arXiv subjects

Helmut Haberzettl

Publications and source records attributed to Helmut Haberzettl.

At least 19 recordsLinked to original sources

arXiv2024

Using gauge invariance to symmetrize the energy-momentum tensor of electrodynamics

It is shown that using Noether's Theorem explicitly employing gauge invariance for variations of the electromagnetic four-potential $A^μ$ straightforwardly ensures that the resulting electromagnetic energy-momentum tensor is symmetric. The Belinfante symmetrization procedure is not necessary. The method is based on Bessel-Hagen's 1921 clarification of Noether's original procedure, suggesting that the symmetry problem arises from an incomplete implementation of Noether's Theorem. The derivation addresses in some detail where the usual application of Noether's Theorem falls short, what the Belinfante procedure actually does to fix the problem, and why the usual unsymmetric canonical energy-momentum tensor can only be used for extracting four-momentum conservation based on translational invariance, but will provide meaningless results when applied to rotations or boosts, unless modified appropriately.

physics.class-ph↗

arXiv2021

Coupled-channel analysis of pion- and eta-electroproduction with the Jülich-Bonn-Washington model

Pion and eta electroproduction data are jointly analyzed for the first time, up to a center-of-mass energy of 1.6 GeV. The framework is a dynamical coupled-channel model, based on the recent Jülich-Bonn-Washington analysis of pion electroproduction data for the same energy range. Comparisons are made to a number of single-channel eta electroproduction fits. By comparing multipoles of comparable fit quality, we find some of these amplitudes are well determined over the near-threshold region, while others will require fits over an extended energy range.

nucl-th↗

arXiv2021

Physics Opportunities with Meson Beams for EIC

Over the past two decades, meson photo- and electroproduction data of unprecedented quality and quantity have been measured at electromagnetic facilities worldwide. By contrast, the meson-beam data for the same hadronic final states are mostly outdated and largely of poor quality, or even non-existent, and thus provide inadequate input to help interpret, analyze, and exploit the full potential of the new electromagnetic data. To reap the full benefit of the high-precision electromagnetic data, new high-statistics data from measurements with meson beams, with good angle and energy coverage for a wide range of reactions, are critically needed to advance our knowledge in baryon and meson spectroscopy and other related areas of hadron physics. To address this situation, a state-of-the-art meson-beam facility needs to be constructed. The present letter summarizes unresolved issues in hadron physics and outlines the vast opportunities and advances that only become possible with such a facility.

nucl-ex↗

arXiv2021

Gauge invariance of meson photo- and electroproduction currents revisited

An exact expression is derived for the meson production current off the nucleon for real and virtual photons which cleanly separates, in a model-independent manner, a tree-level expression that manifestly preserves local gauge invariance in terms of a generalized Ward-Takahashi identity from transverse final-state-interaction (FSI) terms. As discussed in some detail, this exact formulation is particularly well suited for implementing approximation schemes of exchange-current and FSI contributions (which in practice generally will be necessary) at any level of sophistication without violating local gauge invariance.

hep-ph↗

arXiv2021

Jülich-Bonn-Washington Model for Pion Electroproduction Multipoles

Pion electroproduction off the proton is analyzed in a new framework based on a general parametrization of transition amplitudes, including constraints from gauge invariance and threshold behavior. Data with energies $1.13~{\rm GeV}<W<1.6~{\rm GeV}$ and $Q^2$ below $6~{\rm GeV}^2$ are included. The model is an extension of the latest Jülich-Bonn solution incorporating constraints from pion-induced and photoproduction data. Performing large scale fits ($\sim10^5$ data) we find a set of solutions with $χ^2_{\rm dof}=1.69-1.81$ which allows us to assess the systematic uncertainty of the approach.

nucl-th↗

arXiv2019

Model-independent form-factor constraints for electromagnetic spin-1 currents

Using local gauge invariance in the form of the Ward-Takahashi identity and the fact that properly constructed current operators must be free of kinematic singularities, it is shown that the magnetic moment $μ$ and the quadrupole moment $Q$ of an elementary spin-1 particle with mass $m$ and charge $e$ are related by $2 mμ+ m^2 Q = e$, thus constraining the normalizations of the Sachs form factors. This relation holds true as a matter of course at the tree level in the standard model, but we prove it remains true in general for dressed spin-1 states derived from elementary fields. General expressions for spin-1 propagators and currents with arbitrary hadronic dressing are given showing the result to be independent of any dressing effect or model approach.

nucl-th↗

arXiv2019

Electromagnetic currents for dressed hadrons

We propose an extension of the minimal-substitution prescription for coupling the electromagnetic field to hadronic systems with internal structure. The resulting rules of extended substitution necessarily distinguish between couplings to scalar and Dirac particles. Moreover, they allow for the incorporation of electromagnetic form factors for virtual photons in an effective phenomenological framework. Applied to pions and nucleons, assumed to be fully dressed to all orders, the resulting dressed currents are shown to be locally gauge invariant. Moreover, half-on-shell expressions of (hadron propagator)$\times$(electromagnetic current) needed in all descriptions of physical processes will lose \textit{all} information about hadronic dressing for real photons. The Ball-Chiu ansatz for the spin-1/2 current is seen to suffer from an incomplete coupling procedure where some essential aspects of the Dirac particle are effectively treated as those of a scalar particle. Applied to real Compton scattering on pions and nucleons, we find that \emph{all} dressing information cancels exactly when external hadrons are on shell, leaving only gauge-invariant bare Born-type contributions with physical masses. Hence, nontrivial descriptions necessarily require contact-type two-photon processes obtained by hadrons looping around two photon insertion points.

nucl-th↗

arXiv2018

Theory of two-pion photo- and electroproduction off the nucleon

A theory of two-pion photo- and electroproduction off the nucleon is derived considering all explicit three-body mechanisms of the interacting $ππN$ system. The full three-body dynamics of the interacting $ππN$ system is accounted for by the Faddeev-type ordering structure of the Alt-Grassberger-Sandhas equations. The formulation is valid for hadronic two-point and three-point functions dressed by arbitrary internal mechanisms provided all associated electromagnetic currents are constructed to satisfy their respective (generalized) Ward-Takahashi identities. It is shown that coupling the photon to the Faddeev structure of the underlying hadronic two-pion production mechanisms results in a natural expansion of the full two-pion photoproduction current $M_{ππ}^μ$ in terms of multiple dressed loops involving two-body subsystem scattering amplitudes of the $ππN$ system that preserves gauge invariance as a matter of course order by order in the number of (dressed) loops. A closed-form expression is presented for the entire gauge-invariant current $M_{ππ}^μ$ with complete three-body dynamics. Individually gauge-invariant truncations of the full dynamics most relevant for practical applications at the no-loop, one-loop, and two-loop levels are discussed in detail. An approximation scheme to the full two-pion amplitude for calculational purposes is also presented. It approximates, systematically, the full amplitude to any desired order of expansion in the underlying hadronic two-body amplitude. Moreover, it allows for the approximate incorporation of all neglected higher-order mechanisms in terms of a phenomenological remainder current. The effect and phenomenological usefulness of this remainder current is assessed in a tree-level calculation of the $γN \to K K Ξ$ reaction.

nucl-th↗

arXiv2016

Analysis of recent CLAS data on $Σ^{\ast }(1385)$ photoproduction off a neutron target

Based on recent experimental data obtained by the CLAS Collaboration, the $Σ(1385)$ photoproduction off a neutron target at laboratory photon energies $E_γ$ up to 2.5\,GeV is investigated in an effective Lagrangian approach including $s$-, $u$-, and $t$-channel Born-term contributions. The present calculation does not take into account any explicit $s$-channel baryon-resonance contributions, however, in the spirit of duality, we include $t$-channel exchanges of mesonic Regge trajectories. The onset of the Regge regime is controlled by smoothly interpolating between Feynman-type single-meson exchanges and full-fledged Regge-trajectory exchanges. Gauge invariance broken by the Regge treatment is fully restored by introducing contact-type interaction currents that result from the implementation of \textit{local} gauge invariance in terms of generalized Ward-Takahashi identities. The cross sections for the $γn\to K^+Σ^*(1385)^-$ reaction are calculated and compared with experimental results from the CLAS and LEPS collaborations. Despite its simplicity, the present theoretical approach provides a good description of the main features of the data. However, the parameters fitted to the data show that the gauge-invariance-restoring contact term plays a large role which may point to large contributions from final-state interactions.

nucl-th↗

arXiv2015

Preserving Local Gauge Invariance with t-Channel Regge Exchange

Considering single-meson photo- and electroproduction off a baryon, it is shown how to restore local gauge invariance that was broken by replacing standard Feynman-type meson exchange in the t-channel by exchange of a Regge trajectory. This is achieved by constructing a contact current whose four-divergence cancels the gauge-invariance-violating contributions resulting from all states above the base state on the Regge trajectory. To illustrate the procedure, modifications necessary for the process $γ+p \to K^+ + Σ^{*0}$ are discussed in some detail. We also provide the general expression for the contact current for an arbitrary reaction.

hep-ph↗

arXiv2015

Physics Opportunities with Meson Beams

Over the past two decades, meson photo- and electro-production data of unprecedented quality and quantity have been measured at electromagnetic facilities worldwide. By contrast, the meson-beam data for the same hadronic final states are mostly outdated and largely of poor quality, or even nonexistent, and thus provide inadequate input to help interpret, analyze, and exploit the full potential of the new electromagnetic data. To reap the full benefit of the high-precision electromagnetic data, new high-statistics data from measurements with meson beams, with good angle and energy coverage for a wide range of reactions, are critically needed to advance our knowledge in baryon and meson spectroscopy and other related areas of hadron physics. To address this situation, a state of-the-art meson-beam facility needs to be constructed. The present paper summarizes unresolved issues in hadron physics and outlines the vast opportunities and advances that only become possible with such a facility.

hep-ph↗

arXiv2014

Model-independent aspects of the reaction $\bar{K} + N \to K + Ξ$

Various model-independent aspects of the $\bar{K} N \to K Ξ$ reaction are investigated, starting from the determination of the most general structure of the reaction amplitude for $Ξ$ baryons with $J^P=\frac12^\pm$ and $\frac32^\pm$ and the observables that allow a complete determination of these amplitudes. Polarization observables are constructed in terms of spin-density matrix elements. Reflection symmetry about the reaction plane is exploited, in particular, to determine the parity of the produced $Ξ$ in a model-independent way. In addition, extending the work of Biagi $\mathrm{\textit{et al. } [Z. Phys.\ C \textbf{34}, 175 (1987)]}$, a way is presented of determining simultaneously the spin and parity of the ground state of $Ξ$ baryon as well as those of the excited $Ξ$ states.

hep-ph↗

arXiv2012

Gauge-invariant theory of two-pion photo- and electro-production off the nucleon

A field-theoretical description of the photoproduction of two pions off the nucleon is presented that applies to real as well as virtual photons in the one-photon approximation. The Lorentz-covariant theory is complete at the level of all explicit Faddeev-type three-body final-state mechanisms of dressed interacting hadrons, including those of the nonlinear Dyson-Schwinger type. All electromagnetic currents are constructed to satisfy their respective (generalized) Ward-Takahashi identities and thus satisfy local gauge invariance as a matter of course. The Faddeev-type ordering structure results in a natural expansion of the full two-pion photoproduction current $\Mpp^μ$ in terms of multiple loops that preserve gauge invariance order by order in the number of loops, which in turn lends itself naturally to practical applications of increasing sophistication with increasing number of loops.

nucl-th↗

arXiv2012

Production and parity determination of $Ξ$ baryons

To understand the structure of hadrons and their production mechanisms, it is very important to be able to identify their quantum numbers. For investigating the spin and parity quantum numbers of $Ξ$ and $Ω$ baryons, in particular, it is very important to understand strong interactions in the strangeness sector. At present, such quantum numbers are known for only a few of the $Ξ$ baryons, and even the parity of the ground state $Ξ(1318)$ has never been measured. In this article, we present a novel, model-independent way to determine the parity of $Ξ$ baryons solely based on symmetry considerations for the hadronic reaction $\bar{K} N \to K Ξ$.

nucl-th↗

arXiv2000

Pion photo- and electroproduction and the partially-conserved axial current

The relevance of the axial current for pion production processes off the nucleon with real or virtual photons is revisited. Employing the hypothesis of a partially conserved axial current (PCAC), it is shown that, when all of the relevant contributions are taken into account, PCAC does not provide any additional constraint for threshold production processes that goes beyond the Goldberger-Treiman relation. In particular, it is shown that pion electroproduction processes at threshold cannot be used to extract any information regarding the weak axial form factor. The relationships found in previous investigations are seen to be an accident of the approximations usually made in this context.

nucl-th↗

arXiv2000

Preserving the gauge invariance of meson production currents in the presence of explicit final-state interactions

A comprehensive formalism is developed to preserve the gauge invariance of currents describing the photo- or electroproduction of mesons off the nucleon when the final-state interactions of mesons and nucleons is taken into account explicitly. Replacing exchange currents by auxiliary currents, it is found that all contributions due to explicit final-state interactions are purely transverse and do not contain a Kroll-Ruderman-type contact current. The relation of the present formulation to tree-level-type prescriptions is shown.

nucl-th↗

arXiv1998

Propagation of a massive spin-3/2 particle

The propagation of an off-shell spin-3/2 baryon is investigated in a consistent framework using projections corresponding to one irreducible spin-3/2 and two irreducible spin-1/2 representations arising from the usual spinor-vector representation of the spin-3/2 fields. Starting from the most general Lagrangian invariant under point transformations containing first-order derivatives only and imposing the constraint $γ_μψ^μ=0$, we eliminate one of the spin-1/2 contributions. The resulting propagator provides a clean separation of spin-3/2 proper and the one remaining spin-1/2 contribution. In addition to a conventional pole term describing pure spin-3/2, which is identical to the propagator proposed by Williams, this procedure yields a second pole term describing spin-1/2 only, with a pole at twice the mass parameter of the Lagrangian. Its effect on physical observables may manifest itself in a manner which is indistinguishable from a particle in its own right. The second pole term cancels the $1/p^2$ singularity of the Williams propagator and the propagator derived here is well behaved for vanishing $p^2$.

nucl-th↗

arXiv1997

Gauge-invariant theory of pion photoproduction with dressed hadrons

Based on an effective field theory of hadrons in which quantum chromodynamics is assumed to provide the necessary bare cutoff functions, a gauge-invariant theory of pion photoproduction with fully dressed nucleons is described. The formalism provides consistent dynamical descriptions of pi-N --> pi-N scattering and Gamma-N --> pi-N production mechanisms in terms of nonlinear integral equations for fully dressed hadrons. The dressed hadron currents and the pion photoproduction current satisfy gauge invariance in a self-consistent manner. Approximations are discussed that make the nonlinear formalism manageable in practice and yet preserve gauge invariance.

nucl-th↗