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Hans-Christian Pauli

Publications and source records attributed to Hans-Christian Pauli.

At least 19 recordsLinked to original sources
arXiv2005

Retrieving the missed particle-antiparticle degrees of freedom of Dirac particles

The missed particle-antiparticle degrees of freedom are retrieved and the corresponding particle-antiparticle intrinsic space are introduced to study the dynamical symmetry of the Dirac particle. As a result, the particle-antiparticle quantum number appears naturally and the Dirac particle has five quantum numbers instead of four. An anti-symmetry (different from the conventional symmetry) of the Dirac Hamiltonian and a dual symmetry of its eigenfunctions are explored. The $\hatκ$ operator of the Dirac equation in central potentials is found to be the analog of the helicity operator of the free particle--the alignment of the spin along the angular momentum.

hep-th↗
arXiv2003

Solution to the non-perturbative renormalization of gauge theory

The long standing problem of a non-perturbative renormalization of a gauge field theoretical Hamiltonian is addressed and explicitly carried out within an (effective) light-cone Hamiltonian approach to QCD. The procedure is in line with the conventional ideas: The Hamiltonian is first regulated by suitable cut-off functions, and subsequently renormalized by suitable counter terms to make it cut-off independent. Emphasized is the considerable freedom in the cut-off function which eventually can modify the Coulomb potential of two charges at sufficiently small distances. The approach provides new physical insight into the nature of gauge theory and the potential energy of QCD and QED at short distance.

hep-ph↗
arXiv2003

Fine and hyperfine interaction on the light cone

The formalism for the spin interactions in the front form (light-cone) is re-phrased in terms of an instant form formalism. It is shown how to unitarily transform the Brodsky-Lepage spinors to Bjørken-Drell spinors and to re-phrase the so called spinor matrix in terms of the interactions one is familiar with from atomic and Dirac theory. -- One retrieves the (relativistic) kinetic correction, the hyperfine and the Darwin term which acts even when wave function is spherically symmetric. One also retrieves angular momentum dependent terms like the spin-orbit interaction in a relativistically correct way; and one obtains additional terms which thus far have not been reported particularly various $\vec L^2$-dependent terms. Since the approach includes the full retardation, one gets additional, thus far unknown terms. The differ from atomic and Dirac theory, since there only that part of the vector potential is usually included which is generated by the atomic nucleus. Quite on purpose, the paper is kept formal.

hep-ph↗
arXiv2003

A linear potential in a light cone QCD inspired model

The general equation from previous work is specialized to a linear potential $V(r)=-a+F r$ acting in the space of spherically symmetric S wave functions. The fine and hyperfine interaction creates then a $\frac1r$-dependence in the effective potential energy equation and a position dependent mass $\widetilde m(r)$ in the effective kinetic energy of the associated Schrödinger equation. The results are compared with the available experimental and theoretical spectral data on the $π$ and $ρ$. Solving the eigenvalue problem within the analytically tractable Airy-function approach induces a certain amount of arbitrariness (fudge factors). Despite of this, the agreement with experimental data is good and partially better than other calculations, including Godfrey and Isgur \cite{GodIsg85} and Baldicchi and Prosperi \cite{BalPro02}. The short comings of the present model can be removed easily in more elaborate work.

hep-ph↗
arXiv2003

A quadratic potential in a light cone QCD inspired model

The general equation from previous work is specialized to a quadratic potential $V(r)=-a+\frac12 f r^2$ acting in the space of spherically symmetric S wave functions. The fine and hyperfine interaction creates then a position dependent mass $\widetilde m(r)$ in the effective kinetic energy of the associated Schrödinger equation. The results are compared with the available experimental and theoretical spectral data on the $π$ and $ρ$. Solving the eigenvalue problem within the usual oscillator approach induces a certain amount of arbitrariness. Despite of this, the agreement with experimental data is within the experimental error and better than other calculations, including Godfrey and Isgur \cite{GodIsg85} and Baldicchi and Prosperi \cite{BalPro02}. The short coming can be removed easily in more elaborate work.

hep-ph↗
arXiv2003

The hadronic potential at short distance

A fictitious discussion is taken as a point of origin to present novel physical insight into the nature of gauge theory and the potential energy of QCD and QED at short distance. Emphasized is the considerable freedom in the cut-off function which eventually can modify the Coulomb potential of two charges at sufficiently small distances. Emphasized is also that the parameters of the regularization function (the ``cut-off scale'') should not be driven to infinity but kept constant in line with the modern interpretation of renormalization theory. The paper restricts to general aspects. The technical paraphernalia and the comparison with experiment are shifted to a sequence of 4 subsequent stand-alone and sufficiently small papers to be published immediatelely hereafter.

hep-ph↗
arXiv2003

S wave meson spectra from the light cone harmonic oscillator model with a consistent hyperfine interaction

We use a light cone harmonic oscillator model to study S wave meson spectra, namely the pseudoscalar and vector mesons. The model Hamiltonian is a mass squared operator consisting of a central potential (a harmonic oscillator potential) from which a hyperfine interaction is derived. The hyperfine interaction is responsible for the splitting in the pseudoscalar-vector spectra. With 4 parameters for the masses of up/down, strange, charm and bottom quarks, 2 for the harmonic oscillator potential and 1 for the hyperfine interaction, the model presents a reasonably good agreement with the data.

hep-ph↗
arXiv2003

First successful renormalization of a QCD-inspired Hamiltonian

The long standing problem of non perturbative renormalization of a gauge field theoretical Hamiltonian is addressed and explicitly carried out within an (effective) light-cone Hamiltonian approach to QCD. The procedure is in line with the conventional ideas: The Hamiltonian is first regulated by suitable cut-off functions, and subsequently renormalized by suitable counter terms to make it cut-off independent. The formalism is applied to physical mesons with a different flavor of quark and anti-quark. The excitation spectrum of the $ρ$-meson with its excellent agreement between theory and experiment is discussed as a pedagogical example.

hep-ph↗
arXiv2003

Succesful renormalization of a QCD-inspired Hamiltonian

The long standing problem of non perturbative renormalization of a gauge field theoretical Hamiltonian is addressed and explicitly carried out within an (effective) light-cone Hamiltonian approach to QCD. The procedure is in line with the conventional ideas: The Hamiltonian is first regulated by suitable cut-off functions, and subsequently renormalized by suitable counter terms to make it cut-off independent. Emphasized is the considerable freedom in the cut-off function which eventually can modify the Coulomb potential of two charges at sufficiently small distances. The approach provides new physical insight into nature of gauge theory and the potential energy of QCD and QED near the origin. The so obtained formalism is applied to physical mesons with a different flavor of quark and anti-quark. The excitation spectrum of the $ρ$-meson with its excellent agreement between theory and experiment is discussed as a pedagogical example.

hep-ph↗
arXiv2002

Universal description of S-wave meson spectra in a renormalized light-cone QCD-inspired model

A light-cone QCD-inspired model, with the mass squared operator consisting of a harmonic oscillator potential as confinement and a Dirac-delta interaction, is used to study the S-wave meson spectra. The two parameters of the harmonic potential and quark masses are fixed by masses of rho(770), rho(1450), J/psi, psi(2S), K*(892) and B*. We apply a renormalization method to define the model, in which the pseudo-scalar ground state mass fixes the renormalized strength of the Dirac-delta interaction. The model presents an universal and satisfactory description of both singlet and triplet states of S-wave mesons and the corresponding radial excitations.

hep-ph↗
arXiv2002

Splitting of the pi - rho spectrum in a renormalized light-cone QCD-inspired model

We show that the splitting between the light pseudo-scalar and vector meson states is due to the strong short-range attraction in the ^1S_0 sector which makes the pion and the kaon light particles. We use a light-cone QCD-inspired model of the mass squared operator with harmonic confinement and a Dirac-delta interaction. We apply a renormalization method to define the model, in which the pseudo-scalar ground state mass fixes the renormalized strength of the Dirac-delta interaction.

hep-ph↗
arXiv2002

On flavor mixing by an effective Light-Cone QCD-Hamiltonian

The $\uparrow\downarrow$-model has produced the physical masses of all flavor-asymmetric mesons like the $π^\pm$ or the $ρ^\pm$. Can the same model also account for the flavor-symmetric mesons like the $π^0$ or the $ρ^0$? -- By adjusting one parameter in a $5\times5$-matrix, the $π$-$η$ degeneracy is lifted and the $η-η'$ splitting falls into the right ball park. The isospin triplets for pions and rhos are caused the mass-degeneracy of the up and down quark.

hep-ph↗
arXiv2002

On the effective Hamiltonian for QCD: An overview and status report

The session on effective Hamiltonians and chiral dynamics is overviewed, combined with a review on the bound-state problem. The progress during this session allows to remove all dependence on regularization in an effective interaction, thus to renormalize a Hamiltonian for the first time, and to solve front form as if they were instant-form equations, with all the advantages implied.

hep-ph↗
arXiv2001

On helicity and spin on the light cone

Starting from a one-body front-form equation with Lepage-Brodsky spinors we show, with a fair amount of new technology, how an integral equation in standard momentum space with Bjorken-Drell spinors can be obtained. The integral equation decouples for singlets and triplets.

hep-ph↗
arXiv2001

On the structure of the pion: A QCD--inspired point of view

The effective interaction between a quark and an anti-quark as obtained previously with by the method of iterated resolvents is replaced by the so called up-down-model and applied to flavor off-diagonal mesons including the pion. The only free parameters are those of canonical quantum chromo-dynamics (QCD), particularly the coupling constant and the masses of the quarks. The so obtained light-cone wave function can be used to calculate the pion's form factor, particularly its mean-square radius can be computed analytically. The results allow for the exciting conclusion that the pion is built by highly relativistic constituents, in strong contrast to composite systems like atoms or nuclei with non-relativistic constituents.

hep-ph↗
arXiv2001

On the form factor of physical mesons and their distribution function

This work addresses more to the technical rather than to the physical problem, how to calculate analytically the form factor $F(Q)$, the associated mean-square radius $ $, and the distribution function $Φ(x,Q^2)$ for a given light-cone wave function $Ψ_{q\bar q}(x,\vec k_{\perp})$ of the pion. They turn out to be functions of only one dimensionless parameter, which is the ratio of the constituent quark mass and an effective Bohr momentum which measures the width of the wave function in momentum space. Both parameters are subject to change in the future, when the presently used solution for the over simplified $\uparrow\downarrow$-model will be replaced by something better. Their relation to and agreement with experiment is discussed in detail. The procedure can be generalized also to other hadrons.

hep-ph↗