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Stefan Groote

Publications and source records attributed to Stefan Groote.

At least 37 records · Page 2Linked to original sources
arXiv2022

Evaluation of the Gauss integral

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 it is necessary for instance for the error function or the cumulative distribution of the normal distribution, cannot be expressed by analytic functions. This is proven by the Risch algorithm. Still, there are proposals for approximate solutions. In this paper, we give a new solution in terms of normal distributions by applying a geometric procedure iteratively to the problem.

math.NA↗
arXiv2022

Topological tensor invariants and the current algebra approach: Analysis of 196 nonleptonic two-body decays of single and double charm baryons -- a review

We shed new light on the standard current algebra approach to the nonleptonic two-body decays of single and double heavy charm baryons. By making use of the completeness relation for the flavor wave functions of the ground state baryon {\bf 20'} representation we are able to rewrite the results of the current algebra approach in terms of the seven topological tensor invariants describing the decays. The representation of the current algebra results in terms of topological tensor invariants depends only on the initial and final state of the process. The summation over intermediate states inherent to the current algebra result is automatically taken care of in the tensor representation. In this way one arrives at a new, quick and very compact assessment of the results of the current algebra/pole model calculation. For example, one can quickly identify the decays in which the p.v.\ $S$-wave amplitude is predicted to vanish implying zero polarization asymmetries in these decays. We provide tables of the values of the seven topological tensor invariants for all Cabibbo favored and singly and doubly Cabibbo suppressed nonleptonic single and double charm baryon decays. In total we treat 196 charm baryon decays. We also discuss the charm preserving $ΔC=0$ decays of single charm baryons and the usual hyperon decays.

hep-ph↗
arXiv2021

On a novel evalutation of the hadronic contribution to the muon's $g-2$ from QCD

We evaluate the hadronic contribution to the $g-2$ of the muon by deriving the low-energy limit of quantum chromodynamics (QCD) and computing in this way the hadronic vacuum polarization. The low-energy limit is a non-local Nambu--Jona-Lasinio (NJL) model that has all the parameters fixed from QCD, and the only experimental input used is the confinement scale that is known from measurements of hadronic physics. Our estimations provide a novel analytical alternative to the current lattice computations and we find that our result is close to the similar computation performed from experimental data. We also comment on how this analytical approach technique, in general, may provide prospective estimates for hadronic computations from dark sectors and its implication in BSM model-building in future.

hep-ph↗
arXiv2021

Nambu-Jona-Lasinio model correlation functions from QCD

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 with all the parameters properly fixed by the QCD Lagrangian and the determination of the mass gap of the gluon sector.

hep-ph↗
arXiv2021

Form-factor-independent test of lepton universality in semileptonic heavy meson and baryon decays

In the semileptonic decays of heavy mesons and baryons the lepton-mass dependence factors out in the quadratic $\cos^2θ$ coefficient of the differential $\cosθ$ distribution. We call the corresponding normalized coefficient the convexity parameter. This observation opens the path to a test of lepton universality in semileptonic heavy meson and baryon decays that is independent of form-factor effects. By projecting out the quadratic rate coefficient, dividing out the lepton-mass-dependent factor and restricting the phase space integration to the $τ$ lepton phase space, one can define optimized partial rates which, in the Standard Model, are the same for all three $(e,μ,τ)$ modes in a given semileptonic decay process. We discuss how the identity is spoiled by New Physics effects. We discuss semileptonic heavy meson decays such as $\bar{B}^0 \to D^{(\ast)+} \ell^- \barν_\ell$ and $B_c^- \to J/ψ(η_c)\ell^- \barν_\ell$, and semileptonic heavy baryon decays such as $Λ_b \to Λ_c \ell^- \barν_\ell$ for each $\ell=e,μ,τ$.

hep-ph↗
arXiv2020

Gauge dependence of the gauge boson projector

The propagator of a gauge boson, like the massless photon or the massive vector bosons $W^\pm$ and $Z$ of the electroweak theory, can be derived in two different ways, namely via Green's functions (semi-classical approach) or via the vacuum expectation value of the time-ordered product of the field operators (field theoretical approach). Comparing the semi-classical with the field theoretical approach, the central tensorial object can be defined as the gauge boson projector, directly related to the completeness relation for the complete set of polarisation four-vectors. In this paper we explain the relation for this projector to different cases of the $R_ξ$ gauge and explain why the unitary gauge is the default gauge for massive gauge bosons.

hep-ph↗
arXiv2019

A new angle on an old problem: Helicity approach to neutron beta decay in the Standard Model

We elaborate on the dichotomy between the description of the semileptonic decays of heavy hadrons on the one hand and the semileptonic decays of light hadrons such as neutron $β$ decays on the other hand. For example, almost without exception the semileptonic decays of heavy baryons are described in cascade fashion as a sequence of two two-body decays $B_1 \to B_2 + W_{\rm off-shell}$ and $W_{\rm off-shell} \to \ell + ν_\ell$ whereas neutron $β$ decays are analyzed as true three-body decays $n \to p + e^- +\bar ν_e$. Within the cascade approach it is possible to define a set of seven angular observables for polarized neutron $β$ decays as well as the longitudinal, transverse and normal polarization of the decay electron. We determine the dependence of the observables on the usual vector and axial vector form factors. In order to be able to assess the importance of recoil corrections we expand the rate and the $q^2$ averages of the observables up to NLO and NNLO in the recoil parameter $δ=(M_n-M_p)/(M_n+M_p)= 0.689\cdot 10^{-3}$. Remarkably, we find that the rate and three of the four parity conserving polarization observables that we analyze are protected from NLO recoil corrections when the second class current contributions are set to zero.

hep-ph↗
arXiv2019

Hadronic contributions to the muon anomalous moment

We discuss the hadronic contributions to the muon anomalous magnetic moment. They are dominated by light quark contributions which are constrained by the mechanism of chiral symmetry breaking. Using the leading order result based on $e^+ e^-$ scattering data, we show that the next-to-leading order contributions in the fine structure constant $α$ can be reliably calculated. Extending this idea to the hadronic four-point function we give a prediction for the light-by-light contribution.

hep-ph↗
arXiv2019

A first approach to the Galois group of chaotic chains

We explain in detail the definition, construction and generalisation of the Galois group of Chebyshev polynomials of high degree to the Galois group of chaotic chains. The calculations in this paper are performed for Chebyshev polynomials and chaotic chains of degree $N=2$. Insides into possible further steps are given.

nlin.CD↗
arXiv2019

Relativistic entanglement of two particles driven by continuous product momenta

In this paper we explore the entanglement of two relativistic spin-$1/2$ particles with continuous momenta. The spin state is described by the Bell state and the momenta are given by Gaussian distributions of product form. Transformations of the spins are systematically investigated in different boost scenarios by calculating the orbits and concurrence of the spin degree of freedom. By visualizing the behavior of the spin state we get further insight into how and why the entanglement changes in different boost situations.

quant-ph↗
arXiv2018

NLO and NNLO corrections to polarized top quark decays

We present partial results on NLO and NNLO QCD, and NLO electroweak corrections to polarized top quark decays. In parallel we derive positivity bounds for the polarized structure functions in polarized top quark decays and check them against the perturbative corrections to the structure functions.

hep-ph↗
arXiv2018

Analysis of the baryonic state $|[qc]c\rangle$

In this note we analyse the structure of the baryonic state $|[qc]c\rangle$ with a spin-0 diquark $[qc]$, as compared to baryonic states $|(qc)c\rangle$ and $|q(cc)\rangle$ containing internal spin-1 diquark states. While one can identify the state $|q(cc)\rangle$ with the state observed at LHCb, the state $|(qc)c\rangle$ could probably be part of the state $Ξ_{cc}^{++}(3780)$. Accordingly, the ground state of $|[qc]c\rangle$ can be identified with the state $Ξ_{cc}^+(3520)$.

hep-ph↗
arXiv2017

Production of doubly charmed baryons nearly at rest

We investigate the production cross sections, momentum distributions and rapidity distributions for doubly charmed baryons which according to the intrinsic heavy quark mechanism are produced nearly at rest. These events should be measurable at fixed-target experiments like STAR@RHIC and AFTER@LHC.

hep-ph↗
arXiv2017

Double quarkonium production at high Feynman-$x$

In this paper we give estimates for the proton--proton cross sections into pairs of quarkonium states $J/ψ$, $ψ(2S)$, $Υ(1S)$ and $Υ(2S)$ at the scheduled AFTER@LHC energy of $115$GeV. The estimates are based on the intrinsic heavy flavor mechanism which is observable for high values of $x_F$, a range outside the dominance of single parton and double parton scattering.

hep-ph↗