arXiv subjects

Wolfgang Schweiger

Publications and source records attributed to Wolfgang Schweiger.

At least 19 recordsLinked to original sources

arXiv2023

Polynomial Solutions of Generalized Quartic Anharmonic Oscillators

This paper deals with the partial solution of the energy eigenvalue problem for generalized symmetric quartic oscillators. Algebraization of the problem is achieved by expressing the Schroedinger operator in terms of the generators of a nilpotent group, which we call the quartic group. Energy eigenvalues are then seen to depend on the values of the two Casimir operators of the group. This dependence exhibits a scaling law which follows from the scaling properties of the group generators. Demanding that the potential gives rise to polynomial solutions in a particular Lie algebra element puts constraints on the four potential parameters, leaving only two of them free. For potentials satisfying such constraints at least one of the energy eigenvalues and the corresponding eigenfunctions can be obtained in closed analytic form {by pure algebraic means. With our approach we extend the class of quasi-exactly solvable quartic oscillators which have been obtained in the literature by means of the more common sl(2,R) algebraization. Finally we show, how solutions of the generalized quartic oscillator problem give rise to solutions for a charged particle moving in particular non-constant electromagnetic fields.

math-ph↗

arXiv2022

An estimation of non-valence contributions to form factors of heavy-light mesons

We study the influence of non-valence quark-pair contributions in weak transition form factors of heavy-light mesons. Form factors are first calculated for spacelike momentum transfers in a reference frame where such contributions are suppressed. Analytic continuation to the timelike region and a comparison with the direct decay calculation, done with pure valence degrees of freedom, provides an estimate of the role that quark-pair contributions may play. We use the point form of relativistic quantum mechanics, which is particularly useful when treating heavy-light systems.

hep-ph↗

arXiv2022

Weak transition form factors of heavy-light pseudoscalar mesons for space- and timelike momentum transfers

Weak $B^-\rightarrow D^0, π^0$ and $D^-\rightarrow {K}^0, π^0$ transition form factors are described in both the space- and time-like momentum transfer regions, within a constituent-quark model. Neutrino-meson scattering and semileptonic weak decays are formulated within the point form of relativistic quantum mechanics to end up with relativistic invariant process amplitudes from which meson transition currents and form factors are extracted in an unambiguous way. For space-like momentum transfers, form factors depend on the frame in which the $W M M^\prime$ vertex is considered. Such a frame dependence is expected from a pure valence-quark picture, since a complete, frame independent description of form factors is supposed to include non-valence contributions. The most important of such contributions are the $Z$-graphs, which are, however, suppressed in the infinite-momentum frame ($q^2<0$). On the other hand, they can play a significant role in the Breit frame ($q^2<0$) and in the direct decay calculation ($q^2>0$), as a comparison with the infinite-momentum-frame form factors (analytically continued to $q^2>0$) reveals. Numerical results for the analytically continued infinite-momentum-frame form factors agree very well with lattice data in the time-like momentum transfer region and the experimental value for the slope of the $F^+_{B\rightarrow D}$ transition form factor at zero recoil is reproduced satisfactorily. These predictions satisfy heavy-quark-symmetry constraints and their $q^2$ dependence is well approximated by a pole fit, reminiscent of a vector-meson-dominance-like decay mechanism. We discuss how such a decay mechanism can be accommodated within an extension of our constituent-quark model, by allowing for a non-valence component in the meson wave functions. We also address the question of wrong cluster properties inherent in the Bakamjian-Thomas formulation.

hep-ph↗

arXiv2018

Pion-cloud contribution to the $N\rightarrow Δ$ transition form factors

We examine the contribution of the pion cloud to the electromagnetic $N \rightarrow Δ$ transition form factors within a relativistic hybrid constituent-quark model. In this model baryons consist not only of the $3q$ valence component, but contain, in addition, a $3 q π$ non-valence component. We start with constituent quarks which are subject to a scalar, isoscalar confining force. This leads to an $SU(6)$ spin-flavor symmetric spectrum with degenerate nucleon and Delta masses. Mass splitting is caused by pions which are assumed to couple directly to the quarks. The point-form of relativistic quantum mechanics is employed to achieve a relativistically invariant description of this system. The $N \rightarrow Δ$ transition current is then determined from the one-photon exchange contribution to the $Δ$ electroproduction amplitude. We will give predictions for the ratios $R_{EM}$ and $R_{SM}$ of electric to magnetic and Coulomb to magnetic form factors, which are supposed to be most sensitive to pion-cloud effects.

hep-ph↗

arXiv2018

The problem of cluster separability in relativistic few-body systems

An appropriate framework for dealing with hadron structure and hadronic physics in the few-GeV energy range is relativistic quantum mechanics. The Bakamjian-Thomas construction provides a systematic procedure for implementing interactions in a relativistic invariant way. It leads, however, to problems with cluster separability. It has been known for some time, due to Sokolov's pioneering work, that mass operators with correct cluster properties can be obtained through a series of unitary transformations making use of so-called packing operators. In the present contribution we sketch an explicit construction of packing operators for three-particle systems consisting of distinguishable, spinless particles.

nucl-th↗

arXiv2018

Constituent-quark model with pionic contributions: electromagnetic $N\rightarrowΔ$ transition

We report on ongoing work to determine the pion-cloud contribution to the electromagnetic $N\rightarrowΔ$ transition form factors. The starting point is an $SU(6)$ spin-flavor symmetric constituent-quark model with instantaneous confinement that is augmented by dynamical pions which couple directly to the quarks. This system is treated in a relativistically invariant way within the framework of point-form quantum mechanics using a multichannel formulation. The first step is to determine the electromagnetic form factors of the bare particles that consist only of three quarks. These form factors are basic ingredients for calculating the pion-cloud contributions. Already without the pion cloud, electromagnetic nucleon and $N\rightarrow Δ$ transition form factors compare reasonably well with the data. By inclusion of the pion-cloud contribution coming from the $π$-$N$ intermediate state the reproduction of the data is further improved.

nucl-th↗

arXiv2017

$ρ$-Meson Form Factors in the Point Form

We present a calculation of the electromagnetic form factors of the $ρ^+$ meson. Our formalism is based on the point-form of relativistic quantum mechanics. Electron-$ρ$-meson scattering is formulated as a coupled-channel problem for a Bakamjian-Thomas mass operator, such that the dynamics of the exchanged photon is taken explicitly into account. The $ρ$-meson current is extracted from on-shell matrix elements of the optical potential of the scattering process. As a consequence of the violation of cluster separability in the Bakamjian-Thomas framework, our current includes additional, unphysical contributions, which can be separated from the physical ones uniquely. Our results for the form factors are in good agreement with other approaches.

hep-ph↗

arXiv2017

On the microscopic structure of $πNN$, $πNΔ$ and $πΔΔ$ vertices

We use a hybrid constituent-quark model for the microscopic description of $πN N$, $πN Δ$ and $πΔΔ$ vertices. In this model quarks are confined by an instantaneous potential and are allowed to emit and absorb a pion, which is also treated as dynamical degree of freedom. The point form of relativistic quantum mechanics is employed to achieve a relativistically invariant description of this system. Starting with an $SU(6)$ spin-flavor symmetric wave function for $N_0$ and $Δ_0$, i.e. the eigenstates of the pure confinement problem, we calculate the strength of the $πN_0 N_0$, $πN_0 Δ_0$ and $πΔ_0 Δ_0$ couplings and the corresponding vertex form factors. Interestingly the ratios of the resulting couplings resemble strongly those needed in purely hadronic coupled-channel models, but deviate significantly from the ratios following from SU(6) spin-flavor symmetry in the non-relativistic constituent-quark model.

nucl-th↗

arXiv2016

The microscopic structure of $πNN$, $πNΔ$ and $πΔΔ$ vertices in a hybrid constituent quark model

We present a microscopic description of the strong $πNN$, $πNΔ$ and $πΔΔ$ vertices. Our starting point is a constituent-quark model supplemented by an additional $3qπ$ non-valence component. In the spirit of chiral constituent-quark models, quarks are allowed to emit and reabsorb a pion. This multichannel system is treated in a relativistically invariant way within the framework of point-form quantum mechanics. Starting with a common $SU(6)$ spin-flavor-symmetric wave function for $N$ and $Δ$, we calculate the strength of the $πNN$, $πNΔ$ and $πΔΔ$ couplings and the corresponding vertex form factors. Our results are in accordance with phenomenological fits of these quantities that have been obtained within purely hadronic multichannel models for baryon resonances.

nucl-th↗

arXiv2015

The Pion-Cloud Contribution to the Electromagnetic Nucleon Form Factors

We study the electromagnetic structure of the nucleon within a hybrid constituent-quark model that comprises, in addition to the $3q$ valence component, also a $3q$+$π$ non-valence component. To this aim we employ a Poincaré-invariant multichannel formulation based on the point-form of relativistic quantum mechanics. With a simple 3-quark wave function for the bare nucleon, i.e. the $3q$-component, we obtain reasonable results for the nucleon form factors and predict the meson-cloud contribution to be significant only below $Q^2\lesssim 0.5$\,GeV$^2$ amounting to about 10\% for $Q^2\rightarrow 0$, in accordance with the findings of other authors.

hep-ph↗

arXiv2014

$ π^- p \rightarrow D^- Λ_{c}^{+} $ within the Generalized Parton Picture

We investigate the reaction $ π^- p \rightarrow D^- Λ_{c}^{+} $ within the generalized parton picture. The process is described by a handbag-type mechanism with the charm-quark mass acting as the hard scale. As in the case of preceding work on $\bar{p} p \rightarrow \barΛ^-_c Λ_{c}^{+} $ we argue that the process amplitude factorizes into one for the perturbatively calculable partonic subprocess $\bar{u} u\rightarrow \bar{c} c$ and hadronic matrix elements that can be parameterized in terms of generalized parton distributions. Modeling the generalized parton distributions by overlaps of (valence-quark) light-cone wave functions for the hadrons involved, we obtain numerical results for unpolarized differential and integrated cross sections as well as spin observables. Our approach works well above the production threshold ($s \gtrsim 20 $GeV$^2$) in the forward hemisphere and predicts unpolarized cross sections of the order of nb, a finding that could be of interest in view of plans to measure $ π^- p \rightarrow D^- Λ_{c}^{+} $ at J-PARC.

hep-ph↗

arXiv2014

Electromagnetic rho-meson form factors in point-form relativistic quantum mechanics

The relativistic point-form formalism that we proposed for the study of the electroweak structure of few-body bound states is applied to calculate the elastic form factors of spin-1 mesons, such as the rho meson, within constituent-quark models. We treat electron-meson scattering as a Poincare-invariant coupled-channel problem for a Bakamjian-Thomas mass operator and extract the meson current from the resulting invariant 1-photon-exchange amplitude. Wrong cluster properties inherent in the Bakamjian-Thomas framework are seen to cause spurious contributions in the current. These contributions, however, can be separated unambiguously from the physical ones and we end up with a meson current with all required properties. Numerical results for the rho-meson form factors are presented assuming a simple harmonic-oscillator bound-state wave function. The comparison with other approaches reveals a remarkable agreement of our results with those obtained within the covariant light-front scheme proposed by Carbonell et al. [Phys. Rep. 300, 215 (1998)].

hep-ph↗

arXiv2014

Hard exclusive photoproduction of charmed mesons

{We investigate the photoproduction process $ p γ\rightarrow Λ_{c}^{+} \overline{D^{0}}$ within the handbag approach, which we assume to be the dominant mechanism at energies well above the production threshold and in the forward scattering hemisphere.

hep-ph↗

arXiv2013

Meson-cloud effects in the electromagnetic nucleon structure

We study how the electromagnetic structure of the nucleon is influenced by a pion cloud. To this aim we make use of a constituent-quark model with instantaneous confinement and a pion that couples directly to the quarks. To derive the invariant 1- photon-exchange electron-nucleon scattering amplitude we employ a Poincaré- invariant coupled-channel formulation which is based on the point-form of relativistic quantum mechanics. We argue that the electromagnetic nucleon current extracted from this amplitude can be reexpressed in terms of pure hadronic degrees of freedom with the quark substructure of the pion and the nucleon being encoded in electromagnetic and strong vertex form factors. These are form factors of bare particles, i.e. eigenstates of the pure confinement problem. First numerical results for (bare) photon-nucleon and pion-nucleon form factors, which are the basic ingredients of the further calculation, are given for a simple 3-quark wave function of the nucleon.

nucl-th↗

arXiv2013

First results of proton antiproton annihilation into a pion pair at large scattering angles within the handbag approach

We propose to describe the process $ p ~ \bar{p} \rightarrow π^+ ~ π^-$ in a perturbative, QCD motivated framework in which a hard $ud \, \bar{u} \bar{d} \rightarrow d \, \bar{d} $ annihilation factorizes from soft transition distribution amplitudes. We advocate that the scale allowing for this factorization is the large transverse momentum transfer. In our simplified model, in which the proton is considered as a (scalar)diqark-quark system, a transition distribution amplitude describes the non-perturbative transition of the proton to the meson by emission of a scalar, isoscalar $ ud $-diquark and absorption of an antiquark (analogously for $ \bar{p} \rightarrow π^- $). We model the transition distribution amplitudes as an overlap of light-cone wave functions and present first results for the differential cross section. This process will be measured by the $ \bar{\mbox{P}}$ANDA experiment at GSI-FAIR.

hep-ph↗

arXiv2012

Electroweak hadron structure within a point-form approach

We present a relativistic point-form approach for the calculation of electroweak form factors of few-body bound states. As an example, the transition form factors for the semileptonic weak decay $B\to D^*e\bar ν_e$ are discussed and it is sketched how they can be extracted unambiguously from the invariant transition amplitude that describes the process. It is shown how these form factors go over into one universal function, the Isgur-Wise function in the heavy-quark limit, $m_Q\to \infty$, and comparison with the available experimental data is made.

hep-ph↗

arXiv2012

Electroweak hadron structure in point-form dynamics -- heavy-light systems

We present a general formalism that uses the point form of relativistic Hamiltonian dynamics to describe the electroweak structure of heavy-light mesons within constituent quark models. We study the heavy quark limit (i.e. $m_Q\to \infty$) and check that the predictions of heavy quark symmetry are satisfied. A simple analytic expressions is given for the Isgur-Wise function. In addition, cluster properties and the relation of our approach to front form calculations are discussed.

hep-ph↗

arXiv2012

Decaying hadrons within constituent-quark models

Within conventional constituent-quark models hadrons come out as stable bound states of the valence (anti)quarks. Thereby the resonance character of hadronic excitations is completely ignored. A more realistic description of hadron spectra can be achieved by including explicit mesonic degrees of freedom, which couple directly to the constituent quarks. We will present a coupled-channel formalism that describes such hybrid systems in a relativistically invariant way and allows for the decay of excited hadrons. The formalism is based on the point-form of relativistic quantum mechanics. If the confining forces between the (anti)quarks are described by instantaneous interactions it can be formally shown that the mass-eigenvalue problem for a system that consists of dynamical (anti)quarks and mesons reduces to a hadronic eigenvalue problem in which the eigenstates of the pure confinement problem (bare hadrons) are coupled via meson loops. The only point where the quark substructure enters are form factors at the meson-(bare) hadron vertices. The physical picture that emerges resembles the kind of hadronic resonance model that has been developed by Sato and Lee and is now heavily used at the Excited Baryon Analysis Center (EBAC) to fix $N^\ast$ properties. Our approach, however, is in a certain sense inverse to the one of Sato and Lee. Whereas they want to undress physical resonances to end up with bare quantities, we rather want to dress the bound-states resulting from a pure constituent quark model to end up with quantities that can be directly compared with experiment. The way how our approach works will be exemplified by means of a simple quark-antiquark-meson system.

hep-ph↗