arXiv subjects

R. Alkofer

Publications and source records attributed to R. Alkofer.

72 records · Page 4Linked to original sources

arXiv1995

Monopole Excitations of Baryons in the Nambu--Jona--Lasinio Soliton Model

We investigate the monopole excitations of the soliton in the Nambu--Jona--Lasinio model. By studying the solutions to the corresponding Bethe--Salpeter equation in the background of the soliton we exclude the existence of real large amplitude fluctuations. This allows us to treat the collective coordinate for the monopole excitations, which parametrizes the extension of the soliton, in the harmonic approximation. The canonical quantization of this coordinate yields a spectrum which agrees reasonably well with the empirical data for the Roper resonance, N(1440), and the corresponding one for the Delta, $Δ$(1600). We also comment on going beyond the harmonic approximation.

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arXiv1995

On the strange vector form factors of the nucleon in the NJL soliton model

Within the Nambu--Jona--Lasinio model strange degrees of freedom are incorporated into the soliton picture using the collective approach of Yabu and Ando. The form factors of the nucleon associated with the nonet vector current are extracted. The numerical results provide limits for the strange magnetic moment: $-0.05\leμ_s\le0.25$. For the strange magnetic form factor of the nucleon the valence quark and vacuum contributions add coherently while there are significant cancellations for the strange electric form factor.

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arXiv1995

Diquarks in a chiral soliton field

In the Nambu--Jona-Lasinio model baryons are either considered as quark-diquark-composites or the soliton configurations of the model are interpreted as baryons. As a first step towards constructing a hybrid model, which possesses a dynamical interplay between both pictures, the Bethe-Salpeter equation for diquarks in the background of a soliton configuration is solved. The presence of the soliton causes a significant reduction of the resulting bound state eigenenergy of the diquark. As a consequence a unit baryon number configuration may be constructed with a mass lower than the energy of the soliton. An estimate of the influence of the diquark on the meson fields indicates a small decrease of the extension of the soliton due to diquark correlations.

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arXiv1995

Baryons as Chiral Solitons in the Nambu--Jona-Lasinio Model

The description of baryons as chiral solitons of the Nambu--Jona--Lasinio (NJL) model is reviewed. A motivation for the soliton description of baryons is provided from large $N_C$ QCD. Rigorous results on the spontaneous breaking of chiral symmetry in QCD are discussed. It is then argued that the NJL model provides a fair description of low--energy hadron physics. The NJL model is therefore employed to mimic the low--energy chiral flavor dynamics of QCD. The model is bosonized by functional integral techniques and the physical content of the emerging effective meson theory is discussed. In particular, its relation to the Skyrme model is established. The static soliton solutions of the bosonized NJL model are found, their properties discussed, and the influence of various meson fields studied. These considerations provide strong support of Witten's conjecture that baryons can be understood as soliton solutions of effective meson theories. The chiral soliton of the NJL model is then quantized in a semiclassical fashion and various static properties of the nucleon are studied. The dominating $1/N_C$ corrections to the semiclassically quantized soliton are investigated. Time--dependent meson fluctuations off the chiral soliton are explored and employed to estimate the quantum corrections to the soliton mass. Finally, hyperons are described as chiral solitons of the NJL model. This is done in both, the collective rotational approach of Yabu and Ando as well as in the bound state approach of Callan and Klebanov.

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arXiv1994

Estimate of Quantum corrections to the Mass of the Chiral Soliton in the Nambu--Jona--Lasinio Model

The Bethe--Salpeter equation for pion fluctuations off the chiral soliton in the Nambu--Jona--Lasinio model is constructed. By Goldstone's theorem this equation has rotational and translational zero modes because the classical soliton is a localized stationary field configuration which violates rotational and translational invariance. Furthermore, the proper normalization of the fluctuating eigen--modes is obtained. Second quantization of the pion fluctuations off the chiral soliton provides an energy functional of the pion fluctuations which formally coincides with that of a harmonic oscillator. The corresponding quantum corrections to the soliton mass together with the semi--classical cranking prescription yield reasonable predictions for the masses of the nucleon and the $Δ$--resonance when the constituent quark mass is chosen to be about 400MeV. These calculations are, to some extend, hampered by the non--confining character of the Nambu--Jona--Lasinio model. Comments on the $1/N_C$ counting scheme are added.

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arXiv1994

On the analytic properties of chiral solitons in the presence of the $ω$--meson

A thorough study is performed of the analytical properties of the fermion determinant for the case that the time components of (axial) vector fields do not vanish. For this purpose the non--Hermitian Euclidean Dirac Hamiltonian is generalized to the whole complex plane. The Laurent series are proven to reduce to Taylor series for the corresponding eigenvalues and --functions as long as field configurations are assumed for which level crossings do not occur. The condition that no level crossings appears determines the radius convergence. However, the need for regularization prohibits the derivation of an analytic energy functional because real and imaginary parts of the eigenvalues are treated differently. Consistency conditions for a Minkowski energy functional are extracted from global gauge invariance and the current field identity for the baryon current. Various treatments of the Nambu--Jona--Lasinio soliton are examined with respect to these conditions. Motivated by the studies of the Laurent series for the energy functional the Euclidean action is expanded in terms of the $ω$--field. It is argued that for this expansion the proper--time regularization scheme has to be imposed on the operator level rather than on an expression in terms of the one--particle eigenenergies. The latter treatment is plagued by the inexact assumption that the Euclidean Dirac Hamiltonian and its Hermitian conjugate can be diagonalized simultaneously. It is then evident that approaches relying on counting powers of the $ω$--field in the one--particle eigenenergies are

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arXiv1994

The Skyrmion limit of the Nambu--Jona-Lasinio soliton

The special role of the isoscalar mesons ($σ$ and $ω$) in the NJL soliton is discussed. Stable soliton solutions are obtained when the most general ansatz compatible with vanishing grand spin is assumed. These solutions are compared to soliton solutions of a purely pseudoscalar Skyrme type model which is related to the NJL model by a gradient expansion and the limit of infinitely heavy (axial-) vector mesons.

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arXiv1994

Topologically non--trivial chiral transformations: The chiral invariant elimination of the axial vector meson

The role of chiral transformations in effective theories modeling Quantum Chromo Dynamics is reviewed. In the context of the Nambu--Jona--Lasinio model the hidden gauge and massive Yang--Mills approaches to vector mesons are demonstrated to be linked by a special chiral transformation which removes the chiral field from the scalar--pseudoscalar sector. The chirally rotated axial vector meson field ($\tilde A_μ$) transforms homogeneously under flavor rotations and may thus be dropped without violating chiral symmetry. The fermion determinant for static meson field configurations is computed by summing the discretized eigenvalues of the Dirac Hamiltonian. It is discussed how the local chiral transformation loses its unitary character in a finite model space. This technical issue proves to be crucial for the construction of the soliton within the Nambu--Jona--Lasinio model when the chirally rotated axial vector field is neglected. In the background of this soliton the valence quark is strongly bound, and its eigenenergy turns out to be negative. This important physical property which is usually generated only by non--vanishing axial vector is thus carried over by the simplification $\tilde A_μ=0$.

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arXiv1994

Topologically non--trivial chiral transformations and their representations in a finite model space

The role of chiral transformations in effective theories modeling Quantum Chromo Dynamics is reviewed. In the context of the Nambu--Jona--Lasinio model the hidden gauge and massive Yang--Mills approaches to vector mesons are demonstrated to be linked by a special chiral transformation which removes the chiral field from the scalar--pseudoscalar sector. The role of this transformation in the presence of a topologically non--trivial chiral field is illuminated. The fermion determinant for such a field configuration is evaluated by summing the discretized eigenvalues of the Dirac Hamiltonian. This discretization is accomplished by demanding certain boundary conditions on the quark fields leaving a finite model space. The properties of two sets of boundary conditions are compared. When the topologically non-trivial chiral transformation is applied to the meson fields the associated transformation of the boundary conditions is shown to be indispensable. A constructive procedure for transforming the boundary conditions is developed.

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arXiv1993

Strange S--Wave Excitation of the NJL Soliton

The recently developed method to investigate mesonic fluctuations off the chiral soliton in the Nambu--Jona--Lasinio model is applied to kaons in the S--wave channel. It is shown that for commonly accepted choices of parameters the presence of the soliton and the lack of confinement in this model provide an unphysical (valence) quark threshold which is lower than the kaon mass. Choosing parameters such that this threshold is avoided a bound state is obtained in the S--wave channel. After semiclassical quantization this state acquires the quantum numbers of an odd parity $Λ$ and is predicted at about 420MeV above the nucleon mass.

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arXiv1993

Hyperons in the Bound State Approach to the Nambu--Jona-Lasinio Chiral Soliton

For the Nambu--Jona--Lasinio (NJL) model in the proper time regularization scheme the chiral soliton is investigated for the case of three flavors within the framework of the bound state approach to strangeness. For this purpose meson fluctuations off the non--strange soliton are considered. For the kaon P--wave channel the emerging Bethe--Salpeter equation is solved yielding the bound state energy and wave--function. This kaon bound state also induces a strange valence quark wave--function. Collective coordinates are introduced for the SU(2) isorotations and the coupling of the bound state to these rotations is determined. The total spin is decomposed into parts carried by the soliton and the bound state. The absolute value of the former is identical to the total isospin while the latter is demonstrated to be identical to the expectation value of the grand spin, the sum of spin and isospin. The functional trace involves quark states with various grand spins which get polarized by the kaon bound state. This polarization results in a normalization of the coupling between the collective rotation and the bound state different from the Skyrme model. Nevertheless after quantization the expression for the baryon masses can be cast into the form found by Callan and Klebanov for the Skyrme model. Numerical results for the baryon spectrum are compared to those obtained in the same model using the collective approach of Yabu and Ando. It is found that for $\frac{1}{2}^+$ baryons the bound state treatment reproduces the experimental data better than the collective approach while there are only small differences between the two approaches for the $\frac{3}{2}^+$ baryons. Both treatments underestimate the mass splittings for baryons with different strangeness. This short-coming is conjectured to be inherited from the meson sector of the NJL model where too small a ratio of the kaon and pion decay constants is predicted.

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arXiv1993

$1/N_C$ Corrections to $g_A$ in the Light of PCAC$

We comment on recently discovered $1/N_C$ corrections to the ` nucleon axial current in the framework of the Nambu--Jona-Lasinio soliton. This kind of corrections arises only for a special treatment of ordering ambiguities of collective coordinates and operators in the semiclassical quantization. In addition to the missing derivation of this special quantization scheme from first principles its na\"ıve application violates partial conservation of the axial current (PCAC). We show how within this scheme PCAC can be restored and determine the corresponding $1/N_C$ corrections to the equation of motion for the chiral soliton. The resulting self-consistent solution allows to evaluate the nucleon axial coupling constant $g_A$ directly as a matrix element of the axial current as well as indirectly from the pion profile function. Enhancement is found for those baryon properties which are sensitive to the long range behavior of the pion profile.

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arXiv1993

The Nambu-Jona-Lasinio Chiral Soliton with Constrained Baryon Number

A regularization for the baryon number consistent with the energy in the Nambu-Jona-Lasinio model is introduced. The soliton solution is constructed with the regularized baryon number constrained to unity. It is furthermore demonstrated that this constraint prevents the soliton from collapsing when scalar fields are allowed to be space dependent. In this scheme the scalar fields actually vanish at the origin reflecting a partial restoration of chiral symmetry. Also the influence of this constraint on some static properties of baryons is discussed.

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arXiv1993

Diquark electromagnetic form factors in a Nambu-Jona-Lasinio model

Electromagnetic properties of diquarks are investigated in the framework of a color-octet Nambu-Jona-Lasinio model, which describes baryons as bound states of diquarks and quarks. We calculate the electromagnetic form factors of scalar and axial vector diquark bound states using the gauge--invariant proper--time regularization. The nucleon charge radii and magnetic moments are estimated in a simple additive diquark--quark model. This picture reproduces the qualitative features such as the negative charge radius of the neutron. Within this model axial vector diquarks are seen to be important.

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arXiv1993

Strange and Non-Strange Meson Fluctuations off the Nambu--Jona-Lasinio Soliton

Mesonic fluctuations off the chiral soliton of the Nambu--Jona-Lasinio model are investigated. The hedgehog configuration is proven to represent a local extremum of the action. The method is applied to flavor SU(3) and the energy eigenvalue of the kaon bound state in the soliton background is evaluated which is the key ingredient for the Callan-Klebanov approach to hyperons. The energy eigenvalue of the corresponding strange-valence-quark is found to be 183MeV higher than the energy eigenvalue of the up-valence-quark when 400MeV is assumed for the up-quark constituent mass.

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arXiv1993

The Chiral Soliton of the Nambu Jona-Lasinio Model with Vector and Axial Vector Mesons

The self-consistent chiral soliton of the Nambu--Jona-Lasinio model including the $ω,ρ$ and $a_1$ (axial-) vector meson fields besides the chiral angle is investigated. The resulting energy spectrum of the one particle Dirac Hamiltonian is strongly distorted leading to a polarized Dirac sea which carries the complete baryon number. This supports Witten's conjecture that baryons can be described as topological solitons. The exploration of the isoscalar mean squared radius of the nucleon exhibits that the repulsive character of the isoscalar vector field $ω$ as well as the attractive features of the (axial-) vector mesons $ρ$ and $a_1$ are reproduced in the Nambu--Jona-Lasinio model. The axial charge of the nucleon $g_A$ comes out far too small. This can be understood as an artifact of the proper time regularization prescription.

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arXiv1992

The chiral anomaly and electromagnetic pion decay in effective quark models

Within renormalizable theories the triangle diagram correctly reproduces the lifetime of the neutral pion $π^0$. However, effective relativistic quark models which contain a second scale besides the quark mass seem unable to give the correct value for this quantity. In the Instanton Liquid Model this second scale is the mean instanton radius, in the NJL model it is the cutoff. The role of the cutoff within a path integral derivation of the chiral anomaly is clarified and the importance of higher order terms contributing to the $π^0$ decay width and other anomalous processes is pointed out.

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arXiv1992

The Chiral Soliton of the Nambu-Jona-Lasinio Model

The baryon number one soliton of the NJL model is investigated. The Euclidian effective action is regularized using Schwinger's proper time method. Numerical results for the static soliton energy are presented for the cases without and with vector and axialvector fields. It is found that the baryon number is carried by the polarized Dirac sea of the quarks if the $a_1$ meson is included in contrast to the case without $a_1$ where the baryon number resides on valence quarks. Thus the model strongly supports the picture of the baryon as a topological soliton of the meson fields. Including the $ω$ vector meson leads to a non--vanishing imaginary part of the Euclidian effective action even for static solitons. Leaving the chiral circle, i.e.\ including the isoscalar scalar meson, the soliton first seems unstable. However, we demonstrate that a $ϕ^4$ term stabilizes the soliton. Finally, the self--consistent two--flavor chiral soliton is embedded in the SU(3) flavor group and collectively quantized. The predicted mass splittings for the low--lying baryons with different hypercharge are in excellent agreement with the experimental data if the physical value for the kaon decay constant is substituted.

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