arXiv subjects

H. Reinhardt

Publications and source records attributed to H. Reinhardt.

At least 109 records · Page 6Linked to original sources

arXiv1999

A picture of the Yang-Mills deconfinement transition and its lattice verification

In the framework of the center vortex picture of confinement, the nature of the deconfining phase transition is studied. Using recently developed techniques which allow to associate a center vortex configuration with any given lattice gauge configuration, it is demonstrated that the confining phase is a phase in which vortices percolate, whereas the deconfined phase is a phase in which vortices cease to percolate if one considers an appropriate slice of space-time.

hep-ph↗

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.

hep-ph↗

arXiv1999

Magnetic Monopoles, Vortices and the Topology of Gauge Fields

Lattice calculations performed in Abelian gauges give strong evidence that confinement is realized as a dual Meissner effect, implying that the Yang-Mills vacuum consists of a condensate of magnetic monopoles. Alternative lattice caluclations performed in the maximum center gauge give strong support that center vortex configurations are the relevant infrared degrees of freedom responsible for confinement and that the magnetic monopoles are mostly sitting on vortices. In this talk I study the continuum Yang-Mills-theory in Abelian and center gauges. In Polyakov gauge the Pontryagin index of the gauge field is expressed by the magnetic monopole charges. The continuum analogues of center vortices and the continuum version of the maximum center gauge are presented. It is shown that the Pontryagin index of center vortices is given by their self-intersection number, which vanishes unless magnetic monopole currents are flowing on the vortices.

hep-th↗

arXiv1999

Center Projection Vortices in Continuum Yang-Mills Theory

The maximal center gauge, combined with center projection, is a means to associate Yang-Mills lattice gauge configurations with closed center vortex world-surfaces. This technique allows to study center vortex physics in lattice gauge experiments. In the present work, the continuum analogue of the maximal center gauge is constructed. This sheds new light on the meaning of the procedure on the lattice and leads to a sketch of an effective vortex theory in the continuum. Furthermore, the manner in which center vortex configurations generate the Pontryagin index is investigated. The Pontryagin index is built up from self-intersections of the vortex world-surfaces, where it is crucial that the surfaces be globally non-oriented.

hep-th↗

arXiv1999

Deconfinement in SU(2) Yang-Mills theory as a center vortex percolation transition

By fixing lattice Yang-Mills configurations to the maximal center gauge and subsequently applying the technique of center projection, one can identify center vortices in these configurations. Recently, center vortices have been shown to determine the string tension between static quarks at finite temperatures (center dominance); also, they correctly reproduce the deconfining transition to a phase with vanishing string tension. After verifying center dominance also for the so-called spatial string tension, the present analysis focuses on the global topology of vortex networks. General arguments are given supporting the notion that the deconfinement transition in the center vortex picture takes the guise of a percolation transition. This transition is detected in Monte Carlo experiments by concentrating on various slices through the closed vortex surfaces; these slices, representing loops in lattice universes reduced by one dimension, clearly exhibit the expected transition from a percolating to a non-percolating, deconfined, phase. The latter phase contains a large proportion of vortex loops winding around the lattice in the Euclidean time direction. At the same time, an intuitive picture clarifying the persistence of the spatial string tension in the deconfined phase emerges.

hep-lat↗

arXiv1999

Nucleon Structure Functions in the Three Flavor NJL Soliton Model

We study the relevance of strange degrees of freedom for nucleon structure functions. For this purpose we employ the three flavor generalization of the collective quantization approach to the chiral soliton of the bosonized Nambu-Jona-Lasinio model. Contrary to many other soliton models the hadronic tensor is tractable in this model. By applying the Bjorken limit to the hadronic tensor we extract the leading twist contributions to the nucleon structure functions at the low energy scale at which the model is assumed to approximate QCD. After transforming to the infinite momentum frame and performing the DGLAP evolution program to these structure functions we compare with available data for deep inelastic electron-nucleon scattering.

hep-ph↗

arXiv1999

Center vortices of Yang-Mills theory at finite temperatures

Recent lattice calculations performed at zero temperature and in the maximal center gauge indicate that quark confinement can be understood in this gauge as due to fluctuations in the number of magnetic vortices piercing a given Wilson loop. This development has led to a revival of the vortex condensation theory of confinement. For a SU(2) gauge group, we show that also at finite temperatures, center vortices are the relevant collective infrared degrees of freedom determining the long-range static quark potential; in particular, their dynamics reflect the transition to the deconfining phase.

hep-lat↗

arXiv1998

Magnetic Monopoles and Topology of Yang-Mills Theory in Polyakov Gauge

We express the Pontryagin index in Polyakov gauge completely in terms of magnetically charged gauge fixing defects, namely magnetic monopoles, lines, and domain walls. Open lines and domain walls are topologically equivalent to monopoles, which are the genuine defects. The emergence of non-genuine magnetically charged closed domain walls can be avoided by choosing the temporal gauge field smoothly. The Pontryagin index is then exclusively determined by the magnetic monopoles.

hep-th↗

arXiv1998

Magnetic Monopoles and the Topology of Gauge Fields

Lattice calculations performed in Abelian gauges give strong evidence that confinement is realized as a dual Meissner effect, implying that the Yang--Mills vacuum consists of a condensate of magnetic monopoles. We show in Polyakov gauge how the Pontrjagin index of the gauge field is related to the magnetic monopole charges.

hep-th↗

arXiv1998

Nucleon structure functions from a chiral soliton

We study nucleon structure functions within the bosonized version of the Nambu-Jona-Lasinio (NJL) model in which the nucleon emerges as the soliton in the chiral field. Upon boosting to the infinite momentum frame and performing the $q^2$-evolution in the context of the Gottfried sum rule for electron nucleon scattering we determine the intrinsic scale $μ^2$ of the NJL chiral soliton. We also compute the leading twist contributions of the polarized structure functions $g_1$ and $g_2$. We compare these model predictions with experiment by evolving them from $μ^2$ to the scale where the data are taken. Analogously we analyze the chiral-odd structure functions $h_T$ and $h_L$. Finally we generalize the treatment to flavor SU(3).

hep-ph↗

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.

nucl-th↗

arXiv1998

Chiral Odd Structure Functions from a Chiral Soliton

We calculate the chiral odd quark distributions and the corresponding structure functions $h_T(x,Q^2)$ and $h_L(x,Q^2)$ within the Nambu-Jona-Lasinio chiral soliton model for the nucleon. The $Q^2$ evolution of the twist-2 contributions is performed according to the standard GLAP formalism while the twist-three piece, $\bar{h}_L(x)$, is evolved according to the large $N_C$ scheme. We carry out a comparison between the chiral odd structure functions of the proton and the neutron. At the low model scale ($Q_0^2$) we find that the leading twist effective quark distributions,$f_1^{(q)}(x,Q_0^2)$, $g_1^{(q)}(x,Q_0^2)$ and $h_T^{(q)}(x,Q_0^2)$ satisfy Soffer's inequality for both quark flavors $q=u,d$.

hep-ph↗

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.

hep-ph↗

arXiv1998

Strangeness Contribution to the Polarized Nucleon Structure Function $g_1(x)$

The three flavor version of the Nambu-Jona-Lasinio chiral soliton model for baryons is employed to calculate the twist-2 contribution to the polarized nucleon structure function $g_1(x)$. In particular the role of the strange quark degree of freedom as a collective excitation of the chiral soliton is investigated in the context of flavor symmetry breaking. The model prediction for $g_1(x)$ refers to a low momentum scale $Q_0^2$. The leading order corrections to the scale dependence is computed along the QCD evolution program allowing to compare with data from SLAC.

hep-ph↗

arXiv1998

Nucleon Structure Functions from a Chiral Soliton in the Infinite Momentum Frame

We study the frame dependence of nucleon structure functions obtained within a chiral soliton model for the nucleon. Employing light cone coordinates and introducing collective coordinates together with their conjugate momenta, translational invariance of the solitonic quark fields (which describe the nucleon as a localized object) is restored. This formulation allows us to perform a Lorentz boost to the infinite momentum frame of the nucleon. The major result is that the Lorentz contraction associated with this boost causes the leading twist contribution to the structure functions to properly vanish when the Bjorken variable $x$ exceeds unity. Furthermore we demonstrate that for structure functions calculated in the valence quark approximation to the Nambu--Jona--Lasinio chiral soliton model the Lorentz contraction also has significant effects on the structure functions for moderate values of the Bjorken variable $x$.

hep-ph↗

arXiv1998

Field Strength Formulation of SU(2) Yang-Mills Theory in the Maximal Abelian Gauge: Perturbation Theory

We present a reformulation of SU(2) Yang-Mills theory in the maximal Abelian gauge, where the non-Abelian gauge field components are exactly integrated out at the expense of a new Abelian tensor field. The latter can be treated in a semiclassical approximation and the corresponding saddle point equation is derived. Besides the non-trivial solutions, which are presumably related to non-perturbative interactions for the Abelian gauge field, the equation of motion for the tensor fields allows for a trivial solution as well. We show that the semiclassical expansion around this trivial solution is equivalent to the standard perturbation theory. In particular, we calculate the one-loop $β$-function for the running coupling constant in this approach and reproduce the standard result.

hep-th↗

arXiv1998

Interaction of confining vortices in SU(2) lattice gauge theory

Center projection of SU(2) lattice gauge theory allows to isolate magnetic vortices as confining configurations. The vortex density scales according to the renormalization group, implying that the vortices are physical objects rather than lattice artifacts. Here, the binary correlations between points at which vortices pierce a given plane are investigated. We find an attractive interaction between the vortices. The correlations show the correct scaling behavior and are therefore physical. The range of the interaction is found to be (0.4 +/- 0.2) fm, which should be compared with the average planar vortex density of approximately 2 vortices/fm^2. We comment on the implications of these results for recent discussions of the Casimir scaling behavior of higher dimensional representation Wilson loops in the vortex confinement picture.

hep-lat↗

arXiv1997

Ward Identities for Yang-Mills Theory in Abelian Gauges: Abelian Dominance at High Energies

We consider Yang-Mills theory in a general class of Abelian gauges. Exploiting the residual Abelian symmetry on a quantum level, we derive a set of Ward identities in functional form, valid to all orders in perturbation theory. As a consequence, the coupling constant is only renormalised through the Abelian two-point function. This implies that asymptotic freedom in all Abelian gauges can be understood from an effective Abelian theory alone, which can be interpreted as Abelian dominance in the high energy regime.

hep-th↗