Mills at finite temperature beyond lattice: a Dyson--Schwinger approach

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 observables such as energy density and pressure are derived analytically, using Jacobi elliptic functions. The results are compared with lattice results. Good agreement is found at low temperatures, providing a viable scenario of a gas of massive glue states populating higher levels of the spectrum of the theory. At high temperatures a scenario without glue states consistent with a massive scalar field is observed, showing an interesting agreement with lattice data. The possibility is discussed that the results derived in this analysis open up a novel pathway beyond lattice to precision studies of phase transitions with false vacuum and cosmological relics that depend on the equations of state in strong coupled gauge theories of the type of Quantum Chromodynamics (QCD).

hep-ph↗
arXiv2025

Dynamical generation of electroweak scale from the conformal sector: A strongly coupled Higgs via the Dyson--Schwinger approach

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 the exact solution of the background equations of motion in a scalar theory via the Dyson-Schwinger approach. Particularly, we find an analytical result for the Higgs mass in the strongly coupled regime in terms of its quartic self interaction term and the cut-off scale of the theory. We also show that the Higgs sector is an essential part of the Standard Model as, without it, a Yang--Mills gauge theory cannot acquire mass even if a self-interaction term is present. Our analysis lead to a more realistic model building with possible solutions to the gauge hierarchy problem and, in general, to the dynamical generation of any scales scales in nature, be it the visible sector or the dark sector.

hep-ph↗
arXiv2024

Some exact Green function solutions for non-linear classical field theories

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 where the exact solution of the corresponding homogeneous equations can have some known shape. The technique has a formal similarity with the Dyson--Schwinger set of equations to solve quantum field theories. However, there are no physical constraints. Indeed, we show that a complete coincidence with the statistical field model of a quartic scalar theory can be achieved in the Gaussian expansion of the cumulants of the partition function.

math-ph↗
arXiv2024

Renormalisable Non-local Quark-Gluon Interaction: Mass Gap, Chiral Symmetry Breaking & Scale Invariance

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 Bender, Milton and Savage applied to non-local theories, providing a set of Dyson--Schwinger equations in differential form. In the local case, we obtain closed form solutions in the simplest case of the scalar field and extend it to the Yang--Mills field. In general, for non-local theories, we use a perturbative technique and a Fourier series and show how higher-order harmonics are heavily damped due to the presence of the non-local factor. The spectrum of the theory is analysed for the non-local Yang--Mills sector and found to be in agreement with the local results on the lattice in the limit of the non-locality mass parameter running to infinity. In the non-local case, we confine ourselves to a non-locality mass that is sufficiently large compared to the mass scale arising from the integration of the Dyson--Schwinger equations. Such a choice results in good agreement, in the proper limit, with the spectrum of the local theory. We derive the gap equation for the fermions in the theory that gives some indication of quark confinement in the non-local NJL case as well. Confinement seems to be a rather ubiquitous effect that removes some degrees of freedom in the original action, favouring the appearance of new observable states, as seen, e.g.,\ for quantum chromodynamics at lower energies.

hep-ph↗
arXiv2024

Riemann's hypothesis via Robin's Theorem

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 for any $n>5040$.

math.NT↗
arXiv2024

A solvable algebra for massless fermions

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 subgroup. In the absence of mass, particle states are disentangled into left- and right-handed chiral states, governed by the maximal solvable subgroups ${\rm sol}_2^\pm$ of order two. Induced Lorentz transformations are constructed and applied to general representations of particle states. Finally, in our conclusions it is argued how the spin-flip contribution might be closely related to the occurrence of nonphysical spin operators.

physics.gen-ph↗
arXiv2023

Confinement in QCD and generic Yang-Mills theories with matter representations

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 of the theory turns out to be a non-local Nambu-Jona-Lasinio (NJL) model. The effect of non-locality, arising from a gluon propagator that fits quite well to the profile of an instanton liquid, is to produce a phase transition from a chiral condensate to an instanton liquid, as the coupling increases with lower momentum. This phase transition suffices to move the poles of the quark propagator to the complex plane. As a consequence, free quarks are no longer physical states in the spectrum of the theory.

hep-ph↗
arXiv2023

Analytic error function and numeric inverse obtained by geometric means

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 geometric means finally help to systematically derive handy formulas that approximate the inverse error function. Our approach can be used for applications in e.g.\ high-speed Monte Carlo simulations where this function is used extensively.

physics.data-an↗
arXiv2023

Identical particle and lepton mass effects in the decay $H\to Z^\ast(\toτ^+τ^-)+Z^\ast(\toτ^+τ^-)$

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 limits ($4m_τ^2\le p_a^2,p_b^2\le (m_H-2m_τ)^2$) and not by $m_H^2$, lepton mass effects are nonnegligible in particular close to the threshold of the off-shell decays. We calculate the rates and single angle decay distributions and compare them with the corresponding rates and single angle decay distributions for the nonidentical particle decays $H\to Z^\ast(\to e^+e^-)+Z^\ast(\toμ^+μ^-)$ involving negligible lepton masses.

hep-ph↗
arXiv2022

Quark confinement in QCD in the 't Hooft limit

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-local Nambu-Jona-Lasinio model. The corresponding gap equation is then studied to show that such a model has no free quarks in the low-energy limit.

hep-ph↗
arXiv2022

$O(α_s)$ perturbative and nonperturbative corrections to polarized semileptonic $Λ_b$ decay distributions

In this paper we calculate first order radiative QCD corrections to the decay process $b\to cW^-(\to\ell^-\barν_\ell)$ of a polarized bottom quark. Taking into account both the bottom and charm quark masses, the analytical expressions given in this paper allow for a detailed analysis of the differential decay rate of the polarized quark in dependence on the polar and azimuthal angles of the lepton pair and the angle of the polarization vector of the quark relative to the momentum direction of the $W$ boson. The results are given for different polarization states of the charged lepton. In addition, we calculated nonperturbative corrections and estimated their contribution.

hep-ph↗