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B. -J. Schaefer

Publications and source records attributed to B. -J. Schaefer.

15 recordsLinked to original sources
arXiv2017

Center phase transition from matter propagators in (scalar) QCD

Novel order parameters for the confinement-deconfinement phase transition of quenched QCD and fundamentally charged scalar QCD are presented. Similar to the well-known dual condensate, they are defined via generalized matter propagators with $U(1)$-valued boundary conditions. The order parameters are easily accessible with functional methods. Their validity and accessibility is explicitly demonstrated by numerical studies of the Dyson-Schwinger equations for the matter propagators. Even in the case of heavy scalar matter, where the propagator does not show a signature of the phase transition, a discontinuity due to the transition can be extracted in the order parameters, establishing also fundamentally charged scalar matter as a probe for color confinement.

hep-ph↗
arXiv2010

Vacuum fluctuations and the thermodynamics of chiral models

We consider the thermodynamics of chiral models in the mean-field approximation and discuss the relevance of the (frequently omitted) fermion vacuum loop. Within the chiral quark-meson model and its Polyakov loop extended version, we show that the fermion vacuum fluctuations can change the order of the phase transition in the chiral limit and strongly influence physical observables. We compute the temperature-dependent effective potential and baryon number susceptibilities in these models, with and without the vacuum term, and explore the cutoff and the pion mass dependence of the susceptibilities. Finally, in the renormalized model the divergent vacuum contribution is removed using the dimensional regularization.

hep-ph↗
arXiv2009

Fluctuations and isentropes near the chiral critical endpoint

Isentropic trajectories crossing the chiral phase transition near the critical endpoint (CEP) are studied for two light quark flavors. The calculations are performed within an effective chiral model with quark-meson interactions, belonging to the same universality class as QCD. We confront mean-field thermodynamics with the functional renormalization group approach, where fluctuations are properly taken into account. We establish a connection between modifications of the isentropic trajectories found in mean-field calculations at the crossover transition near the CEP and the order of the phase transition in the chiral limit. Furthermore, the isentropes obtained with the renormalization group are completely smooth at the crossover transition and do not in any way reflect the proximity of the CEP. In particular, our results do not show the recently conjectured focussing of isentropes from the crossover region towards the critical endpoint.

hep-ph↗
arXiv2006

On the convergence of multi-channel effective interactions

A detailed analysis of convergence properties of the Andreozzi-Lee-Suzuki iteration method, which is used for the calculation of low-momentum effective potentials Vlowk is presented. After summarizing different modifications of the iteration method for one-flavor channel we introduce a simple model in order to study the generalization of the iteration method to multi-flavor channels. The failure of a straightforward generalization is discussed. The introduction of a channel-dependent cutoff cures the conceptual and technical problems. This novel method has already been applied successfully for realistic hyperon-nucleon interactions.

nucl-th↗
arXiv2005

Low-momentum Hyperon-Nucleon Interactions

We present a first exploratory study for hyperon-nucleon interactions using renormalization group techniques. The effective two-body low-momentum potential V_low-k is obtained by integrating out the high-momentum components from realistic Nijmegen YN potentials. A T-matrix equivalence approach is employed, so that the low-energy phase shifts are reproduced by V_low-k up to a momentum scale Lambda ~ 500 MeV. Although the various bare Nijmegen models differ somewhat from each other, the corresponding V_low-k interactions show convergence in some channels, suggesting a possible unique YN interaction at low momenta.

nucl-th↗
arXiv2002

Finite-Temperature Gluon Condensate with Renormalization Group Flow Equations

Within a self-consistent proper-time Renormalization Group (RG) approach we investigate an effective QCD trace anomaly realization with dilatons and determine the finite-temperature behavior of the gluon condensate. Fixing the effective model at vanishing temperature to the glueball mass and the bag constant a possible gluonic phase transition is explored in detail. Within the RG framework the full non-truncated dilaton potential analysis is compared with a truncated potential version.

hep-th↗
arXiv2000

Renormalization Group Flow Equations For The Scalar O(N) Theory

Self-consistent new renormalization group flow equations for an O(N)-symmetric scalar theory are approximated in next-to-leading order of the derivative expansion. The Wilson-Fisher fixed point in three dimensions is analyzed in detail and various critical exponents are calculated.

hep-ph↗
arXiv2000

Renormalization Group Flow Equations and the Phase Transition in O(N)-models

We derive and solve flow equations for a general O(N)-symmetric effective potential including wavefunction renormalization corrections combined with a heat-kernel regularization. We investigate the model at finite temperature and study the nature of the phase transition in detail. Beta functions, fixed points and critical exponents β, ν, δand ηfor various N are independently calculated which allow for a verification of universal scaling relations.

hep-ph↗
arXiv1999

On the Convergence of the Expansion of Renormalization Group Flow Equation

We compare and discuss the dependence of a polynomial truncation of the effective potential used to solve exact renormalization group flow equation for a model with fermionic interaction (linear sigma model) with a grid solution. The sensitivity of the results on the underlying cutoff function is discussed. We explore the validity of the expansion method for second and first-order phase transitions.

hep-ph↗
arXiv1999

Flow Equations and the Chiral Phase Transition

Flow equations for an O(N)-symmetric effective potential are discussed and solved for the finite temperature case. The model is investigated at the critical point and critical exponents for various N are calculated.

hep-ph↗
arXiv1999

Renormalization Group Flow and Equation of State of Quarks and Mesons

Nonperturbative flow equations within an effective linear sigma model coupled to constituent quarks for two quark flavors are derived and solved. A heat kernel regularization is employed for a renormalization group improved effective potential. We determine the initial values of the coupling constants in the effective potential at zero temperature. Solving the evolution equations with the same initial values at finite temperature in the chiral limit, we find a second order phase transition at T_c \approx 150 MeV. Due to the smooth decoupling of massive modes, we can directly link the low-temperature four-dimensional theory to the three-dimensional high-temperature theory. We calculate the equation of state in the chiral limit and for finite pion masses and determine universal critical exponents.

nucl-th↗
arXiv1997

Nonperturbative Flow Equations with Heat-Kernel Methods at finite Temperature

We derive nonperturbative flow equations within an effective constituent quark model for two quark flavors. Heat-kernel methods are employed for a renormalization group improved effective potential. We study the evolution of the effective potential with respect to an infrared cutoff scale $k$ at vanishing temperature. At the first stage we omit corrections coming from the anomalous dimension. This investigation is extrapolated to finite temperature, where we find a second order phase transition in the chiral limit at $T_c \approx 130$ MeV. Due to a smooth decoupling of massive modes, we can directly link the low-temperature four-dimensional theory to the three-dimensional high-temperature theory and can determine universal critical exponents.

hep-ph↗
arXiv1997

Application of the Heat Kernel Method to the Constituent Quark Model at Finite Temperature

The Heat Kernel Method is applied to the constituent quark model. We calculate the effect of thermal quark fluctuations on the meson action and the resulting quark condensate and pi pi-scattering amplitude at finite temperature. The quarks produce a chiral phase transition only by their effect on the mesonic coupling constants. The s-wave isospin zero pi pi-scattering amplitude diverges near the phase transition showing the necessity for a more sophisticated treatment of meson fluctuations.

hep-ph↗
arXiv1994

QCD Phase Transition in Hot Hadronic Matter

We analyse the QCD chiral phase transition in the nonlinear and linear $σ$-model. The strategy is the same in both cases. We fix the parameters of the effective meson theory at temperature $T=0$ and extrapolate the models to temperatures in the vicinity of the phase transition. The linear $σ$-model in $SU(3)\times SU(3)$ gives a crossover around $T_c\approx190$ MeV. Around this temperature chiral $SU(2)\times SU(2)$ is almost restored. We also calculate meson masses as a function of temperature.

hep-ph↗