arXiv subjects

R. Alkofer

Publications and source records attributed to R. Alkofer.

At least 55 records · Page 3Linked to original sources

arXiv2001

Pair Creation and an X-ray Free Electron Laser

Using a quantum kinetic equation coupled to Maxwell's equation we study the possibility that focused beams at proposed X-ray free electron laser facilities can generate electric field strengths large enough to cause spontaneous electron-positron pair production from the QED vacuum. Our approach yields the time and momentum dependence of the single particle distribution function. Under conditions reckoned achievable at planned facilities, repeated cycles of particle creation and annihilation take place in tune with the laser frequency. However, the peak particle number density is insensitive to this frequency and one can anticipate the production of a few hundred particle pairs per laser period. Field-current feedback and quantum statistical effects are small and can be neglected in this application of non-equilibrium quantum mean field theory.

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arXiv2001

Nucleon Form Factors in the Covariant Diquark-Quark Model

The nucleon is described as a bound state of a quark and an extended diquark. Hereby the notion ``diquark'' refers to the modelling of separable correlations in the two-quark Green's functions. Binding of quarks and diquarks takes place via an exchange interaction and is therefore related to the Pauli principle for three-quark states. Fully Poincare covariant nucleon amplitudes are calculated for free constituent propagators as well as for dressed propagators which parameterise confinement. The corresponding results for space-like form factors differ quantitatively but not qualitatively for various ansätze for the propagators. These results do not allow to draw definite conclusions on the permissibility of different dressing functions. Results for kaon photoproduction, on the other hand, exclude a whole class of constituent propagators.

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arXiv2001

Production Processes as a Tool to Study Parameterizations of Quark Confinement

We introduce diquarks as separable correlations in the two-quark Green's function to facilitate the description of baryons as relativistic three-quark bound states. These states then emerge as solutions of Bethe-Salpeter equations for quarks and diquarks that interact via quark exchange. When solving these equations we consider various dressing functions for the free quark and diquark propagators that prohibit the existence of corresponding asymptotic states and thus effectively parameterize confinement. We study the implications of qualitatively different dressing functions on the model predictions for the masses of the octet baryons as well as the electromagnetic and strong form factors of the nucleon. For different dressing functions we in particular compare the predictions for kaon photoproduction, $γp\to KΛ$, and associated strangeness production, $pp\to pKΛ$ with experimental data. This leads to conclusions on the permissibility of different dressing functions.

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arXiv2000

Nucleon Properties in the Covariant Quark-Diquark Model

In the covariant quark-diquark model the effective Bethe-Salpeter (BS) equations for the nucleon and the $Δ$ are solved including scalar {\em and axialvector} diquark correlations. Their quark substructure is effectively taken into account in both, the interaction kernel of the BS equations and the currents employed to calculate nucleon observables. Electromagnetic current conservation is maintained. The electric form factors of proton and neutron match the data. Their magnetic moments improve considerably by including axialvector diquarks and photon induced scalar-axialvector transitions. The isoscalar magnetic moment can be reproduced, the isovector contribution is about 15% too small. The ratio $μG_E/G_M$ and the axial and strong couplings $g_A$, $g_{πNN}$, provide an upper bound on the relative importance of axialvector diquarks confirming that scalar diquarks nevertheless describe the dominant 2-quark correlations inside nucleons.

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arXiv2000

A Comparison between Relativistic and Semi-Relativistic Treatment in the Diquark-Quark Model

In the diquark-quark model of the nucleon including scalar and axialvector diquarks we compare solutions of the ladder Bethe-Salpeter equation in the instantaneous Salpeter approximation and in the fully covariant (i.e. four-dimensional) treatment. We obtain that the binding energy is severly underestimated in the Salpeter approximation. For the electromagnetic form factors of the nucleon we find that in both approaches the overall shapes of the respective form factors are reasonably similar up to $Q^2 \approx 0.4$ GeV^2. However, the magnetic moments differ substantially as well as results for the pion-nucleon and the axial coupling of the nucleon.

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arXiv1999

Kaon Photoproduction in a Confining and Covariant Diquark Model

Baryons are modeled as bound states of scalar or axialvector diquarks and a constituent quark which interact through quark exchange. This description results as an approximation to the relativistic Faddeev equation for three quarks. The corresponding effective Bethe-Salpeter equation is solved, and fully four-dimensional wave functions for both octet and decuplet baryons are obtained. Confinement of quarks and diquarks is incorporated by modifying their propagators. Results are given for kaon photoproduction which is one of the applications currently under investigation in this model.

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arXiv1999

Form Factors of Baryons in a Confining and Covariant Diquark-Quark Model

We treat baryons as bound states of scalar or axialvector diquarks and a constituent quark which interact through quark exchange. This description results as an approximation to the relativistic Faddeev equation for three quarks which yields an effective Bethe-Salpeter equation. Octet and decuplet masses and fully four-dimensional wave functions have been computed for two cases: assuming an essentially pointlike diquark on the one hand, and a diquark with internal structure on the other hand. Whereas the differences in the mass spectrum are fairly small, the nucleon electromagnetic form factors are greatly improved assuming a diquark with structure. First calculations to the pion-nucleon form factor also suggest improvements.

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arXiv1999

Octet and Decuplet Baryons in a Confining and Covariant Diquark-Quark Model

We treat baryons as bound states of scalar or axialvector diquarks and a constituent quark which interact through quark exchange. We obtain fully four-dimensional wave functions for both octet and decuplet baryons as solutions of the corresponding Bethe-Salpeter equation. Applications currently under investigation are: electromagnetic and strong form factors and strangeness production processes.

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arXiv1999

(In-)Consistencies in the relativistic description of excited states in the Bethe-Salpeter equation

The Bethe-Salpeter equation provides the most widely used technique to extract bound states and resonances in a relativistic Quantum Field Theory. Nevertheless a thorough discussion how to identify its solutions with physical states is still missing. The occurrence of complex eigenvalues of the homogeneous Bethe-Salpeter equation complicates this issue further. Using a perturbative expansion in the mass difference of the constituents we demonstrate for scalar fields bound by a scalar exchange that the underlying mechanism which results in complex eigenvalues is the crossing of a normal (or abnormal) with an abnormal state. Based on an investigation of the renormalization of one-particle properties we argue that these crossings happen beyond the applicability region of the ladder Bethe-Salpeter equation. The implications for a fermion-antifermion bound state in QED are discussed, and a consistent interpretation of the bound state spectrum of QED is proposed.

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arXiv1998

Octet and Decuplet Baryons in a Covariant and Confining Diquark-Quark Model

The baryon octet and decuplet masses and Bethe-Salpeter vertex and wave functions are calculated in the ladder approximation to the quark exchange between a scalar or axialvector diquark and a constituent quark. These functions reflecting full Lorentz covariance are given in terms of an expansion in Gegenbauer polynomials. In the rest frame of the baryon, a complete partial wave decomposition of the Bethe-Salpeter wave function is performed. The confinement of quarks and diquarks is implemented via a parametrisation of the corresponding propagators. We also discuss some aspects of the momentum routing in the ladder approximation to the Bethe-Salpeter equation. Numerical results for the octet and decuplet masses with broken flavour SU(3) in the conserved isospin limit are presented.

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arXiv1998

Baryons in a Covariant and Confining Diquark--Quark Model

In a covariant model where constituent quarks and diquarks interact through quark exchange, the Bethe-Salpeter equation in ladder approximation for octet and decuplet baryons is solved. Quark and diquark confinement is thereby effectively parametrised by choosing appropriately modified propagators. Numerical results for the baryon masses are presented. In a second step electromagnetic, weak and pionic currents are coupled to the bound state according to Mandelstam's technique. The arising matrix elements are evaluated in a generalised impulse approximation and observable form factors are extracted.

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arXiv1997

Diquark confinement in an extended NJL model

In a Nambu-Jona-Lasinio model supplemented with an infrared cutoff in addition to the ultraviolet cutoff we study the issue whether diquarks are confined when the model is extended beyond the rainbow-ladder approximation. The gap equation, obtained in a truncation scheme motivated via a nontrivial quark-gluon vertex function, is solved to determine the constituent quark mass if chiral symmetry is spontaneously broken. In a second step, the Bethe-Salpeter equations for mesons and diquarks beyond ladder approximation are derived, taking care to preserve Goldstone's theorem in the pion channel. While the obtained masses of pseudoscalar and vector mesons are only moderately shifted compared to the values in ladder approximation, we observe that scalar diquarks disappear from the physical spectrum and therefore are confined. For axialvector diquarks we observe indications, that the same mechanism may also work, but the NJL model allows no conclusive answer in this channel.

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arXiv1996

Baryon Structure in a Covariant Diquark-Quark Model

The baryon structure is investigated in a covariant diquark-quark model. In this approach baryons emerge as relativistic bound states of a constituent quark and a $0^{+}$ or $1^{+}$ diquark. After solving the Bethe-Salpeter Equation for the scalar diquark quark system in ladder approximation we couple various external currents to the constituents of the baryon to probe its internal structure. The quark and the diquarks are assumed to be confined which is implemented by suitable choices for the propagators. This leads to nontrivial vertex functions between the constituents and the external current. Baryonic matrix elements are then evaluated to extract observable formfactors.

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arXiv1996

Baryons as Hybrids of Solitons and Three Quark Bound States

A hybrid model for baryons based on a dynamical interplay between relativistic three--quark bound states and soliton configurations of mesons is constructed. The Bethe-Salpeter equation for diquarks and the Faddeev equation for diquark-quark bound states in the background of a soliton is solved. The results show that baryons are very much like hybrids containing both, solitonic meson clouds and three--quark correlations.

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arXiv1996

The Strong Running Coupling from an Approximate Gluon Dyson-Schwinger Equation

Using Mandelstam's approximation to the gluon Dyson-Schwinger equation we calculate the gluon self-energy in a renormalisation group invariant fashion. We obtain a non-perturbative $β$ function. The scaling behaviour near the ultraviolet stable fixed point is in good agreement with perturbative QCD. No further fixed point for positive values of the coupling is found: $α_S$ increases without bound in the infrared.

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arXiv1995

Calculation of the anomalous $γπ^* \to ππ$ form factor

The form factor for the anomalous process $γπ^* \to ππ$, $F^{3π}(s,t,u)$, is calculated as a phenomenological application of the QCD Dyson-Schwinger equations. The chiral-limit value dictated by the electromagnetic, anomalous chiral Ward identity, $F^{3π}(0,0,0)= e N_c/(12π^2 f_π^3)$, is reproduced, {\it independent} of the details of the modelling of the gluon and quark 2-point Schwinger functions. Using a parametrisation of the dressed $u$-$d$ quark 2-point Schwinger function that provides a good description of pion observables, such as $π$-$π$ scattering-lengths and the electromagnetic pion form factor, $F^{3π}(s,t,u)$ is calculated on a kinematic range that proposed experiments plan to explore. Our result confirms the general trend of other calculations; i.e., a monotonic increase with $s$ at fixed $t$ and $u$, but is uniformly larger and exhibits a more rapid rise with $s$.

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arXiv1995

Strangeness content of the nucleon within the NJL soliton model

We investigated the form factors of the nucleon associated with the nonet vector current in the framework of the generalized Yabu--Ando approach to the chiral soliton of the Nambu--Jona--Lasinio model. We introduce a variational parameter to improve the predictions for the baryon mass splittings and, in addition, we take into account $1/N_c$ rotational corrections to accommodate the empirical isovector magnetic moment of the nucleon. We find that the strange magnetic moment lies between -0.05 and 0.25.

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arXiv1995

Strange Nucleons and Hyperons as Chiral Solitons in the NJL Model

In the chirally symmetric Nambu--Jona-Lasinio model baryons are described as chiral solitons of mesonic quark--antiquark bound states. Hyperons are investigated in two complementary pictures: the bound state approach of Callan and Klebanov and the collective approach of Yabu and Ando. The latter is used to compute the strange vector form factors of the nucleon providing estimates for the strange electric mean square radius and the strange magnetic moment of the nucleon.

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