arXiv subjects

Stefan Leupold

Publications and source records attributed to Stefan Leupold.

At least 73 records · Page 4Linked to original sources

arXiv2007

Omega mesons in medium - revisited

Recent experimental observation by the CBELSA/TAPS collaboration indicates a downward mass shift of the $ω$ meson when put into a nuclear medium. Therefore it is worthwhile to take a look at theoretical approaches that can describe this mass shift. One such hadronic model was introduced by Klingl et al. (Nucl.Phys. A650:299-312). We will demonstrate that the heavy baryon limit approximation used there has no justification and returns wrong results. The results obtained with a correct treatment of the relevant $2π$-channel lead to unreasonable results for the $ω$ selfenergy in medium.

hep-ph↗

arXiv2006

Selfconsistent approximations, symmetries and choice of representation

In thermal field theory selfconsistent (Phi-derivable) approximations are used to improve (resum) propagators at the level of two-particle irreducible diagrams. At the same time vertices are treated at the bare level. Therefore such approximations typically violate the Ward identities connected to internal symmetries. Examples are presented how such violations can be tamed by a proper choice of representation for the fields which describe the system under consideration. These examples cover the issue of massless Goldstone bosons in the linear sigma model and the Nambu--Jona-Lasinio model and the problem of current conservation in theories with massive vector mesons.

hep-ph↗

arXiv2006

In-medium Hadrons - Properties, Interaction and Formation

In this talk various aspects of in-medium behavior of hadrons are discussed with an emphasis on observable effects. Examples for theoretical predictions of in-medium spectral functions are given and the importance of resonance-hole excitations is stressed. It is also stressed that final state interactions can have a major effect on observables and thus have to be considered as part of the theory. This is demonstrated with examples from neutrino-nucleus interactions. Finally, the possibility to access hadron formation times in high-energy photonuclear (or neutrino-induced) reactions is illustrated.

nucl-th↗

arXiv2006

Interactions of multi-quark states in the chromodielectric model

We investigate 4-quark ($qq\bar{q}\bar{q}$) systems as well as multi-quark states with a large number of quarks and anti-quarks using the chromodielectric model. In the former type of systems the flux distribution and the corresponding energy of such systems for planar and non-planar geometries are studied. From the comparison to the case of two independent $q\bar{q}$-strings we deduce the interaction potential between two strings. We find an attraction between strings and a characteristic string flip if there are two degenerate string combinations between the four particles. The interaction shows no strong Van-der-Waals forces and the long range behavior of the potential is well described by a Yukawa potential, which might be confirmed in future lattice calculations. The multi-quark states develop an inhomogeneous porous structure even for particle densities large compared to nuclear matter constituent quark densities. We present first results of the dependence of the system on the particle density pointing towards a percolation type of transition from a hadronic matter phase to a quark matter phase. The critical energy density is found at $ε_c = 1.2 GeV/fm^3$.

hep-ph↗

arXiv2006

Fate of QCD sum rules or fate of vector meson dominance in a nuclear medium

A current-current correlator with the quantum numbers of the omega meson is studied in a nuclear medium. Using weighted finite energy sum rules and dispersion relations for the current-nucleon forward scattering amplitude it is shown that strict vector meson dominance and QCD sum rules are incompatible with each other. This implies that at least one of these concepts -- which are both very powerful in the vacuum -- has to fade in the nuclear environment.

hep-ph↗

arXiv2006

Weighted finite energy sum rules for the omega meson in nuclear matter

The possible in-medium changes of the properties of an omega meson placed in cold nuclear matter are constrained by QCD sum rules. It is shown that the sum rules cannot fully determine the in-medium spectral shape of the omega meson. However, for a given parameterization the sum rules can constrain or correlate the hadronic parameters. It is shown that weighted finite energy sum rules provide a proper framework to study directly these constraints/correlations. Two typical parameterizations of possible in-medium omega spectra are analyzed, namely (i) a one-peak structure with arbitrary position and width of the peak and (ii) a structure with two (narrow) peaks, caused by the genuine omega meson and a resonance-hole branch. The sum rules provide for case (i) a mass-width correlation and for case (ii) a correlation between the peak heights and the peak position of the omega branch. It is also analyzed how the obtained results depend on the size of the relevant four-quark operator evaluated with respect to a nucleon. Finally it is argued that a strict vector meson dominance scenario is not compatible with the sum rules.

hep-ph↗

arXiv2006

Four-quark condensates and chiral symmetry restoration in a resonance gas model

As an alternative to the two-quark condensate we propose a specific four-quark condensate as an order parameter of chiral symmetry restoration. We show that this four-quark condensate is closer connected to observable quantities. Within a resonance gas model we calculate the in-medium changes of two- and four-quark condensate as functions of temperature and baryo-chemical potential. In this way we estimate the line of chiral symmetry restoration in the temperature-potential plane and also as a function of energy and baryon density. It turns out that the line determined from the vanishing of the four-quark condensate is extremely constant as a function of the energy density.

hep-ph↗

arXiv2006

Complete Relativistic Description of the N*(1520)

A relativistic description of spin 3/2 resonances and their decay channels is presented by calculating their selfenergies and spectral functions. The full vector-spinor structure is taken into account. Special emphasis is put on the N*(1520) and its decay channels pi N, rho N and pi Δ. All interactions are formulated such that only the correct number of degrees of freedom of a spin 3/2 state is propagated. The obtained results are compared with several approximations frequently used to avoid the complicated vector-spinor structure. Since this structure is taken fully into account here, the quality of the approximations can be judged.

nucl-th↗

arXiv2006

Properties of the vector meson nonet at large N_c beyond the chiral limit

Masses and especially coupling constants of the vector meson nonet are determined in the large-N_c limit, but beyond the chiral limit taking into account terms up to quadratic order in the Goldstone boson masses. With two input parameters five coupling constants for hadronic and dilepton decays are determined which agree very well with the experimental results. The obtained parameters are also used to calculate the pion and kaon decay constant in the large-N_c limit. A consistent picture is only obtained, if the correct assignment of the N_c-dependence of the electromagnetic charges of the quarks is taken into account.

hep-ph↗

arXiv2005

Factorization and Non-Factorization of In-Medium Four-Quark Condensates

It is well-established for the vacuum case that in the limit of a large number of colors N_c the four-quark condensates factorize into products of the two-quark condensate. It is shown that in the combined large-N_c and linear-density approximation four-quark condensates do not factorize in a medium of pions (finite temperature system) but do factorize in a medium of nucleons (nuclear system).

hep-ph↗

arXiv2004

Two- and three-body color flux tubes in the Chromo Dielectric Model

Using the framework of the Chromo Dielectric Model we perform an analysis of color electric flux tubes in meson-like $q\bar{q}$ and baryon-like $qqq$ quark configurations. We discuss the Abelian color structure of the model and point out a symmetry in color space as a remnant of the SU(3) symmetry of QCD. The generic features of the model are discussed by varying the model parameters. We fix these parameters by reproducing the string tension $τ=980 $MeV/fm and the transverse width $ρ=0.35 $fm of the $q\bar{q}$ flux tube obtained in lattice calculations. We use a bag constant $B^{1/4}=(240-260) $MeV, a glueball mass $m_g = (1000-1700) $MeV and a strong coupling constant $C_F α_s = 0.2-0.3$. We show that the asymptotic string profile of an infinitely long flux tube is already reached for $q\bar{q}$ separations $R\ge1.0 $fm. A connection to the Dual Color Superconductor is made by extracting a magnetic current from the model equations and a qualitative agreement between the two descriptions of confinement is shown. In the study of the $qqq$ system we observe a $\mathsfΔ$-like geometry for the color electric fields and a \textsf{Y}-like geometry in the scalar fields both in the energy density distribution and in the corresponding potentials. The resulting total $qqq$ potential is described neither by the $\mathsfΔ$-picture nor by the \textsf{Y}-picture alone.

hep-ph↗

arXiv2004

There is no local chiral perturbation theory at finite temperature

For a low-temperature expansion in QCD it is well-known that the Lagrangian of vacuum chiral perturbation theory can be applied. This is due to the fact that the thermal effects of the heavy modes are Boltzmann suppressed. The present work is concerned with the situation of higher temperatures, but still below the chiral transition. For a systematic approach it would be desirable to have a temperature modified chiral perturbation theory at hand which would yield a chiral power counting scheme. It is shown that this cannot be obtained. In principle, chiral perturbation theory emerges from QCD by (a) integrating out all degrees of freedom besides the Goldstone bosons and (b) expanding the obtained non-local action in terms of derivatives. It is shown that at finite temperature step (b) cannot be carried out due to non-analyticities appearing for vanishing four-momenta. Therefore one cannot obtain a local Lagrangian for the Goldstone boson fields with temperature modified coupling constants. The importance of the non-analyticities is estimated.

hep-ph↗

arXiv2004

QCD sum rules at finite density in the large-N_c limit: The coupling of the rho-nucleon system to the D_{13}(1520)

QCD sum rules are studied for the vector-isovector current at finite baryon density in the limit of large number of colors N_c. For the condensate side it is shown that in this limit the four-quark condensate factorizes also for the finite density case. At the hadronic side the medium dependence is expressed in terms of the current-nucleon forward scattering amplitude. Generalizing vector meson dominance we allow for a direct coupling of the current to the nucleon as well as a coupling via the rho meson. We discuss the N_c dependence of (a) modifications of the pion cloud of the rho meson, (b) mixing with other mesons (in particular a_1 and omega) and (c) resonance-hole excitations R N^{-1}. We show that only the last effect survives in the large-N_c limit. Saturating the sum rules with a simple hadronic ansatz which allows for the excitation of the D_{13}(1520) we determine the coupling of the latter to the rho-nucleon and the photon-nucleon system. These couplings are hard to determine from vacuum physics alone.

nucl-th↗

arXiv2003

Spectral Function of Quarks in Quark Matter

We investigate the spectral function of light quarks in infinite quark matter using a simple, albeit self-consistent model. The interactions between the quarks are described by the SU(2) Nambu--Jona-Lasinio model. Currently mean field effects are neglected and all calculations are performed in the chirally restored phase at zero temperature. Relations between correlation functions and collision rates are used to calculate the spectral function in an iterative process.

nucl-th↗

arXiv2003

Determination of vector meson properties by matching resonance saturation to a constituent quark model

The properties of mesonic resonances can be calculated in terms of the low-energy coefficients of chiral perturbation theory (chiPT) by extending unitarized chiPT to higher energies. On the other hand these low-energy coefficients can be calculated in two different models, namely (i) by assuming resonance saturation and (ii) within a constituent quark model. By matching the expressions of the two models combined with the results of unitarized chiPT and the Weinberg sum rules the properties of vector and axial-vector mesons can be calculated in the combined large-N_c and chiral limit.

hep-ph↗

arXiv2003

Rho meson properties from combining QCD-based models

Aiming at the calculation of the properties of rho-mesons, non-perturbative QCD-based methods are discussed concerning their potentials as well as their short-comings. The latter are overcome by combining these techniques. The utilized methods are (i) the chiral constituent quark model deduced from the instanton vacuum model and large-N_c arguments, (ii) chiral perturbation theory unitarized by the inverse amplitude method and (iii) QCD sum rules. Advantages of the combination of these methods are especially the absence of un-physical quark-production thresholds and parameter-free results. Already in the chiral limit and in leading order in 1/N_c one obtains a reasonable result for the mass of the rho-meson, namely m_rho = 790 \pm 30 MeV. Using the KSFR relation the universality of the rho-meson coupling is recovered. The latter is found to be g = 6.0 \pm 0.3.

hep-ph↗

arXiv2003

Chromofields of Strings and Baryons

We calculate color electric fields of quark/antiquark ($\bar{q}q$) and 3 quark ($qqq$) systems within the chromodielectric model (CDM). We explicitly evaluate the string tension of flux tubes in the $\bar{q}q$--system and analyze their profile. To reproduce results of lattice calculations we use a bag pressure $B = (320 MeV)^4$ from which an effective strong coupling constant $α_s \approx 0.3$ follows. With these parameters we get a $Y$ shaped configuration for large $qqq$--systems.

hep-ph↗

arXiv2003

Gauge covariant heat kernel expansion at finite temperature

The heat kernel method is extended to the case of finite temperature. Special emphasis is given to the study of gauge theories. Due to the compactness of space in the Euclidean time direction (inverse temperature) the field strength cannot completely characterize the gauge fields. This is just a manifestation of the Aharonov-Bohm effect. The field strength has to be supplemented by the Polyakov loop. Only if the latter is taken into account one obtains gauge covariant results for the generalized Seeley-DeWitt coefficients of the heat kernel expansion.

hep-th↗