Axial current matrix elements and pentaquark decay widths in chiral soliton models
Here I explain why in chiral soliton models the hadronic transition operator of the pentaquark decay cannot be identified from the axial current.
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arXiv subjects
H. Weigel
Publications and source records attributed to H. Weigel.
On the width of collective excitations in chiral soliton models
In chiral soliton models for baryons the computation of hadronic decay widths of baryon resonances is a long standing problem. For the three flavor Skyrme model I present a solution to this problem that satisfies large--$N_C$ consistency conditions. As an application I focus on the hadronic decay of the $Θ$ and $Θ^*$ pentaquarks.
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Quantum Energies of Strings in a 2+1 Dimensional Gauge Theory
We study classically unstable string type configurations and compute the renormalized vacuum polarization energies that arise from fermion fluctuations in a 2+1 dimensional analog of the standard model. We then search for a minimum of the total energy (classical plus vacuum polarization energies) by varying the profile functions that characterize the string. We find that typical string configurations bind numerous fermions and that populating these levels is beneficial to further decrease the total energy. Ultimately our goal is to explore the stabilization of string type configurations in the standard model through quantum effects. We compute the vacuum polarization energy within the phase shift formalism which identifies terms in the Born series for scattering data and Feynman diagrams. This approach allows us to implement standard renormalization conditions of perturbation theory and thus yields the unambiguous result for this non--perturbative contribution to the total energy.
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Bound State versus Collective Coordinate Approaches in Chiral Soliton Models and the Width of the $Θ^+$ Pentaquark
We thoroughly compare the bound state and rigid rotator approaches to three--flavored chiral solitons. We establish that these two approaches yield identical results for the baryon spectrum and kaon--nucleon $S$--matrix in the limit that the number of colors ($N_C$) tends to infinity. After proper subtraction of the background phase shift the bound state approach indeed exhibits a clear resonance behavior in the strangeness $S=+1$ channel. We present a first dynamical calculation of the widths of the $Θ^+$ and $Θ^*$ pentaquarks for finite $N_C$ in a chiral soliton model.
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Reply to Cohen's comment on the rotation--vibration coupling in chiral soliton models
In this short note we summarize the main results of our paper [hep-ph/0510055] and reply to a recent comment [hep-ph/0511174] on that paper.
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Soliton Picture for Pentaquarks
In this talk I report on a thorough comparison between the bound state and rigid rotator approaches to generate baryon states with non--zero strangeness in chiral soliton models. This comparison shows that the scattering amplitude in the bound state approach contains contributions generated by the exchange of the rigid pentaquark excitation, and that the two approaches are consistent with each other in the large $N_C$ limit. The comparison paves the way to unambiguously compute the width of the $Θ^+$ pentaquark in chiral soliton models.
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Quantum QED Flux Tubes in 2+1 and 3+1 Dimensions
We compute energies and energy densities of static electromagnetic flux tubes in three and four spacetime dimensions. Our calculation uses scattering data from the potential induced by the flux tube and imposes standard perturbative renormalization conditions. The calculation is exact to one-loop order, with no additional approximation adopted. We embed the flux tube in a configuration with zero total flux so that we can fully apply standard results from scattering theory. We find that upon choosing the same on-shell renormalization conditions, the functional dependence of the energy and energy density on the parameters of the flux tube is very similar for three and four spacetime dimensions. We compare our exact results to those obtained from the derivative and perturbation expansion approximations, and find good agreement for appropriate parameters of the flux tube. This remedies some puzzles in the prior literature.
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Pentaquarks in a Breathing Mode Approach to Chiral Solitons
In this talk I report on a computation of the spectra of exotic pentaquarks and radial excitations of the low--lying ${1/2}^+$ and ${3/2}^+$ baryons in a chiral soliton model. In addition I present model results for the transition magnetic moments between the N(1710) and the nucleon.
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Pentaquarks and Radially Excited Baryons
In this talk I report on a computation of the spectra of exotic pentaquarks and radial excitations of the low--lying ${1/2}^+$ and ${3/2}^+$ baryons in a chiral soliton model.
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Exotic Baryons and Monopole Excitations in a Chiral Soliton Model
We compute the spectra of exotic pentaquarks and monopole excitations of the low--lying ${1/2}^+$ and ${3/2}^+$ baryons in a chiral soliton model. Once the low--lying baryon properties are fit, the other states are predicted without any more adjustable parameters. This approach naturally leads to a scenario in which the mass spectrum of the next to lowest--lying $J^π={1/2}^+$ states is fairly well approximated by the ideal mixing pattern of the $\mathbf{8}\oplus\bar{\mathbf{10}}$ representation of flavor SU(3). We compare our results to predictions obtained in other pictures for pentaquarks and speculate about the spin--parity assignment for $Ξ(1690)$ and $Ξ(1950)$
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Magnetic Moments of Baryons with a Single Heavy Quark
We calculate the magnetic moments of heavy baryons with a single heavy quark in the bound-state approach. In this approach the heavy baryons is considered as a heavy meson bound in the field of a light baryon. The light baryon field is represented as a soliton excitation of the light pseudoscalar and vector meson fields. For these calculations we adopt a model that is both chirally invariant and consistent with the heavy quark spin symmetry. We gauge the model action with respect to photon field in order to extract the electromagnetic current operator and obtain the magnetic moments by computing pertinent matrix elements of this operator between the bound state wavefunctions. We compare our predictions for the magnetic moments with results of alternative approaches for the description of heavy baryon properties.
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Dirichlet Spheres in Continuum Quantum Field Theory
We study the vacuum polarization (Casimir) energy in renormalizable, continuum quantum field theory in the presence of a background field, designed to impose Dirichlet boundary conditions on the fluctuating quantum field. In two and three spatial dimensions the Casimir energy diverges as a background field becomes concentrated on the surface on which the Dirichlet boundary condition would eventually hold. This divergence does not affect the force between rigid bodies, but it does invalidate calculations of Casimir stresses based on idealized boundary conditions.
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The Dirichlet Casimir Problem
Casimir forces are conventionally computed by analyzing the effects of boundary conditions on a fluctuating quantum field. Although this analysis provides a clean and calculationally tractable idealization, it does not always accurately capture the characteristics of real materials, which cannot constrain the modes of the fluctuating field at all energies. We study the vacuum polarization energy of renormalizable, continuum quantum field theory in the presence of a background field, designed to impose a Dirichlet boundary condition in a particular limit. We show that in two and three space dimensions, as a background field becomes concentrated on the surface on which the Dirichlet boundary condition would eventually hold, the Casimir energy diverges. This result implies that the energy depends in detail on the properties of the material, which are not captured by the idealized boundary conditions. This divergence does not affect the force between rigid bodies, but it does invalidate calculations of Casimir stresses based on idealized boundary conditions.
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Magnetic Moments of Baryons with a Heavy Quark
We compute magnetic moments of baryons with a heavy quark in the bound state approach for heavy baryons. In this approach the heavy baryon is considered as a heavy meson bound to a light baryon. The latter is represented as a soliton excitation of light meson fields. We obtain the magnetic moments by sandwiching pertinent components of the electromagnetic current operator between the bound state wave--functions. We extract this current operator from the coupling to the photon field after extending the action to be gauge invariant.
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A Bethe--Salpeter Description of Light Mesons
We present a covariant approach to describe the low--lying scalar, pseudoscalar, vector and axialvector mesons as quark--antiquark bound states.This approach is based on an effective interaction modeling of the non--perturbative structure of the gluon propagator that enters the quark Schwinger--Dyson and meson Bethe--Salpeter equations. We extract the meson masses and compute the pion and kaon decay constants. We obtain a quantitatively correct description for pions, kaons and vector mesons while the calculated spectra of scalar and axialvector mesons suggest that their structure is more complex than being quark--antiquark bound states.
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Heavy Fermion Quantum Effects in SU(2)_L Gauge Theory
We explore the effects of a heavy fermion doublet in a simplified version of the standard electroweak theory. We integrate out the doublet and compute the exact effective energy functional of spatially varying gauge and Higgs fields. We perform a variational search for a local minimum of the effective energy and do not find evidence for a soliton carrying the quantum numbers of the decoupled fermion doublet. The fermion vacuum polarization energy offsets the gain in binding energy previously argued to be sufficient to stabilize a fermionic soliton. The existence of such a soliton would have been a natural way to maintain anomaly cancellation at the level of the states. We also see that the sphaleron energy is significantly increased due to the quantum corrections of the heavy doublet. We find that when the doublet is slightly heavier than the quantum--corrected sphaleron, its decay is exponentially suppressed owing to a new barrier. This barrier exists only for an intermediate range of fermion masses, and a heavy enough doublet is indeed unstable.
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Chiral Quark Model
In this talk I review studies of hadron properties in bosonized chiral quark models for the quark flavor dynamics. Mesons are constructed from Bethe--Salpeter equations and baryons emerge as chiral solitons. Such models require regularization and I show that the two--fold Pauli--Villars regularization scheme not only fully regularizes the effective action but also leads the scaling laws for structure functions. For the nucleon structure functions the present approach serves to determine the regularization prescription for structure functions whose leading moments are not given by matrix elements of local operators. Some numerical results are presented for the spin structure functions.
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Casimir Energies in Light of Quantum Field Theory
We study the Casimir problem as the limit of a conventional quantum field theory coupled to a smooth background. The Casimir energy diverges in the limit that the background forces the field to vanish on a surface. We show that this divergence cannot be absorbed into a renormalization of the parameters of the theory. As a result, the Casimir energy of the surface and other quantities like the surface tension, which are obtained by deforming the surface, cannot be defined independently of the details of the coupling between the field and the matter on the surface. In contrast, the energy density away from the surface and the force between rigid surfaces are finite and independent of these complications.
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