arXiv subjects
Publications and source records attributed to H. Weigel.
We study the radiative decays of $J^π=\frac{3}{2}^+$ baryons in the framework of the SU(3) collective approach to the Skyrme model. We present the predictions for the decay widths and the corresponding $E2/M1$ ratios. We find that all considered ratios are negative and of the order of a few percent only. We discuss the effects of flavor symmetry breaking and compare our results to those obtained in related models.
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.
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.
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.
A generalization of the effective meson Lagrangian possessing the heavy quark symmetry to finite meson masses is employed to study the meson mass dependence of the spectrum of S-- and P wave baryons containing one heavy quark or anti-quark. These baryons are described as respectively heavy mesons or anti-mesons bound in the background of a soliton, which is constructed from light mesons. No further approximation is made to solve the bound state equation. For special cases it is shown that the boundary conditions, which have to be satisfied by the bound state wave--functions and stem from the interaction with the light mesons, may impose additional constraints on the existence of bound states when finite masses are assumed. Two types of models supporting soliton solutions for the light mesons are considered: the Skyrme model of pseudoscalars only as well as an extension containing also light vector mesons. It is shown that only the Skyrme model with vector mesons provides a reasonable description of both light and heavy baryons. Kinematical corrections to the bound state equations are included in the discussion.
We formulate the particle conjugation operation and its convenient realization as $G$--parity in the framework of several chiral soliton models. The Skyrme model, the Skyrme model with vector mesons and the chiral quark model are specifically treated. The vector and axial vector currents are classified according to their behavior under $G$--parity. In the soliton sector particle conjugation constrains {\it a priori} ambiguous orderings of operators in the space of the collective coordinates. In the Skyrme model with vector mesons and in a local chiral model with an explicit valence quark this classification scheme provides consistency conditions for the ordering of the collective operators appearing in the $1/N_C$ corrections to the nucleon axial charge and the isovector magnetic moment. These consistency conditions cause the corrections obtained from an ordinary perturbation expansion to vanish in the context of the collective quantization of the static soliton configuration. This conclusion presumably applies to all local effective chiral models.
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.
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.
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.
We impose the requirement that the isovector axial vector current for the soliton sector of the chiral quark model transforms correctly under particle conjugation. This forces us to choose an otherwise arbitrary ordering of collective space operators in such a way that the next--to--leading $1/N_C$ correction to $g_A$ vanishes.
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.
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
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.
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 $\tilde A_μ=0$.
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.
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.
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.
It is demonstrated how in the soliton approach to baryons a small but non-vanishing matrix element of the axial singlet current is obtained. Furthermore it is shown that these models also provide a mechanism to disentangle the ``matter" and ``glue" contributions to this matrix element. Numerical results indeed exhibit a cancellation between these two components. However, the magnitudes of both turn out to be significantly smaller than unity.