arXiv subjects

H. Reinhardt

Publications and source records attributed to H. Reinhardt.

158 records · Page 9Linked to original sources

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.

hep-ph↗

arXiv1993

Natural Slow-Roll Inflation

It is shown that the non-perturbative dynamics of a phase change to the non-trivial phase of $λφ^4$-theory in the early universe can give rise to slow-rollover inflation without recourse to unnaturally small couplings.

hep-ph↗

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.

hep-ph↗

arXiv1993

Non-Trivial SU(N) Instantons and Exotic Skyrmions

The classical Yang-Mills equations are solved for arbitrary semi-simple gauge groups in the Schwinger-Fock gauge. A new class of SU(N) instantons is presented which are not embeddings of SU(N-1) instantons but have non-trivial SU(N) color structure and carry winding number $n=N(N^{2}-1)/6$. Explicit configurations are given for SU(3) and SU(4) gauge groups. By means of the Atiyah Manton procedure Skyrmion fields are constructed from the SU(N) instantons. These Skyrmions represent exotic baryon states.

hep-ph↗

arXiv1993

Casimir Effect of Strongly Interacting Scalar Fields

Non-trivial $ϕ^{4}$-theory is studied in a renormalisation group invariant approach inside a box consisting of rectangular plates and where the scalar modes satisfy periodic boundary conditions at the plates. It is found that the Casimir energy exponentially approaches the infinite volume limit, the decay rate given by the scalar condensate. It therefore essentially differs from the power law of a free theory. This might provide experimental access to properties of the non-trivial vacuum. At small interplate distances the system can no longer tolerate a scalar condensate, and a first order phase transition to the perturbative phase occurs. The dependence of the vacuum energy density and the scalar condensate on the box dimensions are presented.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

arXiv1993

Non-Trivial Phase Structure of $ϕ^{4}$-Theory at Finite Temperature

The effective potential for the local composite operator $ϕ^{2}(x)$ in $λϕ^{4}$-theory is investigated at finite temperature in an approach based on path-integral linearisation of the $ϕ^4 $-interaction. At zero temperature, the perturbative vacuum is unstable, because a non-trivial phase with a scalar condensate $\langle ϕ^{2} \rangle _{0}$ has lower effective action. Due to field renormalisation, $\langle λϕ^{2} \rangle _{0}$ is renormalisation group invariant and leads to the correct scale anomaly. At a critical temperature $T_{c}$ the non-perturbative phase becomes meta-stable implying a first order phase-transition to the perturbative phase. The ratio $\langleλϕ^{2} \rangle _{0} / T_{c}^{2} \approx 62$ turns out to be a universal constant.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

arXiv1993

The Non-Trivial Phase of $\PHI ^4$-Theory in a Renormalisation Group Invariant Approach

Massless $ϕ^{4}$-theory is investigated in zero and four space-time dimensions. Path-integral linearisation of the $ϕ^{4}$-interaction defines an effective theory, which is investigated in a loop-expansion around the mean field. In zero dimensions this expansion converges rapidly to the exact potential obtained numerically. In four dimensions its lowest order (mean-field approximation) produces a real and convex effective potential. Two phases are found. In one the renormalisation group improved one-loop effective potential is recovered as the leading contribution near the classical minimum. This phase, however, is unstable. The second (precarious) phase is found to have lower vacuum energy density. In this phase a dynamical mass is generated. The results are renormalisation group invariant.

hep-ph↗

arXiv1993

Instanton Condensation in Field Strength Formulated QCD

Field strength formulated Yang-Mills theory is confronted with the traditional formulation in terms of gauge fields. It is shown that both formulations yield the same semiclassics, in particular the same instanton physics. However, at the tree level the field strength approach is superior because it already includes a good deal of of quantum fluctuations of the standard formulation. These quantum fluctuations break the scale invariance of classical QCD and give rise to an instanton interaction and this causes the instantons to condense and form a homogeneous instanton solid. Such the instanton solids show up in the field strength approach as homogeneous (constant up to gauge transformations) vacuum solutions. A new class of SU(N) instantons is presented which are not embeddings of SU(N-1) instantons but have non-trivial SU(N) color structure and carry winding number $n=N(N^{2}-1)/6$. These instantons generate (after condensation) the lowest action solutions of the field strength approach. The statistical weight (entropy) of different homogeneous solutions for SU(3) is numerically estimated by Parisi's stochastic quantization method. Finally, we compare instanton induced quark condensation with the condensation of quarks in the homogeneous field strength solutions. Our investigations show that the homogeneous vacuum of the field strength approach simulates in an efficient way a condensate of instantons.

hep-ph↗

arXiv1993

Instantons in Field Strength Formulated Yang-Mills Theories

It is shown that the field strength formulated Yang-Mills theory yields the same semiclassics as the standard formulation in terms of the gauge potential. This concerns the classical instanton solutions as well as the quantum fluctuations around the instanton.

hep-ph↗

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.

hep-ph↗